Calculation of Pareto-optimal solutions to multiple-objective problems using threshold-of-acceptability constraints

NASA Technical Reports Server (NTRS)

Giesy, D. P.

1978-01-01

A technique is presented for the calculation of Pareto-optimal solutions to a multiple-objective constrained optimization problem by solving a series of single-objective problems. Threshold-of-acceptability constraints are placed on the objective functions at each stage to both limit the area of search and to mathematically guarantee convergence to a Pareto optimum.

Restart Operator Meta-heuristics for a Problem-Oriented Evolutionary Strategies Algorithm in Inverse Mathematical MISO Modelling Problem Solving

NASA Astrophysics Data System (ADS)

Ryzhikov, I. S.; Semenkin, E. S.

2017-02-01

This study is focused on solving an inverse mathematical modelling problem for dynamical systems based on observation data and control inputs. The mathematical model is being searched in the form of a linear differential equation, which determines the system with multiple inputs and a single output, and a vector of the initial point coordinates. The described problem is complex and multimodal and for this reason the proposed evolutionary-based optimization technique, which is oriented on a dynamical system identification problem, was applied. To improve its performance an algorithm restart operator was implemented.

Improving mathematical problem solving skills through visual media

NASA Astrophysics Data System (ADS)

Widodo, S. A.; Darhim; Ikhwanudin, T.

2018-01-01

The purpose of this article was to find out the enhancement of students’ mathematical problem solving by using visual learning media. The ability to solve mathematical problems is the ability possessed by students to solve problems encountered, one of the problem-solving model of Polya. This preliminary study was not to make a model, but it only took a conceptual approach by comparing the various literature of problem-solving skills by linking visual learning media. The results of the study indicated that the use of learning media had not been appropriated so that the ability to solve mathematical problems was not optimal. The inappropriateness of media use was due to the instructional media that was not adapted to the characteristics of the learners. Suggestions that can be given is the need to develop visual media to increase the ability to solve problems.

Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications

DTIC Science & Technology

2015-06-24

WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Arizona State University School of Mathematical & Statistical Sciences 901 S...SUPPLEMENTARY NOTES 14. ABSTRACT The major goals of this project were completed: the exact solution of previously unsolved challenging combinatorial optimization... combinatorial optimization problem, the Directional Sensor Problem, was solved in two ways. First, heuristically in an engineering fashion and second, exactly

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

NASA Technical Reports Server (NTRS)

Frair, L.

1978-01-01

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

Computer Aided Learning of Mathematics: Software Evaluation

ERIC Educational Resources Information Center

Yushau, B.; Bokhari, M. A.; Wessels, D. C. J.

2004-01-01

Computer Aided Learning of Mathematics (CALM) has been in use for some time in the Prep-Year Mathematics Program at King Fahd University of Petroleum & Minerals. Different kinds of software (both locally designed and imported) have been used in the quest of optimizing the recitation/problem session hour of the mathematics classes. This paper…

The Sizing and Optimization Language (SOL): A computer language to improve the user/optimizer interface

NASA Technical Reports Server (NTRS)

Lucas, S. H.; Scotti, S. J.

1989-01-01

The nonlinear mathematical programming method (formal optimization) has had many applications in engineering design. A figure illustrates the use of optimization techniques in the design process. The design process begins with the design problem, such as the classic example of the two-bar truss designed for minimum weight as seen in the leftmost part of the figure. If formal optimization is to be applied, the design problem must be recast in the form of an optimization problem consisting of an objective function, design variables, and constraint function relations. The middle part of the figure shows the two-bar truss design posed as an optimization problem. The total truss weight is the objective function, the tube diameter and truss height are design variables, with stress and Euler buckling considered as constraint function relations. Lastly, the designer develops or obtains analysis software containing a mathematical model of the object being optimized, and then interfaces the analysis routine with existing optimization software such as CONMIN, ADS, or NPSOL. This final state of software development can be both tedious and error-prone. The Sizing and Optimization Language (SOL), a special-purpose computer language whose goal is to make the software implementation phase of optimum design easier and less error-prone, is presented.

Combinatorial optimization in foundry practice

NASA Astrophysics Data System (ADS)

Antamoshkin, A. N.; Masich, I. S.

2016-04-01

The multicriteria mathematical model of foundry production capacity planning is suggested in the paper. The model is produced in terms of pseudo-Boolean optimization theory. Different search optimization methods were used to solve the obtained problem.

Research on NC laser combined cutting optimization model of sheet metal parts

NASA Astrophysics Data System (ADS)

Wu, Z. Y.; Zhang, Y. L.; Li, L.; Wu, L. H.; Liu, N. B.

2017-09-01

The optimization problem for NC laser combined cutting of sheet metal parts was taken as the research object in this paper. The problem included two contents: combined packing optimization and combined cutting path optimization. In the problem of combined packing optimization, the method of “genetic algorithm + gravity center NFP + geometric transformation” was used to optimize the packing of sheet metal parts. In the problem of combined cutting path optimization, the mathematical model of cutting path optimization was established based on the parts cutting constraint rules of internal contour priority and cross cutting. The model played an important role in the optimization calculation of NC laser combined cutting.

Approximate approach for optimization space flights with a low thrust on the basis of sufficient optimality conditions

NASA Astrophysics Data System (ADS)

Salmin, Vadim V.

2017-01-01

Flight mechanics with a low-thrust is a new chapter of mechanics of space flight, considered plurality of all problems trajectory optimization and movement control laws and the design parameters of spacecraft. Thus tasks associated with taking into account the additional factors in mathematical models of the motion of spacecraft becomes increasingly important, as well as additional restrictions on the possibilities of the thrust vector control. The complication of the mathematical models of controlled motion leads to difficulties in solving optimization problems. Author proposed methods of finding approximate optimal control and evaluating their optimality based on analytical solutions. These methods are based on the principle of extending the class of admissible states and controls and sufficient conditions for the absolute minimum. Developed procedures of the estimation enabling to determine how close to the optimal founded solution, and indicate ways to improve them. Authors describes procedures of estimate for approximately optimal control laws for space flight mechanics problems, in particular for optimization flight low-thrust between the circular non-coplanar orbits, optimization the control angle and trajectory movement of the spacecraft during interorbital flights, optimization flights with low-thrust between arbitrary elliptical orbits Earth satellites.

Do Dogs Know Related Rates Rather than Optimization?

ERIC Educational Resources Information Center

Perruchet, Pierre; Gallego, Jorge

2006-01-01

Although dogs seemingly follow the optimal path where they get to a ball thrown into the water, they certainly do not know the minimization function proposed in the calculus books. Trading the optimization problem for a related rates problem leads to a mathematically identical solution, which, it is argued here, is a more plausible model for the…

The optimization problems of CP operation

NASA Astrophysics Data System (ADS)

Kler, A. M.; Stepanova, E. L.; Maximov, A. S.

2017-11-01

The problem of enhancing energy and economic efficiency of CP is urgent indeed. One of the main methods for solving it is optimization of CP operation. To solve the optimization problems of CP operation, Energy Systems Institute, SB of RAS, has developed a software. The software makes it possible to make optimization calculations of CP operation. The software is based on the techniques and software tools of mathematical modeling and optimization of heat and power installations. Detailed mathematical models of new equipment have been developed in the work. They describe sufficiently accurately the processes that occur in the installations. The developed models include steam turbine models (based on the checking calculation) which take account of all steam turbine compartments and regeneration system. They also enable one to make calculations with regenerative heaters disconnected. The software for mathematical modeling of equipment and optimization of CP operation has been developed. It is based on the technique for optimization of CP operating conditions in the form of software tools and integrates them in the common user interface. The optimization of CP operation often generates the need to determine the minimum and maximum possible total useful electricity capacity of the plant at set heat loads of consumers, i.e. it is necessary to determine the interval on which the CP capacity may vary. The software has been applied to optimize the operating conditions of the Novo-Irkutskaya CP of JSC “Irkutskenergo”. The efficiency of operating condition optimization and the possibility for determination of CP energy characteristics that are necessary for optimization of power system operation are shown.

A Dynamic Process Model for Optimizing the Hospital Environment Cash-Flow

NASA Astrophysics Data System (ADS)

Pater, Flavius; Rosu, Serban

2011-09-01

In this article is presented a new approach to some fundamental techniques of solving dynamic programming problems with the use of functional equations. We will analyze the problem of minimizing the cost of treatment in a hospital environment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon.

Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems

NASA Technical Reports Server (NTRS)

Balling, R. J.; Wilkinson, C. A.

1997-01-01

A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.

A Multifaceted Mathematical Approach for Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexander, F.; Anitescu, M.; Bell, J.

2012-03-07

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significantmore » impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.« less

Formulating a stand-growth model for mathematical programming problems in Appalachian forests

Treesearch

Gary W. Miller; Jay Sullivan

1993-01-01

Some growth and yield simulators applicable to central hardwood forests can be formulated for use in mathematical programming models that are designed to optimize multi-stand, multi-resource management problems. Once in the required format, growth equations serve as model constraints, defining the dynamics of stand development brought about by harvesting decisions. In...

Algorithms for Mathematical Programming with Emphasis on Bi-level Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldfarb, Donald; Iyengar, Garud

2014-05-22

The research supported by this grant was focused primarily on first-order methods for solving large scale and structured convex optimization problems and convex relaxations of nonconvex problems. These include optimal gradient methods, operator and variable splitting methods, alternating direction augmented Lagrangian methods, and block coordinate descent methods.

Expected value analysis for integrated supplier selection and inventory control of multi-product inventory system with fuzzy cost

NASA Astrophysics Data System (ADS)

Sutrisno, Widowati, Tjahjana, R. Heru

2017-12-01

The future cost in many industrial problem is obviously uncertain. Then a mathematical analysis for a problem with uncertain cost is needed. In this article, we deals with the fuzzy expected value analysis to solve an integrated supplier selection and supplier selection problem with uncertain cost where the costs uncertainty is approached by a fuzzy variable. We formulate the mathematical model of the problems fuzzy expected value based quadratic optimization with total cost objective function and solve it by using expected value based fuzzy programming. From the numerical examples result performed by the authors, the supplier selection problem was solved i.e. the optimal supplier was selected for each time period where the optimal product volume of all product that should be purchased from each supplier for each time period was determined and the product stock level was controlled as decided by the authors i.e. it was followed the given reference level.

Numerical optimization methods for controlled systems with parameters

NASA Astrophysics Data System (ADS)

Tyatyushkin, A. I.

2017-10-01

First- and second-order numerical methods for optimizing controlled dynamical systems with parameters are discussed. In unconstrained-parameter problems, the control parameters are optimized by applying the conjugate gradient method. A more accurate numerical solution in these problems is produced by Newton's method based on a second-order functional increment formula. Next, a general optimal control problem with state constraints and parameters involved on the righthand sides of the controlled system and in the initial conditions is considered. This complicated problem is reduced to a mathematical programming one, followed by the search for optimal parameter values and control functions by applying a multimethod algorithm. The performance of the proposed technique is demonstrated by solving application problems.

Research on cutting path optimization of sheet metal parts based on ant colony algorithm

NASA Astrophysics Data System (ADS)

Wu, Z. Y.; Ling, H.; Li, L.; Wu, L. H.; Liu, N. B.

2017-09-01

In view of the disadvantages of the current cutting path optimization methods of sheet metal parts, a new method based on ant colony algorithm was proposed in this paper. The cutting path optimization problem of sheet metal parts was taken as the research object. The essence and optimization goal of the optimization problem were presented. The traditional serial cutting constraint rule was improved. The cutting constraint rule with cross cutting was proposed. The contour lines of parts were discretized and the mathematical model of cutting path optimization was established. Thus the problem was converted into the selection problem of contour lines of parts. Ant colony algorithm was used to solve the problem. The principle and steps of the algorithm were analyzed.

Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)

NASA Astrophysics Data System (ADS)

Winda, A.; Sufyani, P.; Elah, N.

2018-05-01

Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.

Fuzzy multiobjective models for optimal operation of a hydropower system

NASA Astrophysics Data System (ADS)

Teegavarapu, Ramesh S. V.; Ferreira, André R.; Simonovic, Slobodan P.

2013-06-01

Optimal operation models for a hydropower system using new fuzzy multiobjective mathematical programming models are developed and evaluated in this study. The models use (i) mixed integer nonlinear programming (MINLP) with binary variables and (ii) integrate a new turbine unit commitment formulation along with water quality constraints used for evaluation of reservoir downstream impairment. Reardon method used in solution of genetic algorithm optimization problems forms the basis for development of a new fuzzy multiobjective hydropower system optimization model with creation of Reardon type fuzzy membership functions. The models are applied to a real-life hydropower reservoir system in Brazil. Genetic Algorithms (GAs) are used to (i) solve the optimization formulations to avoid computational intractability and combinatorial problems associated with binary variables in unit commitment, (ii) efficiently address Reardon method formulations, and (iii) deal with local optimal solutions obtained from the use of traditional gradient-based solvers. Decision maker's preferences are incorporated within fuzzy mathematical programming formulations to obtain compromise operating rules for a multiobjective reservoir operation problem dominated by conflicting goals of energy production, water quality and conservation releases. Results provide insight into compromise operation rules obtained using the new Reardon fuzzy multiobjective optimization framework and confirm its applicability to a variety of multiobjective water resources problems.

Selected Bibliography on Optimizing Techniques in Statistics

DTIC Science & Technology

1981-08-01

problems in business, industry and .ogovern nt ae f rmulated as optimization problem. Topics in optimization constitute an essential area of study in...numerical, iii) mathematical programming, and (iv) variational. We provide pertinent references with statistical applications Sin the above areas in Part I...TMS Advanced Studies in Managentnt Sciences, North-Holland PIIENli iiiany, Amsterdam. (To appear.) Spang, H. A. (1962). A review of minimization

Optimal control of LQR for discrete time-varying systems with input delays

NASA Astrophysics Data System (ADS)

Yin, Yue-Zhu; Yang, Zhong-Lian; Yin, Zhi-Xiang; Xu, Feng

2018-04-01

In this work, we consider the optimal control problem of linear quadratic regulation for discrete time-variant systems with single input and multiple input delays. An innovative and simple method to derive the optimal controller is given. The studied problem is first equivalently converted into a problem subject to a constraint condition. Last, with the established duality, the problem is transformed into a static mathematical optimisation problem without input delays. The optimal control input solution to minimise performance index function is derived by solving this optimisation problem with two methods. A numerical simulation example is carried out and its results show that our two approaches are both feasible and very effective.

Multi-Objective Ant Colony Optimization Based on the Physarum-Inspired Mathematical Model for Bi-Objective Traveling Salesman Problems

PubMed Central

Zhang, Zili; Gao, Chao; Lu, Yuxiao; Liu, Yuxin; Liang, Mingxin

2016-01-01

Bi-objective Traveling Salesman Problem (bTSP) is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs) have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM). PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs. PMID:26751562

Multi-Objective Ant Colony Optimization Based on the Physarum-Inspired Mathematical Model for Bi-Objective Traveling Salesman Problems.

PubMed

Zhang, Zili; Gao, Chao; Lu, Yuxiao; Liu, Yuxin; Liang, Mingxin

2016-01-01

Bi-objective Traveling Salesman Problem (bTSP) is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs) have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM). PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs.

A Genetic Algorithm Approach to Nonlinear Least Squares Estimation

ERIC Educational Resources Information Center

Olinsky, Alan D.; Quinn, John T.; Mangiameli, Paul M.; Chen, Shaw K.

2004-01-01

A common type of problem encountered in mathematics is optimizing nonlinear functions. Many popular algorithms that are currently available for finding nonlinear least squares estimators, a special class of nonlinear problems, are sometimes inadequate. They might not converge to an optimal value, or if they do, it could be to a local rather than…

A chance constraint estimation approach to optimizing resource management under uncertainty

Treesearch

Michael Bevers

2007-01-01

Chance-constrained optimization is an important method for managing risk arising from random variations in natural resource systems, but the probabilistic formulations often pose mathematical programming problems that cannot be solved with exact methods. A heuristic estimation method for these problems is presented that combines a formulation for order statistic...

The Popcorn Box Activity and Reasoning about Optimization

ERIC Educational Resources Information Center

Whiteley, Walter J.; Mamolo, Ami

2012-01-01

A well-known optimization problem is the Popcorn Box investigation, which involves a movie theater snack container. The problem has been tailored for classroom investigations by the Ontario Association for Mathematics Education. The exploration was designed for students in grades 9 through 12. A common strategy proposed for algebra students is to…

Inversion of Robin coefficient by a spectral stochastic finite element approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Optimal harvesting for a predator-prey agent-based model using difference equations.

PubMed

Oremland, Matthew; Laubenbacher, Reinhard

2015-03-01

In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory—we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted κ is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.

Optimization Techniques for Design Problems in Selected Areas in WSNs: A Tutorial

PubMed Central

Ibrahim, Ahmed; Alfa, Attahiru

2017-01-01

This paper is intended to serve as an overview of, and mostly a tutorial to illustrate, the optimization techniques used in several different key design aspects that have been considered in the literature of wireless sensor networks (WSNs). It targets the researchers who are new to the mathematical optimization tool, and wish to apply it to WSN design problems. We hence divide the paper into two main parts. One part is dedicated to introduce optimization theory and an overview on some of its techniques that could be helpful in design problem in WSNs. In the second part, we present a number of design aspects that we came across in the WSN literature in which mathematical optimization methods have been used in the design. For each design aspect, a key paper is selected, and for each we explain the formulation techniques and the solution methods implemented. We also provide in-depth analyses and assessments of the problem formulations, the corresponding solution techniques and experimental procedures in some of these papers. The analyses and assessments, which are provided in the form of comments, are meant to reflect the points that we believe should be taken into account when using optimization as a tool for design purposes. PMID:28763039

Optimization Techniques for Design Problems in Selected Areas in WSNs: A Tutorial.

PubMed

Ibrahim, Ahmed; Alfa, Attahiru

2017-08-01

This paper is intended to serve as an overview of, and mostly a tutorial to illustrate, the optimization techniques used in several different key design aspects that have been considered in the literature of wireless sensor networks (WSNs). It targets the researchers who are new to the mathematical optimization tool, and wish to apply it to WSN design problems. We hence divide the paper into two main parts. One part is dedicated to introduce optimization theory and an overview on some of its techniques that could be helpful in design problem in WSNs. In the second part, we present a number of design aspects that we came across in the WSN literature in which mathematical optimization methods have been used in the design. For each design aspect, a key paper is selected, and for each we explain the formulation techniques and the solution methods implemented. We also provide in-depth analyses and assessments of the problem formulations, the corresponding solution techniques and experimental procedures in some of these papers. The analyses and assessments, which are provided in the form of comments, are meant to reflect the points that we believe should be taken into account when using optimization as a tool for design purposes.

Multiobjective optimization in a pseudometric objective space as applied to a general model of business activities

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2016-09-01

It is shown that finding the equivalence set for solving multiobjective discrete optimization problems is advantageous over finding the set of Pareto optimal decisions. An example of a set of key parameters characterizing the economic efficiency of a commercial firm is proposed, and a mathematical model of its activities is constructed. In contrast to the classical problem of finding the maximum profit for any business, this study deals with a multiobjective optimization problem. A method for solving inverse multiobjective problems in a multidimensional pseudometric space is proposed for finding the best project of firm's activities. The solution of a particular problem of this type is presented.

Dynamic, stochastic models for congestion pricing and congestion securities.

DOT National Transportation Integrated Search

2010-12-01

This research considers congestion pricing under demand uncertainty. In particular, a robust optimization (RO) approach is applied to optimal congestion pricing problems under user equilibrium. A mathematical model is developed and an analysis perfor...

Optimization and Control of Agent-Based Models in Biology: A Perspective.

PubMed

An, G; Fitzpatrick, B G; Christley, S; Federico, P; Kanarek, A; Neilan, R Miller; Oremland, M; Salinas, R; Laubenbacher, R; Lenhart, S

2017-01-01

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

Mathematical model of information process of protection of the social sector

NASA Astrophysics Data System (ADS)

Novikov, D. A.; Tsarkova, E. G.; Dubrovin, A. S.; Soloviev, A. S.

2018-03-01

In work the mathematical model of information protection of society against distribution of extremist moods by means of impact on mass consciousness of information placed in media is investigated. Internal and external channels on which there is a dissemination of information are designated. The problem of optimization consisting in search of the optimum strategy allowing to use most effectively media for dissemination of antiterrorist information with the minimum financial expenses is solved. The algorithm of a numerical method of the solution of a problem of optimization is constructed and also the analysis of results of a computing experiment is carried out.

Evaluation of orbits with incomplete knowledge of the mathematical expectancy and the matrix of covariation of errors

NASA Technical Reports Server (NTRS)

Bakhshiyan, B. T.; Nazirov, R. R.; Elyasberg, P. E.

1980-01-01

The problem of selecting the optimal algorithm of filtration and the optimal composition of the measurements is examined assuming that the precise values of the mathematical expectancy and the matrix of covariation of errors are unknown. It is demonstrated that the optimal algorithm of filtration may be utilized for making some parameters more precise (for example, the parameters of the gravitational fields) after preliminary determination of the elements of the orbit by a simpler method of processing (for example, the method of least squares).

Network models for solving the problem of multicriterial adaptive optimization of investment projects control with several acceptable technologies

NASA Astrophysics Data System (ADS)

Shorikov, A. F.; Butsenko, E. V.

2017-10-01

This paper discusses the problem of multicriterial adaptive optimization the control of investment projects in the presence of several technologies. On the basis of network modeling proposed a new economic and mathematical model and a method for solving the problem of multicriterial adaptive optimization the control of investment projects in the presence of several technologies. Network economic and mathematical modeling allows you to determine the optimal time and calendar schedule for the implementation of the investment project and serves as an instrument to increase the economic potential and competitiveness of the enterprise. On a meaningful practical example, the processes of forming network models are shown, including the definition of the sequence of actions of a particular investment projecting process, the network-based work schedules are constructed. The calculation of the parameters of network models is carried out. Optimal (critical) paths have been formed and the optimal time for implementing the chosen technologies of the investment project has been calculated. It also shows the selection of the optimal technology from a set of possible technologies for project implementation, taking into account the time and cost of the work. The proposed model and method for solving the problem of managing investment projects can serve as a basis for the development, creation and application of appropriate computer information systems to support the adoption of managerial decisions by business people.

Aspects of job scheduling

NASA Technical Reports Server (NTRS)

Phillips, K.

1976-01-01

A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Communications Complex, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germane to scheduling are presented.

Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Numerical Analysis and Computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haslinger, Jaroslav, E-mail: hasling@karlin.mff.cuni.cz; Stebel, Jan, E-mail: stebel@math.cas.cz

2011-04-15

We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.

Stochastic Robust Mathematical Programming Model for Power System Optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Cong; Changhyeok, Lee; Haoyong, Chen

2016-01-01

This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.

Control optimization, stabilization and computer algorithms for aircraft applications

NASA Technical Reports Server (NTRS)

1975-01-01

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Optimal Shakedown of the Thin-Wall Metal Structures Under Strength and Stiffness Constraints

NASA Astrophysics Data System (ADS)

Alawdin, Piotr; Liepa, Liudas

2017-06-01

Classical optimization problems of metal structures confined mainly with 1st class cross-sections. But in practice it is common to use the cross-sections of higher classes. In this paper, a new mathematical model for described shakedown optimization problem for metal structures, which elements are designed from 1st to 4th class cross-sections, under variable quasi-static loads is presented. The features of limited plastic redistribution of forces in the structure with thin-walled elements there are taken into account. Authors assume the elastic-plastic flexural buckling in one plane without lateral torsional buckling behavior of members. Design formulae for Methods 1 and 2 for members are analyzed. Structures stiffness constrains are also incorporated in order to satisfy the limit serviceability state requirements. With the help of mathematical programming theory and extreme principles the structure optimization algorithm is developed and justified with the numerical experiment for the metal plane frames.

Three essays on multi-level optimization models and applications

NASA Astrophysics Data System (ADS)

Rahdar, Mohammad

The general form of a multi-level mathematical programming problem is a set of nested optimization problems, in which each level controls a series of decision variables independently. However, the value of decision variables may also impact the objective function of other levels. A two-level model is called a bilevel model and can be considered as a Stackelberg game with a leader and a follower. The leader anticipates the response of the follower and optimizes its objective function, and then the follower reacts to the leader's action. The multi-level decision-making model has many real-world applications such as government decisions, energy policies, market economy, network design, etc. However, there is a lack of capable algorithms to solve medium and large scale these types of problems. The dissertation is devoted to both theoretical research and applications of multi-level mathematical programming models, which consists of three parts, each in a paper format. The first part studies the renewable energy portfolio under two major renewable energy policies. The potential competition for biomass for the growth of the renewable energy portfolio in the United States and other interactions between two policies over the next twenty years are investigated. This problem mainly has two levels of decision makers: the government/policy makers and biofuel producers/electricity generators/farmers. We focus on the lower-level problem to predict the amount of capacity expansions, fuel production, and power generation. In the second part, we address uncertainty over demand and lead time in a multi-stage mathematical programming problem. We propose a two-stage tri-level optimization model in the concept of rolling horizon approach to reducing the dimensionality of the multi-stage problem. In the third part of the dissertation, we introduce a new branch and bound algorithm to solve bilevel linear programming problems. The total time is reduced by solving a smaller relaxation problem in each node and decreasing the number of iterations. Computational experiments show that the proposed algorithm is faster than the existing ones.

Nash equilibrium and multi criterion aerodynamic optimization

NASA Astrophysics Data System (ADS)

Tang, Zhili; Zhang, Lianhe

2016-06-01

Game theory and its particular Nash Equilibrium (NE) are gaining importance in solving Multi Criterion Optimization (MCO) in engineering problems over the past decade. The solution of a MCO problem can be viewed as a NE under the concept of competitive games. This paper surveyed/proposed four efficient algorithms for calculating a NE of a MCO problem. Existence and equivalence of the solution are analyzed and proved in the paper based on fixed point theorem. Specific virtual symmetric Nash game is also presented to set up an optimization strategy for single objective optimization problems. Two numerical examples are presented to verify proposed algorithms. One is mathematical functions' optimization to illustrate detailed numerical procedures of algorithms, the other is aerodynamic drag reduction of civil transport wing fuselage configuration by using virtual game. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques.

PubMed

Vilas, Carlos; Balsa-Canto, Eva; García, Maria-Sonia G; Banga, Julio R; Alonso, Antonio A

2012-07-02

Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.

Inverse problems in the design, modeling and testing of engineering systems

NASA Technical Reports Server (NTRS)

Alifanov, Oleg M.

1991-01-01

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming

NASA Technical Reports Server (NTRS)

Tapia, R. A.; Vanrooy, D. L.

1976-01-01

A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

Structural optimization: Status and promise

NASA Astrophysics Data System (ADS)

Kamat, Manohar P.

Chapters contained in this book include fundamental concepts of optimum design, mathematical programming methods for constrained optimization, function approximations, approximate reanalysis methods, dual mathematical programming methods for constrained optimization, a generalized optimality criteria method, and a tutorial and survey of multicriteria optimization in engineering. Also included are chapters on the compromise decision support problem and the adaptive linear programming algorithm, sensitivity analyses of discrete and distributed systems, the design sensitivity analysis of nonlinear structures, optimization by decomposition, mixed elements in shape sensitivity analysis of structures based on local criteria, and optimization of stiffened cylindrical shells subjected to destabilizing loads. Other chapters are on applications to fixed-wing aircraft and spacecraft, integrated optimum structural and control design, modeling concurrency in the design of composite structures, and tools for structural optimization. (No individual items are abstracted in this volume)

Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bulicek, Miroslav; Haslinger, Jaroslav; Malek, Josef

2009-10-15

We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and tomore » the shape optimization problem.« less

New Mathematical Strategy Using Branch and Bound Method

NASA Astrophysics Data System (ADS)

Tarray, Tanveer Ahmad; Bhat, Muzafar Rasool

In this paper, the problem of optimal allocation in stratified random sampling is used in the presence of nonresponse. The problem is formulated as a nonlinear programming problem (NLPP) and is solved using Branch and Bound method. Also the results are formulated through LINGO.

Optimal multi-floor plant layout based on the mathematical programming and particle swarm optimization.

PubMed

Lee, Chang Jun

2015-01-01

In the fields of researches associated with plant layout optimization, the main goal is to minimize the costs of pipelines and pumping between connecting equipment under various constraints. However, what is the lacking of considerations in previous researches is to transform various heuristics or safety regulations into mathematical equations. For example, proper safety distances between equipments have to be complied for preventing dangerous accidents on a complex plant. Moreover, most researches have handled single-floor plant. However, many multi-floor plants have been constructed for the last decade. Therefore, the proper algorithm handling various regulations and multi-floor plant should be developed. In this study, the Mixed Integer Non-Linear Programming (MINLP) problem including safety distances, maintenance spaces, etc. is suggested based on mathematical equations. The objective function is a summation of pipeline and pumping costs. Also, various safety and maintenance issues are transformed into inequality or equality constraints. However, it is really hard to solve this problem due to complex nonlinear constraints. Thus, it is impossible to use conventional MINLP solvers using derivatives of equations. In this study, the Particle Swarm Optimization (PSO) technique is employed. The ethylene oxide plant is illustrated to verify the efficacy of this study.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent advances in the analytical and numerical treatment of physical and engineering problems are discussed in reviews and reports. Topics addressed include fluid mechanics, numerical methods for differential equations, FEM approaches, and boundary-element methods. Consideration is given to optimization, decision theory, stochastics, actuarial mathematics, applied mathematics and mathematical physics, and numerical analysis.

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

NASA Astrophysics Data System (ADS)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

SOL - SIZING AND OPTIMIZATION LANGUAGE COMPILER

NASA Technical Reports Server (NTRS)

Scotti, S. J.

1994-01-01

SOL is a computer language which is geared to solving design problems. SOL includes the mathematical modeling and logical capabilities of a computer language like FORTRAN but also includes the additional power of non-linear mathematical programming methods (i.e. numerical optimization) at the language level (as opposed to the subroutine level). The language-level use of optimization has several advantages over the traditional, subroutine-calling method of using an optimizer: first, the optimization problem is described in a concise and clear manner which closely parallels the mathematical description of optimization; second, a seamless interface is automatically established between the optimizer subroutines and the mathematical model of the system being optimized; third, the results of an optimization (objective, design variables, constraints, termination criteria, and some or all of the optimization history) are output in a form directly related to the optimization description; and finally, automatic error checking and recovery from an ill-defined system model or optimization description is facilitated by the language-level specification of the optimization problem. Thus, SOL enables rapid generation of models and solutions for optimum design problems with greater confidence that the problem is posed correctly. The SOL compiler takes SOL-language statements and generates the equivalent FORTRAN code and system calls. Because of this approach, the modeling capabilities of SOL are extended by the ability to incorporate existing FORTRAN code into a SOL program. In addition, SOL has a powerful MACRO capability. The MACRO capability of the SOL compiler effectively gives the user the ability to extend the SOL language and can be used to develop easy-to-use shorthand methods of generating complex models and solution strategies. The SOL compiler provides syntactic and semantic error-checking, error recovery, and detailed reports containing cross-references to show where each variable was used. The listings summarize all optimizations, listing the objective functions, design variables, and constraints. The compiler offers error-checking specific to optimization problems, so that simple mistakes will not cost hours of debugging time. The optimization engine used by and included with the SOL compiler is a version of Vanderplatt's ADS system (Version 1.1) modified specifically to work with the SOL compiler. SOL allows the use of the over 100 ADS optimization choices such as Sequential Quadratic Programming, Modified Feasible Directions, interior and exterior penalty function and variable metric methods. Default choices of the many control parameters of ADS are made for the user, however, the user can override any of the ADS control parameters desired for each individual optimization. The SOL language and compiler were developed with an advanced compiler-generation system to ensure correctness and simplify program maintenance. Thus, SOL's syntax was defined precisely by a LALR(1) grammar and the SOL compiler's parser was generated automatically from the LALR(1) grammar with a parser-generator. Hence unlike ad hoc, manually coded interfaces, the SOL compiler's lexical analysis insures that the SOL compiler recognizes all legal SOL programs, can recover from and correct for many errors and report the location of errors to the user. This version of the SOL compiler has been implemented on VAX/VMS computer systems and requires 204 KB of virtual memory to execute. Since the SOL compiler produces FORTRAN code, it requires the VAX FORTRAN compiler to produce an executable program. The SOL compiler consists of 13,000 lines of Pascal code. It was developed in 1986 and last updated in 1988. The ADS and other utility subroutines amount to 14,000 lines of FORTRAN code and were also updated in 1988.

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing.

PubMed

Wang, Lipo; Li, Sa; Tian, Fuyu; Fu, Xiuju

2004-10-01

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

Dynamic programming methods for concurrent design and dynamic allocation of vehicles embedded in a system-of-systems

NASA Astrophysics Data System (ADS)

Nusawardhana

2007-12-01

Recent developments indicate a changing perspective on how systems or vehicles should be designed. Such transition comes from the way decision makers in defense related agencies address complex problems. Complex problems are now often posed in terms of the capabilities desired, rather than in terms of requirements for a single systems. As a result, the way to provide a set of capabilities is through a collection of several individual, independent systems. This collection of individual independent systems is often referred to as a "System of Systems'' (SoS). Because of the independent nature of the constituent systems in an SoS, approaches to design an SoS, and more specifically, approaches to design a new system as a member of an SoS, will likely be different than the traditional design approaches for complex, monolithic (meaning the constituent parts have no ability for independent operation) systems. Because a system of system evolves over time, this simultaneous system design and resource allocation problem should be investigated in a dynamic context. Such dynamic optimization problems are similar to conventional control problems. However, this research considers problems which not only seek optimizing policies but also seek the proper system or vehicle to operate under these policies. This thesis presents a framework and a set of analytical tools to solve a class of SoS problems that involves the simultaneous design of a new system and allocation of the new system along with existing systems. Such a class of problems belongs to the problems of concurrent design and control of a new systems with solutions consisting of both optimal system design and optimal control strategy. Rigorous mathematical arguments show that the proposed framework solves the concurrent design and control problems. Many results exist for dynamic optimization problems of linear systems. In contrary, results on optimal nonlinear dynamic optimization problems are rare. The proposed framework is equipped with the set of analytical tools to solve several cases of nonlinear optimal control problems: continuous- and discrete-time nonlinear problems with applications on both optimal regulation and tracking. These tools are useful when mathematical descriptions of dynamic systems are available. In the absence of such a mathematical model, it is often necessary to derive a solution based on computer simulation. For this case, a set of parameterized decision may constitute a solution. This thesis presents a method to adjust these parameters based on the principle of stochastic approximation simultaneous perturbation using continuous measurements. The set of tools developed here mostly employs the methods of exact dynamic programming. However, due to the complexity of SoS problems, this research also develops suboptimal solution approaches, collectively recognized as approximate dynamic programming solutions, for large scale problems. The thesis presents, explores, and solves problems from an airline industry, in which a new aircraft is to be designed and allocated along with an existing fleet of aircraft. Because the life cycle of an aircraft is on the order of 10 to 20 years, this problem is to be addressed dynamically so that the new aircraft design is the best design for the fleet over a given time horizon.

Algorithm for solving of two-level hierarchical minimax program control problem of final state the regional socio-economic system in the presence of risks

NASA Astrophysics Data System (ADS)

Shorikov, A. F.

2017-10-01

In this paper we study the problem of optimization of guaranteed result for program control by the final state of regional social and economic system in the presence of risks. For this problem we propose a mathematical model in the form of two-level hierarchical minimax program control problem of the final state of this process with incomplete information. For solving of its problem we constructed the common algorithm that has a form of a recurrent procedure of solving a linear programming and a finite optimization problems.

About some types of constraints in problems of routing

NASA Astrophysics Data System (ADS)

Petunin, A. A.; Polishuk, E. G.; Chentsov, A. G.; Chentsov, P. A.; Ukolov, S. S.

2016-12-01

Many routing problems arising in different applications can be interpreted as a discrete optimization problem with additional constraints. The latter include generalized travelling salesman problem (GTSP), to which task of tool routing for CNC thermal cutting machines is sometimes reduced. Technological requirements bound to thermal fields distribution during cutting process are of great importance when developing algorithms for this task solution. These requirements give rise to some specific constraints for GTSP. This paper provides a mathematical formulation for the problem of thermal fields calculating during metal sheet thermal cutting. Corresponding algorithm with its programmatic implementation is considered. The mathematical model allowing taking such constraints into account considering other routing problems is discussed either.

Solving Optimization Problems with Spreadsheets

ERIC Educational Resources Information Center

Beigie, Darin

2017-01-01

Spreadsheets provide a rich setting for first-year algebra students to solve problems. Individual spreadsheet cells play the role of variables, and creating algebraic expressions for a spreadsheet to perform a task allows students to achieve a glimpse of how mathematics is used to program a computer and solve problems. Classic optimization…

GlobiPack v. 1.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bartlett, Roscoe

2010-03-31

GlobiPack contains a small collection of optimization globalization algorithms. These algorithms are used by optimization and various nonlinear equation solver algorithms.Used as the line-search procedure with Newton and Quasi-Newton optimization and nonlinear equation solver methods. These are standard published 1-D line search algorithms such as are described in the book Nocedal and Wright Numerical Optimization: 2nd edition, 2006. One set of algorithms were copied and refactored from the existing open-source Trilinos package MOOCHO where the linear search code is used to globalize SQP methods. This software is generic to any mathematical optimization problem where smooth derivatives exist. There is nomore » specific connection or mention whatsoever to any specific application, period. You cannot find more general mathematical software.« less

Optimization methods of laws control of electric propulsion spacecraft in the restricted three-body task

NASA Astrophysics Data System (ADS)

Starinova, Olga L.

2014-12-01

This paper outlines the optimization methods of the control law of the low thrust spacecraft for the restrict problem of three-body. The conditions for fragmentation trajectory on the specific parts of trajectory are formulated. The mathematical statement and methods to solve the optimal control problem on these parts are stated. Results of the decision of applied problems for various classes of spacecrafts which are carrying out maneuvers with low thrust are presented. In particular, the non-coplanar maneuvers of the low thrust spacecraft in the Earth-Moon system are viewed.

Modeling of tool path for the CNC sheet cutting machines

NASA Astrophysics Data System (ADS)

Petunin, Aleksandr A.

2015-11-01

In the paper the problem of tool path optimization for CNC (Computer Numerical Control) cutting machines is considered. The classification of the cutting techniques is offered. We also propose a new classification of toll path problems. The tasks of cost minimization and time minimization for standard cutting technique (Continuous Cutting Problem, CCP) and for one of non-standard cutting techniques (Segment Continuous Cutting Problem, SCCP) are formalized. We show that the optimization tasks can be interpreted as discrete optimization problem (generalized travel salesman problem with additional constraints, GTSP). Formalization of some constraints for these tasks is described. For the solution GTSP we offer to use mathematical model of Prof. Chentsov based on concept of a megalopolis and dynamic programming.

Final Technical Report for "Applied Mathematics Research: Simulation Based Optimization and Application to Electromagnetic Inverse Problems"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haber, Eldad

2014-03-17

The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequality constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.

A dynamic model of functioning of a bank

NASA Astrophysics Data System (ADS)

Malafeyev, Oleg; Awasthi, Achal; Zaitseva, Irina; Rezenkov, Denis; Bogdanova, Svetlana

2018-04-01

In this paper, we analyze dynamic programming as a novel approach to solve the problem of maximizing the profits of a bank. The mathematical model of the problem and the description of bank's work is described in this paper. The problem is then approached using the method of dynamic programming. Dynamic programming makes sure that the solutions obtained are globally optimal and numerically stable. The optimization process is set up as a discrete multi-stage decision process and solved with the help of dynamic programming.

E-Learning Technologies: Employing Matlab Web Server to Facilitate the Education of Mathematical Programming

ERIC Educational Resources Information Center

Karagiannis, P.; Markelis, I.; Paparrizos, K.; Samaras, N.; Sifaleras, A.

2006-01-01

This paper presents new web-based educational software (webNetPro) for "Linear Network Programming." It includes many algorithms for "Network Optimization" problems, such as shortest path problems, minimum spanning tree problems, maximum flow problems and other search algorithms. Therefore, webNetPro can assist the teaching process of courses such…

Compressed modes for variational problems in mathematics and physics

PubMed Central

Ozoliņš, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-01-01

This article describes a general formalism for obtaining spatially localized (“sparse”) solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger’s equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support (“compressed modes”). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. PMID:24170861

Compressed modes for variational problems in mathematics and physics.

PubMed

Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-11-12

This article describes a general formalism for obtaining spatially localized ("sparse") solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support ("compressed modes"). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size.

Expected value based fuzzy programming approach to solve integrated supplier selection and inventory control problem with fuzzy demand

NASA Astrophysics Data System (ADS)

Sutrisno; Widowati; Sunarsih; Kartono

2018-01-01

In this paper, a mathematical model in quadratic programming with fuzzy parameter is proposed to determine the optimal strategy for integrated inventory control and supplier selection problem with fuzzy demand. To solve the corresponding optimization problem, we use the expected value based fuzzy programming. Numerical examples are performed to evaluate the model. From the results, the optimal amount of each product that have to be purchased from each supplier for each time period and the optimal amount of each product that have to be stored in the inventory for each time period were determined with minimum total cost and the inventory level was sufficiently closed to the reference level.

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations

PubMed Central

Duarte, Belmiro P.M.; Wong, Weng Kee; Oliveira, Nuno M.C.

2015-01-01

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D–, A– and E–optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D–optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice. PMID:26949279

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee; Oliveira, Nuno M C

2016-02-15

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D -, A - and E -optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D -optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.

Introduction to Numerical Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoonover, Joseph A.

2016-06-14

These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.

Optimal Strategy for Integrated Dynamic Inventory Control and Supplier Selection in Unknown Environment via Stochastic Dynamic Programming

NASA Astrophysics Data System (ADS)

Sutrisno; Widowati; Solikhin

2016-06-01

In this paper, we propose a mathematical model in stochastic dynamic optimization form to determine the optimal strategy for an integrated single product inventory control problem and supplier selection problem where the demand and purchasing cost parameters are random. For each time period, by using the proposed model, we decide the optimal supplier and calculate the optimal product volume purchased from the optimal supplier so that the inventory level will be located at some point as close as possible to the reference point with minimal cost. We use stochastic dynamic programming to solve this problem and give several numerical experiments to evaluate the model. From the results, for each time period, the proposed model was generated the optimal supplier and the inventory level was tracked the reference point well.

Optimal control of LQG problem with an explicit trade-off between mean and variance

NASA Astrophysics Data System (ADS)

Qian, Fucai; Xie, Guo; Liu, Ding; Xie, Wenfang

2011-12-01

For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean-variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.

The mathematical statement for the solving of the problem of N-version software system design

NASA Astrophysics Data System (ADS)

Kovalev, I. V.; Kovalev, D. I.; Zelenkov, P. V.; Voroshilova, A. A.

2015-10-01

The N-version programming, as a methodology of the fault-tolerant software systems design, allows successful solving of the mentioned tasks. The use of N-version programming approach turns out to be effective, since the system is constructed out of several parallel executed versions of some software module. Those versions are written to meet the same specification but by different programmers. The problem of developing an optimal structure of N-version software system presents a kind of very complex optimization problem. This causes the use of deterministic optimization methods inappropriate for solving the stated problem. In this view, exploiting heuristic strategies looks more rational. In the field of pseudo-Boolean optimization theory, the so called method of varied probabilities (MVP) has been developed to solve problems with a large dimensionality.

Solving Optimization Problems with Dynamic Geometry Software: The Airport Problem

ERIC Educational Resources Information Center

Contreras, José

2014-01-01

This paper describes how the author's students (in-service and pre-service secondary mathematics teachers) enrolled in college geometry courses use the Geometers' Sketchpad (GSP) to gain insight to formulate, confirm, test, and refine conjectures to solve the classical airport problem for triangles. The students are then provided with strategic…

Mathematical theory of a relaxed design problem in structural optimization

NASA Technical Reports Server (NTRS)

Kikuchi, Noboru; Suzuki, Katsuyuki

1990-01-01

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

An electromagnetism-like metaheuristic for open-shop problems with no buffer

NASA Astrophysics Data System (ADS)

Naderi, Bahman; Najafi, Esmaeil; Yazdani, Mehdi

2012-12-01

This paper considers open-shop scheduling with no intermediate buffer to minimize total tardiness. This problem occurs in many production settings, in the plastic molding, chemical, and food processing industries. The paper mathematically formulates the problem by a mixed integer linear program. The problem can be optimally solved by the model. The paper also develops a novel metaheuristic based on an electromagnetism algorithm to solve the large-sized problems. The paper conducts two computational experiments. The first includes small-sized instances by which the mathematical model and general performance of the proposed metaheuristic are evaluated. The second evaluates the metaheuristic for its performance to solve some large-sized instances. The results show that the model and algorithm are effective to deal with the problem.

Optimal starting conditions for the rendezvous maneuver: Analytical and computational approach

NASA Astrophysics Data System (ADS)

Ciarcia, Marco

The three-dimensional rendezvous between two spacecraft is considered: a target spacecraft on a circular orbit around the Earth and a chaser spacecraft initially on some elliptical orbit yet to be determined. The chaser spacecraft has variable mass, limited thrust, and its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We seek the time history of the controls in such a way that the propellant mass required to execute the rendezvous maneuver is minimized. Two cases are considered: (i) time-to-rendezvous free and (ii) time-to-rendezvous given, respectively equivalent to (i) free angular travel and (ii) fixed angular travel for the target spacecraft. The above problem has been studied by several authors under the assumption that the initial separation coordinates and the initial separation velocities are given, hence known initial conditions for the chaser spacecraft. In this paper, it is assumed that both the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given so as to prevent the occurrence of trivial solutions. Two approaches are employed: optimal control formulation (Part A) and mathematical programming formulation (Part B). In Part A, analyses are performed with the multiple-subarc sequential gradient-restoration algorithm for optimal control problems. They show that the fuel-optimal trajectory is zero-bang, namely it is characterized by two subarcs: a long coasting zero-thrust subarc followed by a short powered max-thrust braking subarc. While the thrust direction of the powered subarc is continuously variable for the optimal trajectory, its replacement with a constant (yet optimized) thrust direction produces a very efficient guidance trajectory. Indeed, for all values of the initial distance, the fuel required by the guidance trajectory is within less than one percent of the fuel required by the optimal trajectory. For the guidance trajectory, because of the replacement of the variable thrust direction of the powered subarc with a constant thrust direction, the optimal control problem degenerates into a mathematical programming problem with a relatively small number of degrees of freedom, more precisely: three for case (i) time-to-rendezvous free and two for case (ii) time-to-rendezvous given. In particular, we consider the rendezvous between the Space Shuttle (chaser) and the International Space Station (target). Once a given initial distance SS-to-ISS is preselected, the present work supplies not only the best initial conditions for the rendezvous trajectory, but simultaneously the corresponding final conditions for the ascent trajectory. In Part B, an analytical solution of the Clohessy-Wiltshire equations is presented (i) neglecting the change of the spacecraft mass due to the fuel consumption and (ii) and assuming that the thrust is finite, that is, the trajectory includes powered subarcs flown with max thrust and coasting subarc flown with zero thrust. Then, employing the found analytical solution, we study the rendezvous problem under the assumption that the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given. The main contribution of Part B is the development of analytical solutions for the powered subarcs, an important extension of the analytical solutions already available for the coasting subarcs. One consequence is that the entire optimal trajectory can be described analytically. Another consequence is that the optimal control problems degenerate into mathematical programming problems. A further consequence is that, vis-a-vis the optimal control formulation, the mathematical programming formulation reduces the CPU time by a factor of order 1000. Key words. Space trajectories, rendezvous, optimization, guidance, optimal control, calculus of variations, Mayer problems, Bolza problems, transformation techniques, multiple-subarc sequential gradient-restoration algorithm.

System principles, mathematical models and methods to ensure high reliability of safety systems

NASA Astrophysics Data System (ADS)

Zaslavskyi, V.

2017-04-01

Modern safety and security systems are composed of a large number of various components designed for detection, localization, tracking, collecting, and processing of information from the systems of monitoring, telemetry, control, etc. They are required to be highly reliable in a view to correctly perform data aggregation, processing and analysis for subsequent decision making support. On design and construction phases of the manufacturing of such systems a various types of components (elements, devices, and subsystems) are considered and used to ensure high reliability of signals detection, noise isolation, and erroneous commands reduction. When generating design solutions for highly reliable systems a number of restrictions and conditions such as types of components and various constrains on resources should be considered. Various types of components perform identical functions; however, they are implemented using diverse principles, approaches and have distinct technical and economic indicators such as cost or power consumption. The systematic use of different component types increases the probability of tasks performing and eliminates the common cause failure. We consider type-variety principle as an engineering principle of system analysis, mathematical models based on this principle, and algorithms for solving optimization problems of highly reliable safety and security systems design. Mathematical models are formalized in a class of two-level discrete optimization problems of large dimension. The proposed approach, mathematical models, algorithms can be used for problem solving of optimal redundancy on the basis of a variety of methods and control devices for fault and defects detection in technical systems, telecommunication networks, and energy systems.

A coherent Ising machine for 2000-node optimization problems

NASA Astrophysics Data System (ADS)

Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki

2016-11-01

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

Mathematical programming formulations for satellite synthesis

NASA Technical Reports Server (NTRS)

Bhasin, Puneet; Reilly, Charles H.

1987-01-01

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

A generalized network flow model for the multi-mode resource-constrained project scheduling problem with discounted cash flows

NASA Astrophysics Data System (ADS)

Chen, Miawjane; Yan, Shangyao; Wang, Sin-Siang; Liu, Chiu-Lan

2015-02-01

An effective project schedule is essential for enterprises to increase their efficiency of project execution, to maximize profit, and to minimize wastage of resources. Heuristic algorithms have been developed to efficiently solve the complicated multi-mode resource-constrained project scheduling problem with discounted cash flows (MRCPSPDCF) that characterize real problems. However, the solutions obtained in past studies have been approximate and are difficult to evaluate in terms of optimality. In this study, a generalized network flow model, embedded in a time-precedence network, is proposed to formulate the MRCPSPDCF with the payment at activity completion times. Mathematically, the model is formulated as an integer network flow problem with side constraints, which can be efficiently solved for optimality, using existing mathematical programming software. To evaluate the model performance, numerical tests are performed. The test results indicate that the model could be a useful planning tool for project scheduling in the real world.

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem.

PubMed

Rajeswari, M; Amudhavel, J; Pothula, Sujatha; Dhavachelvan, P

2017-01-01

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria.

Optimal Control of Thermo--Fluid Phenomena in Variable Domains

NASA Astrophysics Data System (ADS)

Volkov, Oleg; Protas, Bartosz

2008-11-01

This presentation concerns our continued research on adjoint--based optimization of viscous incompressible flows (the Navier--Stokes problem) coupled with heat conduction involving change of phase (the Stefan problem), and occurring in domains with variable boundaries. This problem is motivated by optimization of advanced welding techniques used in automotive manufacturing, where the goal is to determine an optimal heat input, so as to obtain a desired shape of the weld pool surface upon solidification. We argue that computation of sensitivities (gradients) in such free--boundary problems requires the use of the shape--differential calculus as a key ingredient. We also show that, with such tools available, the computational solution of the direct and inverse (optimization) problems can in fact be achieved in a similar manner and in a comparable computational time. Our presentation will address certain mathematical and computational aspects of the method. As an illustration we will consider the two--phase Stefan problem with contact point singularities where our approach allows us to obtain a thermodynamically consistent solution.

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem

PubMed Central

Amudhavel, J.; Pothula, Sujatha; Dhavachelvan, P.

2017-01-01

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria. PMID:28473849

Liquid disinfection using power impulse laser

NASA Astrophysics Data System (ADS)

Gribin, S.; Assaoul, Viktor; Markova, Elena; Gromova, Ludmila P.; Spesivtsev, Boris; Bazanov, V.

1996-05-01

The presented method is based on the bactericidal effect of micro-blast induced by various sources (laser breakdown, electrohydraulic effect...). Using elaborated conception of physical phenomena providing liquid disinfection it is possible to determine optimal conditions of water treatment. The problem of optimization is solved using methods of mathematical modeling and special experiments.

Liquid disinfection using power impulse laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gribin, S.; Assaoul, V.; Markova, E.

1996-12-31

The presented method is based on the bactericidal effect of micro-blast induced by various sources (laser breakdown, electrohydraulic effect ... ). Using elaborated conception of physical phenomena providing liquid disinfection it is possible to determine optimal conditions of water treatment. The problem of optimization is solved using methods of mathematical modeling and special experiments.

Finding the Optimal Guidance for Enhancing Anchored Instruction

ERIC Educational Resources Information Center

Zydney, Janet Mannheimer; Bathke, Arne; Hasselbring, Ted S.

2014-01-01

This study investigated the effect of different methods of guidance with anchored instruction on students' mathematical problem-solving performance. The purpose of this research was to iteratively design a learning environment to find the optimal level of guidance. Two iterations of the software were compared. The first iteration used explicit…

Optimization-based additive decomposition of weakly coercive problems with applications

DOE PAGES

Bochev, Pavel B.; Ridzal, Denis

2016-01-27

In this study, we present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem,more » our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.« less

Wine and maths: mathematical solutions to wine-inspired problems

NASA Astrophysics Data System (ADS)

Cadeddu, L.; Cauli, A.

2018-04-01

We deal with an application of partial differential equations to the correct definition of a wine cellar. We present some historical details about this problem. We also discuss how to build or renew a wine cellar, creating ideal conditions for the ageing process and improving the quality of wines. Our goal is to calculate the optimal depth z0 of a wine cellar in order to attenuate the periodic temperature fluctuations. What follows is a kind of survey of wine-related and optimization problems which have been solved by means of powerful math tools.

Optimization techniques applied to spectrum management for communications satellites

NASA Astrophysics Data System (ADS)

Ottey, H. R.; Sullivan, T. M.; Zusman, F. S.

This paper describes user requirements, algorithms and software design features for the application of optimization techniques to the management of the geostationary orbit/spectrum resource. Relevant problems include parameter sensitivity analyses, frequency and orbit position assignment coordination, and orbit position allotment planning. It is shown how integer and nonlinear programming as well as heuristic search techniques can be used to solve these problems. Formalized mathematical objective functions that define the problems are presented. Constraint functions that impart the necessary solution bounds are described. A versatile program structure is outlined, which would allow problems to be solved in stages while varying the problem space, solution resolution, objective function and constraints.

The Secretary Problem from the Applicant's Point of View

ERIC Educational Resources Information Center

Glass, Darren

2012-01-01

A 1960 "Mathematical Games" column describes the problem, now known as the Secretary Problem, which asks how someone interviewing candidates for a position should maximize the chance of hiring the best applicant. This note looks at how an applicant should respond, if they know the interviewer uses this optimal strategy. We show that all but the…

Optimization of computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mikhalevich, V.S.; Sergienko, I.V.; Zadiraka, V.K.

1994-11-01

This article examines some topics of optimization of computations, which have been discussed at 25 seminar-schools and symposia organized by the V.M. Glushkov Institute of Cybernetics of the Ukrainian Academy of Sciences since 1969. We describe the main directions in the development of computational mathematics and present some of our own results that reflect a certain design conception of speed-optimal and accuracy-optimal (or nearly optimal) algorithms for various classes of problems, as well as a certain approach to optimization of computer computations.

Review: Optimization methods for groundwater modeling and management

NASA Astrophysics Data System (ADS)

Yeh, William W.-G.

2015-09-01

Optimization methods have been used in groundwater modeling as well as for the planning and management of groundwater systems. This paper reviews and evaluates the various optimization methods that have been used for solving the inverse problem of parameter identification (estimation), experimental design, and groundwater planning and management. Various model selection criteria are discussed, as well as criteria used for model discrimination. The inverse problem of parameter identification concerns the optimal determination of model parameters using water-level observations. In general, the optimal experimental design seeks to find sampling strategies for the purpose of estimating the unknown model parameters. A typical objective of optimal conjunctive-use planning of surface water and groundwater is to minimize the operational costs of meeting water demand. The optimization methods include mathematical programming techniques such as linear programming, quadratic programming, dynamic programming, stochastic programming, nonlinear programming, and the global search algorithms such as genetic algorithms, simulated annealing, and tabu search. Emphasis is placed on groundwater flow problems as opposed to contaminant transport problems. A typical two-dimensional groundwater flow problem is used to explain the basic formulations and algorithms that have been used to solve the formulated optimization problems.

Linear quadratic optimization for positive LTI system

NASA Astrophysics Data System (ADS)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

Application of the gravity search algorithm to multi-reservoir operation optimization

NASA Astrophysics Data System (ADS)

Bozorg-Haddad, Omid; Janbaz, Mahdieh; Loáiciga, Hugo A.

2016-12-01

Complexities in river discharge, variable rainfall regime, and drought severity merit the use of advanced optimization tools in multi-reservoir operation. The gravity search algorithm (GSA) is an evolutionary optimization algorithm based on the law of gravity and mass interactions. This paper explores the GSA's efficacy for solving benchmark functions, single reservoir, and four-reservoir operation optimization problems. The GSA's solutions are compared with those of the well-known genetic algorithm (GA) in three optimization problems. The results show that the GSA's results are closer to the optimal solutions than the GA's results in minimizing the benchmark functions. The average values of the objective function equal 1.218 and 1.746 with the GSA and GA, respectively, in solving the single-reservoir hydropower operation problem. The global solution equals 1.213 for this same problem. The GSA converged to 99.97% of the global solution in its average-performing history, while the GA converged to 97% of the global solution of the four-reservoir problem. Requiring fewer parameters for algorithmic implementation and reaching the optimal solution in fewer number of functional evaluations are additional advantages of the GSA over the GA. The results of the three optimization problems demonstrate a superior performance of the GSA for optimizing general mathematical problems and the operation of reservoir systems.

Enriching Practical Knowledge: Exploring Student Teachers' Competence in Integrating Theory and Practice of Mathematics Teaching

ERIC Educational Resources Information Center

Oonk, Wil; Verloop, Nico; Gravemeijer, Koeno P. E.

2015-01-01

This study concentrated on the theory-practice problem in mathematics teacher education. We examined 13 student teachers' use of theory when they reflected on teaching practice in a class specifically designed to optimize the chance for theory use. We developed a Reflection Analysis Instrument with which the student teachers' use of theory could…

Applications of numerical optimization methods to helicopter design problems: A survey

NASA Technical Reports Server (NTRS)

Miura, H.

1984-01-01

A survey of applications of mathematical programming methods is used to improve the design of helicopters and their components. Applications of multivariable search techniques in the finite dimensional space are considered. Five categories of helicopter design problems are considered: (1) conceptual and preliminary design, (2) rotor-system design, (3) airframe structures design, (4) control system design, and (5) flight trajectory planning. Key technical progress in numerical optimization methods relevant to rotorcraft applications are summarized.

Applications of numerical optimization methods to helicopter design problems - A survey

NASA Technical Reports Server (NTRS)

Miura, H.

1985-01-01

A survey of applications of mathematical programming methods is used to improve the design of helicopters and their components. Applications of multivariable search techniques in the finite dimensional space are considered. Five categories of helicopter design problems are considered: (1) conceptual and preliminary design, (2) rotor-system design, (3) airframe structures design, (4) control system design, and (5) flight trajectory planning. Key technical progress in numerical optimization methods relevant to rotorcraft applications are summarized.

Applications of numerical optimization methods to helicopter design problems - A survey

NASA Technical Reports Server (NTRS)

Miura, H.

1984-01-01

A survey of applications of mathematical programming methods is used to improve the design of helicopters and their components. Applications of multivariable search techniques in the finite dimensional space are considered. Five categories of helicopter design problems are considered: (1) conceptual and preliminary design, (2) rotor-system design, (3) airframe structures design, (4) control system design, and (5) flight trajectory planning. Key technical progress in numerical optimization methods relevant to rotorcraft applications are summarized.

Tuning Parameters in Heuristics by Using Design of Experiments Methods

NASA Technical Reports Server (NTRS)

Arin, Arif; Rabadi, Ghaith; Unal, Resit

2010-01-01

With the growing complexity of today's large scale problems, it has become more difficult to find optimal solutions by using exact mathematical methods. The need to find near-optimal solutions in an acceptable time frame requires heuristic approaches. In many cases, however, most heuristics have several parameters that need to be "tuned" before they can reach good results. The problem then turns into "finding best parameter setting" for the heuristics to solve the problems efficiently and timely. One-Factor-At-a-Time (OFAT) approach for parameter tuning neglects the interactions between parameters. Design of Experiments (DOE) tools can be instead employed to tune the parameters more effectively. In this paper, we seek the best parameter setting for a Genetic Algorithm (GA) to solve the single machine total weighted tardiness problem in which n jobs must be scheduled on a single machine without preemption, and the objective is to minimize the total weighted tardiness. Benchmark instances for the problem are available in the literature. To fine tune the GA parameters in the most efficient way, we compare multiple DOE models including 2-level (2k ) full factorial design, orthogonal array design, central composite design, D-optimal design and signal-to-noise (SIN) ratios. In each DOE method, a mathematical model is created using regression analysis, and solved to obtain the best parameter setting. After verification runs using the tuned parameter setting, the preliminary results for optimal solutions of multiple instances were found efficiently.

The individual time trial as an optimal control problem

PubMed Central

de Jong, Jenny; Fokkink, Robbert; Olsder, Geert Jan; Schwab, AL

2017-01-01

In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial and involves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial. PMID:29388631

Interior search algorithm (ISA): a novel approach for global optimization.

PubMed

Gandomi, Amir H

2014-07-01

This paper presents the interior search algorithm (ISA) as a novel method for solving optimization tasks. The proposed ISA is inspired by interior design and decoration. The algorithm is different from other metaheuristic algorithms and provides new insight for global optimization. The proposed method is verified using some benchmark mathematical and engineering problems commonly used in the area of optimization. ISA results are further compared with well-known optimization algorithms. The results show that the ISA is efficiently capable of solving optimization problems. The proposed algorithm can outperform the other well-known algorithms. Further, the proposed algorithm is very simple and it only has one parameter to tune. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Achieving Optimal Best: Instructional Efficiency and the Use of Cognitive Load Theory in Mathematical Problem Solving

ERIC Educational Resources Information Center

Phan, Huy P.; Ngu, Bing H.; Yeung, Alexander S.

2017-01-01

We recently developed the "Framework of Achievement Bests" to explain the importance of effective functioning, personal growth, and enrichment of well-being experiences. This framework postulates a concept known as "optimal achievement best," which stipulates the idea that individuals may, in general, strive to achieve personal…

Models of resource allocation optimization when solving the control problems in organizational systems

NASA Astrophysics Data System (ADS)

Menshikh, V.; Samorokovskiy, A.; Avsentev, O.

2018-03-01

The mathematical model of optimizing the allocation of resources to reduce the time for management decisions and algorithms to solve the general problem of resource allocation. The optimization problem of choice of resources in organizational systems in order to reduce the total execution time of a job is solved. This problem is a complex three-level combinatorial problem, for the solving of which it is necessary to implement the solution to several specific problems: to estimate the duration of performing each action, depending on the number of performers within the group that performs this action; to estimate the total execution time of all actions depending on the quantitative composition of groups of performers; to find such a distribution of the existing resource of performers in groups to minimize the total execution time of all actions. In addition, algorithms to solve the general problem of resource allocation are proposed.

Simulation of a class of hazardous situations in the ICS «INM RAS - Baltic Sea»

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Agoshkov, Valery; Aseev, Nikita; Parmuzin, Eugene; Sheloput, Tateana; Shutyaev, Victor

2017-04-01

Development of Informational Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in mathematical modeling, theory of adjoint equations and optimal control, inverse problems, numerical methods theory, numerical algebra, scientific computing and processing of satellite data. In this work the results on the ICS development for PC-ICS "INM RAS - Baltic Sea" are presented. We discuss practical problems studied by ICS. The System includes numerical model of the Baltic Sea thermodynamics, the new oil spill model describing the propagation of a slick at the Sea surface (Agoshkov, Aseev et al., 2014) and the optimal ship route calculating block (Agoshkov, Zayachkovsky et al., 2014). The ICS is based on the INMOM numerical model of the Baltic Sea thermodynamics (Zalesny et al., 2013). It is possible to calculate main hydrodynamic parameters (temperature, salinity, velocities, sea level) using user-friendly interface of the ICS. The System includes data assimilation procedures (Agoshkov, 2003, Parmuzin, Agoshkov, 2012) and one can use the block of variational assimilation of the sea surface temperature in order to obtain main hydrodynamic parameters. Main possibilities of the ICS and several numerical experiments are presented in the work. By the problem of risk control is meant a problem of determination of optimal resources quantity which are necessary for decreasing the risk to some acceptable value. Mass of oil slick is chosen as a function of control. For the realization of the random variable the quadratic "functional of cost" is introduced. It comprises cleaning costs and deviation of damage of oil pollution from its acceptable value. The problem of minimization of this functional is solved based on the methods of optimal control and the theory of adjoint equations. The solution of this problem is explicitly found. The study was supported by the Russian Foundation for Basic Research (project 16-31-00510) and by the Russian Science Foundation (project №14-11-00609). V. I. Agoshkov, Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). V. B. Zalesny, A. V. Gusev, V. O. Ivchenko, R. Tamsalu, and R. Aps, Numerical model of the Baltic Sea circulation. Russ. J. Numer. Anal. Math. Modelling 28 (2013), No. 1, 85-100. V.I. Agoshkov, A.O. Zayachkovskiy, R. Aps, P. Kujala, and J. Rytkönen. Risk theory based solution to the problem of optimal vessel route // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 69-78. Agoshkov, V., Aseev, N., Aps, R., Kujala, P., Rytkönen, J., Zalesny, V. The problem of control of oil pollution risk in the Baltic Sea // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 93-105. E. I. Parmuzin and V. I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling 27 (2012), No. 1, 69-94. Olof Liungman and Johan Mattsson. Scientic Documentation of Seatrack Web; physical processes, algorithms and references, 2011.

An approach to optimal semi-active control of vibration energy harvesting based on MEMS

NASA Astrophysics Data System (ADS)

Rojas, Rafael A.; Carcaterra, Antonio

2018-07-01

In this paper the energy harvesting problem involving typical MEMS technology is reduced to an optimal control problem, where the objective function is the absorption of the maximum amount of energy in a given time interval from a vibrating environment. The interest here is to identify a physical upper bound for this energy storage. The mathematical tool is a new optimal control called Krotov's method, that has not yet been applied to engineering problems, except in quantum dynamics. This approach leads to identify new maximum bounds to the energy harvesting performance. Novel MEMS-based device control configurations for vibration energy harvesting are proposed with particular emphasis to piezoelectric, electromagnetic and capacitive circuits.

An overview of the mathematical and statistical analysis component of RICIS

NASA Technical Reports Server (NTRS)

Hallum, Cecil R.

1987-01-01

Mathematical and statistical analysis components of RICIS (Research Institute for Computing and Information Systems) can be used in the following problem areas: (1) quantification and measurement of software reliability; (2) assessment of changes in software reliability over time (reliability growth); (3) analysis of software-failure data; and (4) decision logic for whether to continue or stop testing software. Other areas of interest to NASA/JSC where mathematical and statistical analysis can be successfully employed include: math modeling of physical systems, simulation, statistical data reduction, evaluation methods, optimization, algorithm development, and mathematical methods in signal processing.

A simple technique to increase profits in wood products marketing

Treesearch

George B. Harpole

1971-01-01

Mathematical models can be used to solve quickly some simple day-to-day marketing problems. This note explains how a sawmill production manager, who has an essentially fixed-capacity mill, can solve several optimization problems by using pencil and paper, a forecast of market prices, and a simple algorithm. One such problem is to maximize profits in an operating period...

Optimization of controlled processes in combined-cycle plant (new developments and researches)

NASA Astrophysics Data System (ADS)

Tverskoy, Yu S.; Muravev, I. K.

2017-11-01

All modern complex technical systems, including power units of TPP and nuclear power plants, work in the system-forming structure of multifunctional APCS. The development of the modern APCS mathematical support allows bringing the automation degree to the solution of complex optimization problems of equipment heat-mass-exchange processes in real time. The difficulty of efficient management of a binary power unit is related to the need to solve jointly at least three problems. The first problem is related to the physical issues of combined-cycle technologies. The second problem is determined by the criticality of the CCGT operation to changes in the regime and climatic factors. The third problem is related to a precise description of a vector of controlled coordinates of a complex technological object. To obtain a joint solution of this complex of interconnected problems, the methodology of generalized thermodynamic analysis, methods of the theory of automatic control and mathematical modeling are used. In the present report, results of new developments and studies are shown. These results allow improving the principles of process control and the automatic control systems structural synthesis of power units with combined-cycle plants that provide attainable technical and economic efficiency and operational reliability of equipment.

Boundary elements; Proceedings of the Fifth International Conference, Hiroshima, Japan, November 8-11, 1983

NASA Astrophysics Data System (ADS)

Brebbia, C. A.; Futagami, T.; Tanaka, M.

The boundary-element method (BEM) in computational fluid and solid mechanics is examined in reviews and reports of theoretical studies and practical applications. Topics presented include the fundamental mathematical principles of BEMs, potential problems, EM-field problems, heat transfer, potential-wave problems, fluid flow, elasticity problems, fracture mechanics, plates and shells, inelastic problems, geomechanics, dynamics, industrial applications of BEMs, optimization methods based on the BEM, numerical techniques, and coupling.

Combinatorial and Algorithmic Rigidity: Beyond Two Dimensions

DTIC Science & Technology

2012-12-01

problem. Manuscript, 2010. [35] G. Panina and I. Streinu. Flattening single-vertex origami : the non- expansive case. Computational Geometry : Theory and...in 2008, under the DARPA solicitation “Mathemat- ical Challenges, BAA 07-68”. It addressed Mathematical Challenge Ten: Al- gorithmic Origami and...a number of optimal algorithms and provided critical complexity analysis. The topic of algorithmic origami was successfully engaged from the same

Optimal maintenance of a multi-unit system under dependencies

NASA Astrophysics Data System (ADS)

Sung, Ho-Joon

The availability, or reliability, of an engineering component greatly influences the operational cost and safety characteristics of a modern system over its life-cycle. Until recently, the reliance on past empirical data has been the industry-standard practice to develop maintenance policies that provide the minimum level of system reliability. Because such empirically-derived policies are vulnerable to unforeseen or fast-changing external factors, recent advancements in the study of topic on maintenance, which is known as optimal maintenance problem, has gained considerable interest as a legitimate area of research. An extensive body of applicable work is available, ranging from those concerned with identifying maintenance policies aimed at providing required system availability at minimum possible cost, to topics on imperfect maintenance of multi-unit system under dependencies. Nonetheless, these existing mathematical approaches to solve for optimal maintenance policies must be treated with caution when considered for broader applications, as they are accompanied by specialized treatments to ease the mathematical derivation of unknown functions in both objective function and constraint for a given optimal maintenance problem. These unknown functions are defined as reliability measures in this thesis, and theses measures (e.g., expected number of failures, system renewal cycle, expected system up time, etc.) do not often lend themselves to possess closed-form formulas. It is thus quite common to impose simplifying assumptions on input probability distributions of components' lifetime or repair policies. Simplifying the complex structure of a multi-unit system to a k-out-of-n system by neglecting any sources of dependencies is another commonly practiced technique intended to increase the mathematical tractability of a particular model. This dissertation presents a proposal for an alternative methodology to solve optimal maintenance problems by aiming to achieve the same end-goals as Reliability Centered Maintenance (RCM). RCM was first introduced to the aircraft industry in an attempt to bridge the gap between the empirically-driven and theory-driven approaches to establishing optimal maintenance policies. Under RCM, qualitative processes that enable the prioritizing of functions based on the criticality and influence would be combined with mathematical modeling to obtain the optimal maintenance policies. Where this thesis work deviates from RCM is its proposal to directly apply quantitative processes to model the reliability measures in optimal maintenance problem. First, Monte Carlo (MC) simulation, in conjunction with a pre-determined Design of Experiments (DOE) table, can be used as a numerical means of obtaining the corresponding discrete simulated outcomes of the reliability measures based on the combination of decision variables (e.g., periodic preventive maintenance interval, trigger age for opportunistic maintenance, etc.). These discrete simulation results can then be regressed as Response Surface Equations (RSEs) with respect to the decision variables. Such an approach to represent the reliability measures with continuous surrogate functions (i.e., the RSEs) not only enables the application of the numerical optimization technique to solve for optimal maintenance policies, but also obviates the need to make mathematical assumptions or impose over-simplifications on the structure of a multi-unit system for the sake of mathematical tractability. The applicability of the proposed methodology to a real-world optimal maintenance problem is showcased through its application to a Time Limited Dispatch (TLD) of Full Authority Digital Engine Control (FADEC) system. In broader terms, this proof-of-concept exercise can be described as a constrained optimization problem, whose objective is to identify the optimal system inspection interval that guarantees a certain level of availability for a multi-unit system. A variety of reputable numerical techniques were used to model the problem as accurately as possible, including algorithms for the MC simulation, imperfect maintenance model from quasi renewal processes, repair time simulation, and state transition rules. Variance Reduction Techniques (VRTs) were also used in an effort to enhance MC simulation efficiency. After accurate MC simulation results are obtained, the RSEs are generated based on the goodness-of-fit measure to yield as parsimonious model as possible to construct the optimization problem. Under the assumption of constant failure rate for lifetime distributions, the inspection interval from the proposed methodology was found to be consistent with the one from the common approach used in industry that leverages Continuous Time Markov Chain (CTMC). While the latter does not consider maintenance cost settings, the proposed methodology enables an operator to consider different types of maintenance cost settings, e.g., inspection cost, system corrective maintenance cost, etc., to result in more flexible maintenance policies. When the proposed methodology was applied to the same TLD of FADEC example, but under the more generalized assumption of strictly Increasing Failure Rate (IFR) for lifetime distribution, it was shown to successfully capture component wear-out, as well as the economic dependencies among the system components.

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

PubMed

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

Solving NP-Hard Problems with Physarum-Based Ant Colony System.

PubMed

Liu, Yuxin; Gao, Chao; Zhang, Zili; Lu, Yuxiao; Chen, Shi; Liang, Mingxin; Tao, Li

2017-01-01

NP-hard problems exist in many real world applications. Ant colony optimization (ACO) algorithms can provide approximate solutions for those NP-hard problems, but the performance of ACO algorithms is significantly reduced due to premature convergence and weak robustness, etc. With these observations in mind, this paper proposes a Physarum-based pheromone matrix optimization strategy in ant colony system (ACS) for solving NP-hard problems such as traveling salesman problem (TSP) and 0/1 knapsack problem (0/1 KP). In the Physarum-inspired mathematical model, one of the unique characteristics is that critical tubes can be reserved in the process of network evolution. The optimized updating strategy employs the unique feature and accelerates the positive feedback process in ACS, which contributes to the quick convergence of the optimal solution. Some experiments were conducted using both benchmark and real datasets. The experimental results show that the optimized ACS outperforms other meta-heuristic algorithms in accuracy and robustness for solving TSPs. Meanwhile, the convergence rate and robustness for solving 0/1 KPs are better than those of classical ACS.

Optimizing decentralized production-distribution planning problem in a multi-period supply chain network under uncertainty

NASA Astrophysics Data System (ADS)

Nourifar, Raheleh; Mahdavi, Iraj; Mahdavi-Amiri, Nezam; Paydar, Mohammad Mahdi

2017-09-01

Decentralized supply chain management is found to be significantly relevant in today's competitive markets. Production and distribution planning is posed as an important optimization problem in supply chain networks. Here, we propose a multi-period decentralized supply chain network model with uncertainty. The imprecision related to uncertain parameters like demand and price of the final product is appropriated with stochastic and fuzzy numbers. We provide mathematical formulation of the problem as a bi-level mixed integer linear programming model. Due to problem's convolution, a structure to solve is developed that incorporates a novel heuristic algorithm based on Kth-best algorithm, fuzzy approach and chance constraint approach. Ultimately, a numerical example is constructed and worked through to demonstrate applicability of the optimization model. A sensitivity analysis is also made.

Statistical physics of hard combinatorial optimization: Vertex cover problem

NASA Astrophysics Data System (ADS)

Zhao, Jin-Hua; Zhou, Hai-Jun

2014-07-01

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

Mathematical improvement of the Hopfield model for feasible solutions to the traveling salesman problem by a synapse dynamical system.

PubMed

Takahashi, Y

1998-01-01

It is well known that the Hopfield Model (HM) for neural networks to solve the Traveling Salesman Problem (TSP) suffers from three major drawbacks. (1) It can converge on nonoptimal locally minimum solutions. (2) It can converge on infeasible solutions. (3) Results are very sensitive to the careful tuning of its parameters. A number of methods have been proposed to overcome (a) well. In contrast, work on (b) and (c) has not been sufficient; techniques have not been generalized to more general optimization problems. Thus this paper mathematically resolves (b) and (c) to such an extent that the resolution can be applied to solving with some general network continuous optimization problems including the Hopfield version of the TSP. It first constructs an Extended HM (E-HM) that overcomes both (b) and (c). Fundamental techniques of the E-HM lie in the addition of a synapse dynamical system cooperated with the current HM unit dynamical system. It is this synapse dynamical system that makes the TSP constraint hold at any final states for whatever choices of the IIM parameters and an initial state. The paper then generalizes the E-HM further to a network that can solve a class of continuous optimization problems with a constraint equation where both of the objective function and the constraint function are nonnegative and continuously differentiable.

Useful Material Efficiency Green Metrics Problem Set Exercises for Lecture and Laboratory

ERIC Educational Resources Information Center

Andraos, John

2015-01-01

A series of pedagogical problem set exercises are posed that illustrate the principles behind material efficiency green metrics and their application in developing a deeper understanding of reaction and synthesis plan analysis and strategies to optimize them. Rigorous, yet simple, mathematical proofs are given for some of the fundamental concepts,…

Image processing and reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chartrand, Rick

2012-06-15

This talk will examine some mathematical methods for image processing and the solution of underdetermined, linear inverse problems. The talk will have a tutorial flavor, mostly accessible to undergraduates, while still presenting research results. The primary approach is the use of optimization problems. We will find that relaxing the usual assumption of convexity will give us much better results.

Algorithms for Scheduling and Network Problems

DTIC Science & Technology

1991-09-01

time. We already know, by Lemma 2.2.1, that WOPT = O(log( mpU )), so if we could solve this integer program optimally we would be done. However, the...Folydirat, 15:177-191, 1982. [6] I.S. Belov and Ya. N. Stolin. An algorithm in a single path operations scheduling problem. In Mathematical Economics and

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

NASA Technical Reports Server (NTRS)

Parrish, R. V.; Dieudonne, J. E.; Filippas, T. A.

1971-01-01

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

MADS Users' Guide

NASA Technical Reports Server (NTRS)

Moerder, Daniel D.

2014-01-01

MADS (Minimization Assistant for Dynamical Systems) is a trajectory optimization code in which a user-specified performance measure is directly minimized, subject to constraints placed on a low-order discretization of user-supplied plant ordinary differential equations. This document describes the mathematical formulation of the set of trajectory optimization problems for which MADS is suitable, and describes the user interface. Usage examples are provided.

An optimal control approach to the design of moving flight simulators

NASA Technical Reports Server (NTRS)

Sivan, R.; Ish-Shalom, J.; Huang, J.-K.

1982-01-01

An abstract flight simulator design problem is formulated in the form of an optimal control problem, which is solved for the linear-quadratic-Gaussian special case using a mathematical model of the vestibular organs. The optimization criterion used is the mean-square difference between the physiological outputs of the vestibular organs of the pilot in the aircraft and the pilot in the simulator. The dynamical equations are linearized, and the output signal is modeled as a random process with rational power spectral density. The method described yields the optimal structure of the simulator's motion generator, or 'washout filter'. A two-degree-of-freedom flight simulator design, including single output simulations, is presented.

Complex optimization for big computational and experimental neutron datasets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Complex optimization for big computational and experimental neutron datasets

DOE PAGES

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard; ...

2016-11-07

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Analysis of parameter estimation and optimization application of ant colony algorithm in vehicle routing problem

NASA Astrophysics Data System (ADS)

Xu, Quan-Li; Cao, Yu-Wei; Yang, Kun

2018-03-01

Ant Colony Optimization (ACO) is the most widely used artificial intelligence algorithm at present. This study introduced the principle and mathematical model of ACO algorithm in solving Vehicle Routing Problem (VRP), and designed a vehicle routing optimization model based on ACO, then the vehicle routing optimization simulation system was developed by using c ++ programming language, and the sensitivity analyses, estimations and improvements of the three key parameters of ACO were carried out. The results indicated that the ACO algorithm designed in this paper can efficiently solve rational planning and optimization of VRP, and the different values of the key parameters have significant influence on the performance and optimization effects of the algorithm, and the improved algorithm is not easy to locally converge prematurely and has good robustness.

All-Optical Implementation of the Ant Colony Optimization Algorithm

PubMed Central

Hu, Wenchao; Wu, Kan; Shum, Perry Ping; Zheludev, Nikolay I.; Soci, Cesare

2016-01-01

We report all-optical implementation of the optimization algorithm for the famous “ant colony” problem. Ant colonies progressively optimize pathway to food discovered by one of the ants through identifying the discovered route with volatile chemicals (pheromones) secreted on the way back from the food deposit. Mathematically this is an important example of graph optimization problem with dynamically changing parameters. Using an optical network with nonlinear waveguides to represent the graph and a feedback loop, we experimentally show that photons traveling through the network behave like ants that dynamically modify the environment to find the shortest pathway to any chosen point in the graph. This proof-of-principle demonstration illustrates how transient nonlinearity in the optical system can be exploited to tackle complex optimization problems directly, on the hardware level, which may be used for self-routing of optical signals in transparent communication networks and energy flow in photonic systems. PMID:27222098

Hierarchical winner-take-all particle swarm optimization social network for neural model fitting.

PubMed

Coventry, Brandon S; Parthasarathy, Aravindakshan; Sommer, Alexandra L; Bartlett, Edward L

2017-02-01

Particle swarm optimization (PSO) has gained widespread use as a general mathematical programming paradigm and seen use in a wide variety of optimization and machine learning problems. In this work, we introduce a new variant on the PSO social network and apply this method to the inverse problem of input parameter selection from recorded auditory neuron tuning curves. The topology of a PSO social network is a major contributor to optimization success. Here we propose a new social network which draws influence from winner-take-all coding found in visual cortical neurons. We show that the winner-take-all network performs exceptionally well on optimization problems with greater than 5 dimensions and runs at a lower iteration count as compared to other PSO topologies. Finally we show that this variant of PSO is able to recreate auditory frequency tuning curves and modulation transfer functions, making it a potentially useful tool for computational neuroscience models.

Rival framings: A framework for discovering how problem formulation uncertainties shape risk management trade-offs in water resources systems

NASA Astrophysics Data System (ADS)

Quinn, J. D.; Reed, P. M.; Giuliani, M.; Castelletti, A.

2017-08-01

Managing water resources systems requires coordinated operation of system infrastructure to mitigate the impacts of hydrologic extremes while balancing conflicting multisectoral demands. Traditionally, recommended management strategies are derived by optimizing system operations under a single problem framing that is assumed to accurately represent the system objectives, tacitly ignoring the myriad of effects that could arise from simplifications and mathematical assumptions made when formulating the problem. This study illustrates the benefits of a rival framings framework in which analysts instead interrogate multiple competing hypotheses of how complex water management problems should be formulated. Analyzing rival framings helps discover unintended consequences resulting from inherent biases of alternative problem formulations. We illustrate this on the monsoonal Red River basin in Vietnam by optimizing operations of the system's four largest reservoirs under several different multiobjective problem framings. In each rival framing, we specify different quantitative representations of the system's objectives related to hydropower production, agricultural water supply, and flood protection of the capital city of Hanoi. We find that some formulations result in counterintuitive behavior. In particular, policies designed to minimize expected flood damages inadvertently increase the risk of catastrophic flood events in favor of hydropower production, while min-max objectives commonly used in robust optimization provide poor representations of system tradeoffs due to their instability. This study highlights the importance of carefully formulating and evaluating alternative mathematical abstractions of stakeholder objectives describing the multisectoral water demands and risks associated with hydrologic extremes.

Metaheuristic Optimization and its Applications in Earth Sciences

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

A common but challenging task in modelling geophysical and geological processes is to handle massive data and to minimize certain objectives. This can essentially be considered as an optimization problem, and thus many new efficient metaheuristic optimization algorithms can be used. In this paper, we will introduce some modern metaheuristic optimization algorithms such as genetic algorithms, harmony search, firefly algorithm, particle swarm optimization and simulated annealing. We will also discuss how these algorithms can be applied to various applications in earth sciences, including nonlinear least-squares, support vector machine, Kriging, inverse finite element analysis, and data-mining. We will present a few examples to show how different problems can be reformulated as optimization. Finally, we will make some recommendations for choosing various algorithms to suit various problems. References 1) D. H. Wolpert and W. G. Macready, No free lunch theorems for optimization, IEEE Trans. Evolutionary Computation, Vol. 1, 67-82 (1997). 2) X. S. Yang, Nature-Inspired Metaheuristic Algorithms, Luniver Press, (2008). 3) X. S. Yang, Mathematical Modelling for Earth Sciences, Dunedin Academic Press, (2008).

Mixed integer simulation optimization for optimal hydraulic fracturing and production of shale gas fields

NASA Astrophysics Data System (ADS)

Li, J. C.; Gong, B.; Wang, H. G.

2016-08-01

Optimal development of shale gas fields involves designing a most productive fracturing network for hydraulic stimulation processes and operating wells appropriately throughout the production time. A hydraulic fracturing network design-determining well placement, number of fracturing stages, and fracture lengths-is defined by specifying a set of integer ordered blocks to drill wells and create fractures in a discrete shale gas reservoir model. The well control variables such as bottom hole pressures or production rates for well operations are real valued. Shale gas development problems, therefore, can be mathematically formulated with mixed-integer optimization models. A shale gas reservoir simulator is used to evaluate the production performance for a hydraulic fracturing and well control plan. To find the optimal fracturing design and well operation is challenging because the problem is a mixed integer optimization problem and entails computationally expensive reservoir simulation. A dynamic simplex interpolation-based alternate subspace (DSIAS) search method is applied for mixed integer optimization problems associated with shale gas development projects. The optimization performance is demonstrated with the example case of the development of the Barnett Shale field. The optimization results of DSIAS are compared with those of a pattern search algorithm.

Dynamic optimization approach for integrated supplier selection and tracking control of single product inventory system with product discount

NASA Astrophysics Data System (ADS)

Sutrisno; Widowati; Heru Tjahjana, R.

2017-01-01

In this paper, we propose a mathematical model in the form of dynamic/multi-stage optimization to solve an integrated supplier selection problem and tracking control problem of single product inventory system with product discount. The product discount will be stated as a piece-wise linear function. We use dynamic programming to solve this proposed optimization to determine the optimal supplier and the optimal product volume that will be purchased from the optimal supplier for each time period so that the inventory level tracks a reference trajectory given by decision maker with minimal total cost. We give a numerical experiment to evaluate the proposed model. From the result, the optimal supplier was determined for each time period and the inventory level follows the given reference well.

Preliminary Development of an Object-Oriented Optimization Tool

NASA Technical Reports Server (NTRS)

Pak, Chan-gi

2011-01-01

The National Aeronautics and Space Administration Dryden Flight Research Center has developed a FORTRAN-based object-oriented optimization (O3) tool that leverages existing tools and practices and allows easy integration and adoption of new state-of-the-art software. The object-oriented framework can integrate the analysis codes for multiple disciplines, as opposed to relying on one code to perform analysis for all disciplines. Optimization can thus take place within each discipline module, or in a loop between the central executive module and the discipline modules, or both. Six sample optimization problems are presented. The first four sample problems are based on simple mathematical equations; the fifth and sixth problems consider a three-bar truss, which is a classical example in structural synthesis. Instructions for preparing input data for the O3 tool are presented.

An Algorithm for the Mixed Transportation Network Design Problem

PubMed Central

Liu, Xinyu; Chen, Qun

2016-01-01

This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately. PMID:27626803

Stochastic Optimization For Water Resources Allocation

NASA Astrophysics Data System (ADS)

Yamout, G.; Hatfield, K.

2003-12-01

For more than 40 years, water resources allocation problems have been addressed using deterministic mathematical optimization. When data uncertainties exist, these methods could lead to solutions that are sub-optimal or even infeasible. While optimization models have been proposed for water resources decision-making under uncertainty, no attempts have been made to address the uncertainties in water allocation problems in an integrated approach. This paper presents an Integrated Dynamic, Multi-stage, Feedback-controlled, Linear, Stochastic, and Distributed parameter optimization approach to solve a problem of water resources allocation. It attempts to capture (1) the conflict caused by competing objectives, (2) environmental degradation produced by resource consumption, and finally (3) the uncertainty and risk generated by the inherently random nature of state and decision parameters involved in such a problem. A theoretical system is defined throughout its different elements. These elements consisting mainly of water resource components and end-users are described in terms of quantity, quality, and present and future associated risks and uncertainties. Models are identified, modified, and interfaced together to constitute an integrated water allocation optimization framework. This effort is a novel approach to confront the water allocation optimization problem while accounting for uncertainties associated with all its elements; thus resulting in a solution that correctly reflects the physical problem in hand.

Wine and Maths: Mathematical Solutions to Wine-Inspired Problems

ERIC Educational Resources Information Center

Cadeddu, L.; Cauli, A.

2018-01-01

We deal with an application of partial differential equations to the correct definition of a wine cellar. We present some historical details about this problem. We also discuss how to build or renew a wine cellar, creating ideal conditions for the ageing process and improving the quality of wines. Our goal is to calculate the optimal depth…

Scheduling IT Staff at a Bank: A Mathematical Programming Approach

PubMed Central

Labidi, M.; Mrad, M.; Gharbi, A.; Louly, M. A.

2014-01-01

We address a real-world optimization problem: the scheduling of a Bank Information Technologies (IT) staff. This problem can be defined as the process of constructing optimized work schedules for staff. In a general sense, it requires the allocation of suitably qualified staff to specific shifts to meet the demands for services of an organization while observing workplace regulations and attempting to satisfy individual work preferences. A monthly shift schedule is prepared to determine the shift duties of each staff considering shift coverage requirements, seniority-based workload rules, and staff work preferences. Due to the large number of conflicting constraints, a multiobjective programming model has been proposed to automate the schedule generation process. The suggested mathematical model has been implemented using Lingo software. The results indicate that high quality solutions can be obtained within a few seconds compared to the manually prepared schedules. PMID:24772032

Scheduling IT staff at a bank: a mathematical programming approach.

PubMed

Labidi, M; Mrad, M; Gharbi, A; Louly, M A

2014-01-01

We address a real-world optimization problem: the scheduling of a Bank Information Technologies (IT) staff. This problem can be defined as the process of constructing optimized work schedules for staff. In a general sense, it requires the allocation of suitably qualified staff to specific shifts to meet the demands for services of an organization while observing workplace regulations and attempting to satisfy individual work preferences. A monthly shift schedule is prepared to determine the shift duties of each staff considering shift coverage requirements, seniority-based workload rules, and staff work preferences. Due to the large number of conflicting constraints, a multiobjective programming model has been proposed to automate the schedule generation process. The suggested mathematical model has been implemented using Lingo software. The results indicate that high quality solutions can be obtained within a few seconds compared to the manually prepared schedules.

Continued research on selected parameters to minimize community annoyance from airplane noise

NASA Technical Reports Server (NTRS)

Frair, L.

1981-01-01

Results from continued research on selected parameters to minimize community annoyance from airport noise are reported. First, a review of the initial work on this problem is presented. Then the research focus is expanded by considering multiobjective optimization approaches for this problem. A multiobjective optimization algorithm review from the open literature is presented. This is followed by the multiobjective mathematical formulation for the problem of interest. A discussion of the appropriate solution algorithm for the multiobjective formulation is conducted. Alternate formulations and associated solution algorithms are discussed and evaluated for this airport noise problem. Selected solution algorithms that have been implemented are then used to produce computational results for example airports. These computations involved finding the optimal operating scenario for a moderate size airport and a series of sensitivity analyses for a smaller example airport.

A Parallel Biological Optimization Algorithm to Solve the Unbalanced Assignment Problem Based on DNA Molecular Computing.

PubMed

Wang, Zhaocai; Pu, Jun; Cao, Liling; Tan, Jian

2015-10-23

The unbalanced assignment problem (UAP) is to optimally resolve the problem of assigning n jobs to m individuals (m < n), such that minimum cost or maximum profit obtained. It is a vitally important Non-deterministic Polynomial (NP) complete problem in operation management and applied mathematics, having numerous real life applications. In this paper, we present a new parallel DNA algorithm for solving the unbalanced assignment problem using DNA molecular operations. We reasonably design flexible-length DNA strands representing different jobs and individuals, take appropriate steps, and get the solutions of the UAP in the proper length range and O(mn) time. We extend the application of DNA molecular operations and simultaneity to simplify the complexity of the computation.

Risk Analysis for Resource Planning Optimization

NASA Technical Reports Server (NTRS)

Chueng, Kar-Ming

2008-01-01

The main purpose of this paper is to introduce a risk management approach that allows planners to quantify the risk and efficiency tradeoff in the presence of uncertainties, and to make forward-looking choices in the development and execution of the plan. Demonstrate a planning and risk analysis framework that tightly integrates mathematical optimization, empirical simulation, and theoretical analysis techniques to solve complex problems.

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

Distributed Constrained Optimization with Semicoordinate Transformations

NASA Technical Reports Server (NTRS)

Macready, William; Wolpert, David

2006-01-01

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Optimal shielding design for minimum materials cost or mass

DOE PAGES

Woolley, Robert D.

2015-12-02

The mathematical underpinnings of cost optimal radiation shielding designs based on an extension of optimal control theory are presented, a heuristic algorithm to iteratively solve the resulting optimal design equations is suggested, and computational results for a simple test case are discussed. A typical radiation shielding design problem can have infinitely many solutions, all satisfying the problem's specified set of radiation attenuation requirements. Each such design has its own total materials cost. For a design to be optimal, no admissible change in its deployment of shielding materials can result in a lower cost. This applies in particular to very smallmore » changes, which can be restated using the calculus of variations as the Euler-Lagrange equations. Furthermore, the associated Hamiltonian function and application of Pontryagin's theorem lead to conditions for a shield to be optimal.« less

Application of multi-objective optimization to pooled experiments of next generation sequencing for detection of rare mutations.

PubMed

Zilinskas, Julius; Lančinskas, Algirdas; Guarracino, Mario Rosario

2014-01-01

In this paper we propose some mathematical models to plan a Next Generation Sequencing experiment to detect rare mutations in pools of patients. A mathematical optimization problem is formulated for optimal pooling, with respect to minimization of the experiment cost. Then, two different strategies to replicate patients in pools are proposed, which have the advantage to decrease the overall costs. Finally, a multi-objective optimization formulation is proposed, where the trade-off between the probability to detect a mutation and overall costs is taken into account. The proposed solutions are devised in pursuance of the following advantages: (i) the solution guarantees mutations are detectable in the experimental setting, and (ii) the cost of the NGS experiment and its biological validation using Sanger sequencing is minimized. Simulations show replicating pools can decrease overall experimental cost, thus making pooling an interesting option.

A stochastic model for optimizing composite predictors based on gene expression profiles.

PubMed

Ramanathan, Murali

2003-07-01

This project was done to develop a mathematical model for optimizing composite predictors based on gene expression profiles from DNA arrays and proteomics. The problem was amenable to a formulation and solution analogous to the portfolio optimization problem in mathematical finance: it requires the optimization of a quadratic function subject to linear constraints. The performance of the approach was compared to that of neighborhood analysis using a data set containing cDNA array-derived gene expression profiles from 14 multiple sclerosis patients receiving intramuscular inteferon-beta1a. The Markowitz portfolio model predicts that the covariance between genes can be exploited to construct an efficient composite. The model predicts that a composite is not needed for maximizing the mean value of a treatment effect: only a single gene is needed, but the usefulness of the effect measure may be compromised by high variability. The model optimized the composite to yield the highest mean for a given level of variability or the least variability for a given mean level. The choices that meet this optimization criteria lie on a curve of composite mean vs. composite variability plot referred to as the "efficient frontier." When a composite is constructed using the model, it outperforms the composite constructed using the neighborhood analysis method. The Markowitz portfolio model may find potential applications in constructing composite biomarkers and in the pharmacogenomic modeling of treatment effects derived from gene expression endpoints.

Neural networks: What non-linearity to choose

NASA Technical Reports Server (NTRS)

Kreinovich, Vladik YA.; Quintana, Chris

1991-01-01

Neural networks are now one of the most successful learning formalisms. Neurons transform inputs (x(sub 1),...,x(sub n)) into an output f(w(sub 1)x(sub 1) + ... + w(sub n)x(sub n)), where f is a non-linear function and w, are adjustable weights. What f to choose? Usually the logistic function is chosen, but sometimes the use of different functions improves the practical efficiency of the network. The problem of choosing f as a mathematical optimization problem is formulated and solved under different optimality criteria. As a result, a list of functions f that are optimal under these criteria are determined. This list includes both the functions that were empirically proved to be the best for some problems, and some new functions that may be worth trying.

A roadmap for optimal control: the right way to commute.

PubMed

Ross, I Michael

2005-12-01

Optimal control theory is the foundation for many problems in astrodynamics. Typical examples are trajectory design and optimization, relative motion control of distributed space systems and attitude steering. Many such problems in astrodynamics are solved by an alternative route of mathematical analysis and deep physical insight, in part because of the perception that an optimal control framework generates hard problems. Although this is indeed true of the Bellman and Pontryagin frameworks, the covector mapping principle provides a neoclassical approach that renders hard problems easy. That is, although the origins of this philosophy can be traced back to Bernoulli and Euler, it is essentially modern as a result of the strong linkage between approximation theory, set-valued analysis and computing technology. Motivated by the broad success of this approach, mission planners are now conceiving and demanding higher performance from space systems. This has resulted in new set of theoretical and computational problems. Recently, under the leadership of NASA-GRC, several workshops were held to address some of these problems. This paper outlines the theoretical issues stemming from practical problems in astrodynamics. Emphasis is placed on how it pertains to advanced mission design problems.

[Mathematical model of technical equipment of a clinical-diagnostic laboratory].

PubMed

Bukin, S I; Busygin, D V; Tilevich, M E

1990-01-01

The paper is concerned with the problems of technical equipment of standard clinico-diagnostic laboratories (CDL) in this country. The authors suggest a mathematic model that may minimize expenditures for laboratory studies. The model enables the following problems to be solved: to issue scientifically-based recommendations for technical equipment of CDL; to validate the medico-technical requirements for newly devised items; to select the optimum types of uniform items; to define optimal technical decisions at the stage of the design; to determine the lab assistant's labour productivity and the cost of some investigations; to compute the medical laboratory engineering requirement for treatment and prophylactic institutions of this country.

Topology optimization for nonlinear dynamic problems: Considerations for automotive crashworthiness

NASA Astrophysics Data System (ADS)

Kaushik, Anshul; Ramani, Anand

2014-04-01

Crashworthiness of automotive structures is most often engineered after an optimal topology has been arrived at using other design considerations. This study is an attempt to incorporate crashworthiness requirements upfront in the topology synthesis process using a mathematically consistent framework. It proposes the use of equivalent linear systems from the nonlinear dynamic simulation in conjunction with a discrete-material topology optimizer. Velocity and acceleration constraints are consistently incorporated in the optimization set-up. Issues specific to crash problems due to the explicit solution methodology employed, nature of the boundary conditions imposed on the structure, etc. are discussed and possible resolutions are proposed. A demonstration of the methodology on two-dimensional problems that address some of the structural requirements and the types of loading typical of frontal and side impact is provided in order to show that this methodology has the potential for topology synthesis incorporating crashworthiness requirements.

Optimal growth trajectories with finite carrying capacity.

PubMed

Caravelli, F; Sindoni, L; Caccioli, F; Ududec, C

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Sequential quadratic programming-based fast path planning algorithm subject to no-fly zone constraints

NASA Astrophysics Data System (ADS)

Liu, Wei; Ma, Shunjian; Sun, Mingwei; Yi, Haidong; Wang, Zenghui; Chen, Zengqiang

2016-08-01

Path planning plays an important role in aircraft guided systems. Multiple no-fly zones in the flight area make path planning a constrained nonlinear optimization problem. It is necessary to obtain a feasible optimal solution in real time. In this article, the flight path is specified to be composed of alternate line segments and circular arcs, in order to reformulate the problem into a static optimization one in terms of the waypoints. For the commonly used circular and polygonal no-fly zones, geometric conditions are established to determine whether or not the path intersects with them, and these can be readily programmed. Then, the original problem is transformed into a form that can be solved by the sequential quadratic programming method. The solution can be obtained quickly using the Sparse Nonlinear OPTimizer (SNOPT) package. Mathematical simulations are used to verify the effectiveness and rapidity of the proposed algorithm.

Optimal growth trajectories with finite carrying capacity

NASA Astrophysics Data System (ADS)

Caravelli, F.; Sindoni, L.; Caccioli, F.; Ududec, C.

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Coevolutionary Free Lunches

NASA Technical Reports Server (NTRS)

Wolpert, David H.; Macready, William G.

2005-01-01

Recent work on the mathematical foundations of optimization has begun to uncover its rich structure. In particular, the "No Free Lunch" (NFL) theorems state that any two algorithms are equivalent when their performance is averaged across all possible problems. This highlights the need for exploiting problem-specific knowledge to achieve better than random performance. In this paper we present a general framework covering more search scenarios. In addition to the optimization scenarios addressed in the NFL results, this framework covers multi-armed bandit problems and evolution of multiple co-evolving players. As a particular instance of the latter, it covers "self-play" problems. In these problems the set of players work together to produce a champion, who then engages one or more antagonists in a subsequent multi-player game. In contrast to the traditional optimization case where the NFL results hold, we show that in self-play there are free lunches: in coevolution some algorithms have better performance than other algorithms, averaged across all possible problems. We consider the implications of these results to biology where there is no champion.

Methodology and Results of Mathematical Modelling of Complex Technological Processes

NASA Astrophysics Data System (ADS)

Mokrova, Nataliya V.

2018-03-01

The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Universitaet Regensburg, Regensburg, West Germany, April 16-19, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Problems in applied mathematics and mechanics are addressed in reviews and reports. Areas covered are vibration and stability, elastic and plastic mechanics, fluid mechanics, the numerical treatment of differential equations (general theory and finite-element methods in particular), optimization, decision theory, stochastics, actuarial mathematics, applied analysis and mathematical physics, and numerical analysis. Included are major lectures on separated flows, the transition regime of rarefied-gas dynamics, recent results in nonlinear elasticity, fluid-elastic vibration, the new computer arithmetic, and unsteady wave propagation in layered elastic bodies.

Algorithms for Maneuvering Spacecraft Around Small Bodies

NASA Technical Reports Server (NTRS)

Acikmese, A. Bechet; Bayard, David

2006-01-01

A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.

Performance evaluation of coherent Ising machines against classical neural networks

NASA Astrophysics Data System (ADS)

Haribara, Yoshitaka; Ishikawa, Hitoshi; Utsunomiya, Shoko; Aihara, Kazuyuki; Yamamoto, Yoshihisa

2017-12-01

The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators and a field programmable gate array circuit. The similar mathematical models were proposed three decades ago by Hopfield et al in the context of classical neural networks. In this article, we compare the computational performance of both models.

An ant colony optimization heuristic for an integrated production and distribution scheduling problem

NASA Astrophysics Data System (ADS)

Chang, Yung-Chia; Li, Vincent C.; Chiang, Chia-Ju

2014-04-01

Make-to-order or direct-order business models that require close interaction between production and distribution activities have been adopted by many enterprises in order to be competitive in demanding markets. This article considers an integrated production and distribution scheduling problem in which jobs are first processed by one of the unrelated parallel machines and then distributed to corresponding customers by capacitated vehicles without intermediate inventory. The objective is to find a joint production and distribution schedule so that the weighted sum of total weighted job delivery time and the total distribution cost is minimized. This article presents a mathematical model for describing the problem and designs an algorithm using ant colony optimization. Computational experiments illustrate that the algorithm developed is capable of generating near-optimal solutions. The computational results also demonstrate the value of integrating production and distribution in the model for the studied problem.

Manual of phosphoric acid fuel cell power plant optimization model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

An optimized cost and performance model for a phosphoric acid fuel cell power plant system was derived and developed into a modular FORTRAN computer code. Cost, energy, mass, and electrochemical analyses were combined to develop a mathematical model for optimizing the steam to methane ratio in the reformer, hydrogen utilization in the PAFC plates per stack. The nonlinear programming code, COMPUTE, was used to solve this model, in which the method of mixed penalty function combined with Hooke and Jeeves pattern search was chosen to evaluate this specific optimization problem.

Discrete optimal control approach to a four-dimensional guidance problem near terminal areas

NASA Technical Reports Server (NTRS)

Nagarajan, N.

1974-01-01

Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.

Approximation concepts for efficient structural synthesis

NASA Technical Reports Server (NTRS)

Schmit, L. A., Jr.; Miura, H.

1976-01-01

It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.

A Parallel Biological Optimization Algorithm to Solve the Unbalanced Assignment Problem Based on DNA Molecular Computing

PubMed Central

Wang, Zhaocai; Pu, Jun; Cao, Liling; Tan, Jian

2015-01-01

The unbalanced assignment problem (UAP) is to optimally resolve the problem of assigning n jobs to m individuals (m < n), such that minimum cost or maximum profit obtained. It is a vitally important Non-deterministic Polynomial (NP) complete problem in operation management and applied mathematics, having numerous real life applications. In this paper, we present a new parallel DNA algorithm for solving the unbalanced assignment problem using DNA molecular operations. We reasonably design flexible-length DNA strands representing different jobs and individuals, take appropriate steps, and get the solutions of the UAP in the proper length range and O(mn) time. We extend the application of DNA molecular operations and simultaneity to simplify the complexity of the computation. PMID:26512650

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1987-01-01

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Design for Warehouse with Product Flow Type Allocation using Linear Programming: A Case Study in a Textile Industry

NASA Astrophysics Data System (ADS)

Khannan, M. S. A.; Nafisah, L.; Palupi, D. L.

2018-03-01

Sari Warna Co. Ltd, a company engaged in the textile industry, is experiencing problems in the allocation and placement of goods in the warehouse. During this time the company has not implemented the product flow type allocation and product placement to the respective products resulting in a high total material handling cost. Therefore, this study aimed to determine the allocation and placement of goods in the warehouse corresponding to product flow type with minimal total material handling cost. This research is a quantitative research based on the theory of storage and warehouse that uses a mathematical model of optimization problem solving using mathematical optimization model approach belongs to Heragu (2005), aided by software LINGO 11.0 in the calculation of the optimization model. Results obtained from this study is the proportion of the distribution for each functional area is the area of cross-docking at 0.0734, the reserve area at 0.1894, and the forward area at 0.7372. The allocation of product flow type 1 is 5 products, the product flow type 2 is 9 products, the product flow type 3 is 2 products, and the product flow type 4 is 6 products. The optimal total material handling cost by using this mathematical model equal to Rp43.079.510 while it is equal to Rp 49.869.728 by using the company’s existing method. It saves Rp6.790.218 for the total material handling cost. Thus, all of the products can be allocated in accordance with the product flow type with minimal total material handling cost.

Development and Evaluation of a Casualty Evacuation Model for a European Conflict.

DTIC Science & Technology

1987-08-18

W Applications and Computations," lIE Transactions, 16, 2, 127-134 "- ( 1984 ).-,’’ ,., 3. Ali, A. I., Helgason, R. V., Kennington, J. L., and kall ...Part II," Mathematical Programming, 1, 6-25 ( 1971 ). 38. Held, M., Wolfe, P., and Crowder, H., "Validation of Subgradient Optimization", Mathematical...California, Los Angeles, CA, ( 1971 ). Si 66. Swoveland, C., "A Two-Stage Decomposition Algorithm for a Generalized Muticommodity Flow Problem," INFOR

Hierarchical Winner-Take-All Particle Swarm Optimization Social Network for Neural Model Fitting

PubMed Central

Coventry, Brandon S.; Parthasarathy, Aravindakshan; Sommer, Alexandra L.; Bartlett, Edward L.

2016-01-01

Particle swarm optimization (PSO) has gained widespread use as a general mathematical programming paradigm and seen use in a wide variety of optimization and machine learning problems. In this work, we introduce a new variant on the PSO social network and apply this method to the inverse problem of input parameter selection from recorded auditory neuron tuning curves. The topology of a PSO social network is a major contributor to optimization success. Here we propose a new social network which draws influence from winner-take-all coding found in visual cortical neurons. We show that the winner-take-all network performs exceptionally well on optimization problems with greater than 5 dimensions and runs at a lower iteration count as compared to other PSO topologies. Finally we show that this variant of PSO is able to recreate auditory frequency tuning curves and modulation transfer functions, making it a potentially useful tool for computational neuroscience models. PMID:27726048

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

NASA Technical Reports Server (NTRS)

Cheung, Kar-Ming; Lee, Charles H.

2012-01-01

We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.

The effect of brain based learning with contextual approach viewed from adversity quotient

NASA Astrophysics Data System (ADS)

Kartikaningtyas, V.; Kusmayadi, T. A.; Riyadi, R.

2018-05-01

The aim of this research was to find out the effect of Brain Based Learning (BBL) with contextual approach viewed from adversity quotient (AQ) on mathematics achievement. BBL-contextual is the model to optimize the brain in the new concept learning and real life problem solving by making the good environment. Adversity Quotient is the ability to response and faces the problems. In addition, it is also about how to turn the difficulties into chances. This AQ classified into quitters, campers, and climbers. The research method used in this research was quasi experiment by using 2x3 factorial designs. The sample was chosen by using stratified cluster random sampling. The instruments were test and questionnaire for the data of AQ. The results showed that (1) BBL-contextual is better than direct learning on mathematics achievement, (2) there is no significant difference between each types of AQ on mathematics achievement, and (3) there is no interaction between learning model and AQ on mathematics achievement.

Resource allocation for error resilient video coding over AWGN using optimization approach.

PubMed

An, Cheolhong; Nguyen, Truong Q

2008-12-01

The number of slices for error resilient video coding is jointly optimized with 802.11a-like media access control and the physical layers with automatic repeat request and rate compatible punctured convolutional code over additive white gaussian noise channel as well as channel times allocation for time division multiple access. For error resilient video coding, the relation between the number of slices and coding efficiency is analyzed and formulated as a mathematical model. It is applied for the joint optimization problem, and the problem is solved by a convex optimization method such as the primal-dual decomposition method. We compare the performance of a video communication system which uses the optimal number of slices with one that codes a picture as one slice. From numerical examples, end-to-end distortion of utility functions can be significantly reduced with the optimal slices of a picture especially at low signal-to-noise ratio.

Genetic learning in rule-based and neural systems

NASA Technical Reports Server (NTRS)

Smith, Robert E.

1993-01-01

The design of neural networks and fuzzy systems can involve complex, nonlinear, and ill-conditioned optimization problems. Often, traditional optimization schemes are inadequate or inapplicable for such tasks. Genetic Algorithms (GA's) are a class of optimization procedures whose mechanics are based on those of natural genetics. Mathematical arguments show how GAs bring substantial computational leverage to search problems, without requiring the mathematical characteristics often necessary for traditional optimization schemes (e.g., modality, continuity, availability of derivative information, etc.). GA's have proven effective in a variety of search tasks that arise in neural networks and fuzzy systems. This presentation begins by introducing the mechanism and theoretical underpinnings of GA's. GA's are then related to a class of rule-based machine learning systems called learning classifier systems (LCS's). An LCS implements a low-level production-system that uses a GA as its primary rule discovery mechanism. This presentation illustrates how, despite its rule-based framework, an LCS can be thought of as a competitive neural network. Neural network simulator code for an LCS is presented. In this context, the GA is doing more than optimizing and objective function. It is searching for an ecology of hidden nodes with limited connectivity. The GA attempts to evolve this ecology such that effective neural network performance results. The GA is particularly well adapted to this task, given its naturally-inspired basis. The LCS/neural network analogy extends itself to other, more traditional neural networks. Conclusions to the presentation discuss the implications of using GA's in ecological search problems that arise in neural and fuzzy systems.

Application of an Evolution Strategy in Planetary Ephemeris Optimization

NASA Astrophysics Data System (ADS)

Mai, E.

2016-12-01

Classical planetary ephemeris construction comprises three major steps, which are performed iteratively: simultaneous numerical integration of coupled equations of motion of a multi-body system (propagator step), reduction of thousands of observations (reduction step), and optimization of various selected model parameters (adjustment step). This traditional approach is challenged by ongoing refinements in force modeling, e.g. inclusion of much more significant minor bodies, an ever-growing number of planetary observations, e.g. vast amount of spacecraft tracking data, etc. To master the high computational burden and in order to circumvent the need for inversion of huge normal equation matrices, we propose an alternative ephemeris construction method. The main idea is to solve the overall optimization problem by a straightforward direct evaluation of the whole set of mathematical formulas involved, rather than to solve it as an inverse problem with all its tacit mathematical assumptions and numerical difficulties. We replace the usual gradient search by a stochastic search, namely an evolution strategy, the latter of which is also perfect for the exploitation of parallel computing capabilities. Furthermore, this new approach enables multi-criteria optimization and time-varying optima. This issue will become important in future once ephemeris construction is just one part of even larger optimization problems, e.g. the combined and consistent determination of the physical state (orbit, size, shape, rotation, gravity,…) of celestial bodies (planets, satellites, asteroids, or comets), and if one seeks near real-time solutions. Here we outline the general idea and discuss first results. As an example, we present a simultaneous optimization of high-correlated asteroidal ring model parameters (total mass and heliocentric radius), based on simulations.

Investigating the enhanced Best Performance Algorithm for Annual Crop Planning problem based on economic factors.

PubMed

Adewumi, Aderemi Oluyinka; Chetty, Sivashan

2017-01-01

The Annual Crop Planning (ACP) problem was a recently introduced problem in the literature. This study further expounds on this problem by presenting a new mathematical formulation, which is based on market economic factors. To determine solutions, a new local search metaheuristic algorithm is investigated which is called the enhanced Best Performance Algorithm (eBPA). eBPA's results are compared against two well-known local search metaheuristic algorithms; these include Tabu Search and Simulated Annealing. The results show the potential of the eBPA for continuous optimization problems.

[Optimal solution and analysis of muscular force during standing balance].

PubMed

Wang, Hongrui; Zheng, Hui; Liu, Kun

2015-02-01

The present study was aimed at the optimal solution of the main muscular force distribution in the lower extremity during standing balance of human. The movement musculoskeletal system of lower extremity was simplified to a physical model with 3 joints and 9 muscles. Then on the basis of this model, an optimum mathematical model was built up to solve the problem of redundant muscle forces. Particle swarm optimization (PSO) algorithm is used to calculate the single objective and multi-objective problem respectively. The numerical results indicated that the multi-objective optimization could be more reasonable to obtain the distribution and variation of the 9 muscular forces. Finally, the coordination of each muscle group during maintaining standing balance under the passive movement was qualitatively analyzed using the simulation results obtained.

Scheduler Design Criteria: Requirements and Considerations

NASA Technical Reports Server (NTRS)

Lee, Hanbong

2016-01-01

This presentation covers fundamental requirements and considerations for developing schedulers in airport operations. We first introduce performance and functional requirements for airport surface schedulers. Among various optimization problems in airport operations, we focus on airport surface scheduling problem, including runway and taxiway operations. We then describe a basic methodology for airport surface scheduling such as node-link network model and scheduling algorithms previously developed. Next, we explain how to design a mathematical formulation in more details, which consists of objectives, decision variables, and constraints. Lastly, we review other considerations, including optimization tools, computational performance, and performance metrics for evaluation.

A stochastic optimization model under modeling uncertainty and parameter certainty for groundwater remediation design--part I. Model development.

PubMed

He, L; Huang, G H; Lu, H W

2010-04-15

Solving groundwater remediation optimization problems based on proxy simulators can usually yield optimal solutions differing from the "true" ones of the problem. This study presents a new stochastic optimization model under modeling uncertainty and parameter certainty (SOMUM) and the associated solution method for simultaneously addressing modeling uncertainty associated with simulator residuals and optimizing groundwater remediation processes. This is a new attempt different from the previous modeling efforts. The previous ones focused on addressing uncertainty in physical parameters (i.e. soil porosity) while this one aims to deal with uncertainty in mathematical simulator (arising from model residuals). Compared to the existing modeling approaches (i.e. only parameter uncertainty is considered), the model has the advantages of providing mean-variance analysis for contaminant concentrations, mitigating the effects of modeling uncertainties on optimal remediation strategies, offering confidence level of optimal remediation strategies to system designers, and reducing computational cost in optimization processes. 2009 Elsevier B.V. All rights reserved.

Mathematical modelling and simulation of a tennis racket.

PubMed

Brannigan, M; Adali, S

1981-01-01

By constructing a mathematical model, we consider the dynamics of a tennis racket hit by a ball. Using this model, known experimental results can be simulated on the computer, and it becomes possible to make a parametric study of a racket. Such a simulation is essential in the study of two important problems related to tennis: computation of the resulting forces and moments transferred to the hand should assist understanding of the medical problem 'tennis elbow'; secondly, simulation will enable a study to be made of the relationships between the impact time, tension in the strings, forces transmitted to the rim and return velocity of the ball, all of which can lead to the optimal design of rackets.

Computer Language For Optimization Of Design

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.; Lucas, Stephen H.

1991-01-01

SOL is computer language geared to solution of design problems. Includes mathematical modeling and logical capabilities of computer language like FORTRAN; also includes additional power of nonlinear mathematical programming methods at language level. SOL compiler takes SOL-language statements and generates equivalent FORTRAN code and system calls. Provides syntactic and semantic checking for recovery from errors and provides detailed reports containing cross-references to show where each variable used. Implemented on VAX/VMS computer systems. Requires VAX FORTRAN compiler to produce executable program.

A Mathematical Formulation of the SCOLE Control Problem. Part 2: Optimal Compensator Design

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1988-01-01

The study initiated in Part 1 of this report is concluded and optimal feedback control (compensator) design for stability augmentation is considered, following the mathematical formulation developed in Part 1. Co-located (rate) sensors and (force and moment) actuators are assumed, and allowing for both sensor and actuator noise, stabilization is formulated as a stochastic regulator problem. Specializing the general theory developed by the author, a complete, closed form solution (believed to be new with this report) is obtained, taking advantage of the fact that the inherent structural damping is light. In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation formulation. The results thus hold for any multibody system so long as the basic model is linear.

Multimodal optimization by using hybrid of artificial bee colony algorithm and BFGS algorithm

NASA Astrophysics Data System (ADS)

Anam, S.

2017-10-01

Optimization has become one of the important fields in Mathematics. Many problems in engineering and science can be formulated into optimization problems. They maybe have many local optima. The optimization problem with many local optima, known as multimodal optimization problem, is how to find the global solution. Several metaheuristic methods have been proposed to solve multimodal optimization problems such as Particle Swarm Optimization (PSO), Genetics Algorithm (GA), Artificial Bee Colony (ABC) algorithm, etc. The performance of the ABC algorithm is better than or similar to those of other population-based algorithms with the advantage of employing a fewer control parameters. The ABC algorithm also has the advantages of strong robustness, fast convergence and high flexibility. However, it has the disadvantages premature convergence in the later search period. The accuracy of the optimal value cannot meet the requirements sometimes. Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is a good iterative method for finding a local optimum. Compared with other local optimization methods, the BFGS algorithm is better. Based on the advantages of the ABC algorithm and the BFGS algorithm, this paper proposes a hybrid of the artificial bee colony algorithm and the BFGS algorithm to solve the multimodal optimization problem. The first step is that the ABC algorithm is run to find a point. In the second step is that the point obtained by the first step is used as an initial point of BFGS algorithm. The results show that the hybrid method can overcome from the basic ABC algorithm problems for almost all test function. However, if the shape of function is flat, the proposed method cannot work well.

A Matrix-Free Algorithm for Multidisciplinary Design Optimization

NASA Astrophysics Data System (ADS)

Lambe, Andrew Borean

Multidisciplinary design optimization (MDO) is an approach to engineering design that exploits the coupling between components or knowledge disciplines in a complex system to improve the final product. In aircraft design, MDO methods can be used to simultaneously design the outer shape of the aircraft and the internal structure, taking into account the complex interaction between the aerodynamic forces and the structural flexibility. Efficient strategies are needed to solve such design optimization problems and guarantee convergence to an optimal design. This work begins with a comprehensive review of MDO problem formulations and solution algorithms. First, a fundamental MDO problem formulation is defined from which other formulations may be obtained through simple transformations. Using these fundamental problem formulations, decomposition methods from the literature are reviewed and classified. All MDO methods are presented in a unified mathematical notation to facilitate greater understanding. In addition, a novel set of diagrams, called extended design structure matrices, are used to simultaneously visualize both data communication and process flow between the many software components of each method. For aerostructural design optimization, modern decomposition-based MDO methods cannot efficiently handle the tight coupling between the aerodynamic and structural states. This fact motivates the exploration of methods that can reduce the computational cost. A particular structure in the direct and adjoint methods for gradient computation motivates the idea of a matrix-free optimization method. A simple matrix-free optimizer is developed based on the augmented Lagrangian algorithm. This new matrix-free optimizer is tested on two structural optimization problems and one aerostructural optimization problem. The results indicate that the matrix-free optimizer is able to efficiently solve structural and multidisciplinary design problems with thousands of variables and constraints. On the aerostructural test problem formulated with thousands of constraints, the matrix-free optimizer is estimated to reduce the total computational time by up to 90% compared to conventional optimizers.

A Matrix-Free Algorithm for Multidisciplinary Design Optimization

NASA Astrophysics Data System (ADS)

Lambe, Andrew Borean

Multidisciplinary design optimization (MDO) is an approach to engineering design that exploits the coupling between components or knowledge disciplines in a complex system to improve the final product. In aircraft design, MDO methods can be used to simultaneously design the outer shape of the aircraft and the internal structure, taking into account the complex interaction between the aerodynamic forces and the structural flexibility. Efficient strategies are needed to solve such design optimization problems and guarantee convergence to an optimal design. This work begins with a comprehensive review of MDO problem formulations and solution algorithms. First, a fundamental MDO problem formulation is defined from which other formulations may be obtained through simple transformations. Using these fundamental problem formulations, decomposition methods from the literature are reviewed and classified. All MDO methods are presented in a unified mathematical notation to facilitate greater understanding. In addition, a novel set of diagrams, called extended design structure matrices, are used to simultaneously visualize both data communication and process flow between the many software components of each method. For aerostructural design optimization, modern decomposition-based MDO methods cannot efficiently handle the tight coupling between the aerodynamic and structural states. This fact motivates the exploration of methods that can reduce the computational cost. A particular structure in the direct and adjoint methods for gradient computation. motivates the idea of a matrix-free optimization method. A simple matrix-free optimizer is developed based on the augmented Lagrangian algorithm. This new matrix-free optimizer is tested on two structural optimization problems and one aerostructural optimization problem. The results indicate that the matrix-free optimizer is able to efficiently solve structural and multidisciplinary design problems with thousands of variables and constraints. On the aerostructural test problem formulated with thousands of constraints, the matrix-free optimizer is estimated to reduce the total computational time by up to 90% compared to conventional optimizers.

A mathematical framework for the selection of an optimal set of peptides for epitope-based vaccines.

PubMed

Toussaint, Nora C; Dönnes, Pierre; Kohlbacher, Oliver

2008-12-01

Epitope-based vaccines (EVs) have a wide range of applications: from therapeutic to prophylactic approaches, from infectious diseases to cancer. The development of an EV is based on the knowledge of target-specific antigens from which immunogenic peptides, so-called epitopes, are derived. Such epitopes form the key components of the EV. Due to regulatory, economic, and practical concerns the number of epitopes that can be included in an EV is limited. Furthermore, as the major histocompatibility complex (MHC) binding these epitopes is highly polymorphic, every patient possesses a set of MHC class I and class II molecules of differing specificities. A peptide combination effective for one person can thus be completely ineffective for another. This renders the optimal selection of these epitopes an important and interesting optimization problem. In this work we present a mathematical framework based on integer linear programming (ILP) that allows the formulation of various flavors of the vaccine design problem and the efficient identification of optimal sets of epitopes. Out of a user-defined set of predicted or experimentally determined epitopes, the framework selects the set with the maximum likelihood of eliciting a broad and potent immune response. Our ILP approach allows an elegant and flexible formulation of numerous variants of the EV design problem. In order to demonstrate this, we show how common immunological requirements for a good EV (e.g., coverage of epitopes from each antigen, coverage of all MHC alleles in a set, or avoidance of epitopes with high mutation rates) can be translated into constraints or modifications of the objective function within the ILP framework. An implementation of the algorithm outperforms a simple greedy strategy as well as a previously suggested evolutionary algorithm and has runtimes on the order of seconds for typical problem sizes.

Optimal parameter estimation with a fixed rate of abstention

NASA Astrophysics Data System (ADS)

Gendra, B.; Ronco-Bonvehi, E.; Calsamiglia, J.; Muñoz-Tapia, R.; Bagan, E.

2013-07-01

The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or abstention. It is shown that such schemes enable drastic improvements, up to the extent of attaining the Heisenberg limit in some cases, and the required amount of abstention is quantified. A general mathematical framework to deal with the asymptotic limit of many qubits or large angular momentum is introduced and used to obtain analytical results for all the relevant cases under consideration. Parameter estimation with abstention is also formulated as a semidefinite programming problem, for which very efficient numerical optimization techniques exist.

Mathematical model of the metal mould surface temperature optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mlynek, Jaroslav, E-mail: jaroslav.mlynek@tul.cz; Knobloch, Roman, E-mail: roman.knobloch@tul.cz; Srb, Radek, E-mail: radek.srb@tul.cz

2015-11-30

The article is focused on the problem of generating a uniform temperature field on the inner surface of shell metal moulds. Such moulds are used e.g. in the automotive industry for artificial leather production. To produce artificial leather with uniform surface structure and colour shade the temperature on the inner surface of the mould has to be as homogeneous as possible. The heating of the mould is realized by infrared heaters located above the outer mould surface. The conceived mathematical model allows us to optimize the locations of infrared heaters over the mould, so that approximately uniform heat radiation intensitymore » is generated. A version of differential evolution algorithm programmed in Matlab development environment was created by the authors for the optimization process. For temperate calculations software system ANSYS was used. A practical example of optimization of heaters locations and calculation of the temperature of the mould is included at the end of the article.« less

Method of optimization onboard communication network

NASA Astrophysics Data System (ADS)

Platoshin, G. A.; Selvesuk, N. I.; Semenov, M. E.; Novikov, V. M.

2018-02-01

In this article the optimization levels of onboard communication network (OCN) are proposed. We defined the basic parameters, which are necessary for the evaluation and comparison of modern OCN, we identified also a set of initial data for possible modeling of the OCN. We also proposed a mathematical technique for implementing the OCN optimization procedure. This technique is based on the principles and ideas of binary programming. It is shown that the binary programming technique allows to obtain an inherently optimal solution for the avionics tasks. An example of the proposed approach implementation to the problem of devices assignment in OCN is considered.

Constrained Optimization Methods in Health Services Research-An Introduction: Report 1 of the ISPOR Optimization Methods Emerging Good Practices Task Force.

PubMed

Crown, William; Buyukkaramikli, Nasuh; Thokala, Praveen; Morton, Alec; Sir, Mustafa Y; Marshall, Deborah A; Tosh, Jon; Padula, William V; Ijzerman, Maarten J; Wong, Peter K; Pasupathy, Kalyan S

2017-03-01

Providing health services with the greatest possible value to patients and society given the constraints imposed by patient characteristics, health care system characteristics, budgets, and so forth relies heavily on the design of structures and processes. Such problems are complex and require a rigorous and systematic approach to identify the best solution. Constrained optimization is a set of methods designed to identify efficiently and systematically the best solution (the optimal solution) to a problem characterized by a number of potential solutions in the presence of identified constraints. This report identifies 1) key concepts and the main steps in building an optimization model; 2) the types of problems for which optimal solutions can be determined in real-world health applications; and 3) the appropriate optimization methods for these problems. We first present a simple graphical model based on the treatment of "regular" and "severe" patients, which maximizes the overall health benefit subject to time and budget constraints. We then relate it back to how optimization is relevant in health services research for addressing present day challenges. We also explain how these mathematical optimization methods relate to simulation methods, to standard health economic analysis techniques, and to the emergent fields of analytics and machine learning. Copyright © 2017 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

Hybrid surrogate-model-based multi-fidelity efficient global optimization applied to helicopter blade design

NASA Astrophysics Data System (ADS)

Ariyarit, Atthaphon; Sugiura, Masahiko; Tanabe, Yasutada; Kanazaki, Masahiro

2018-06-01

A multi-fidelity optimization technique by an efficient global optimization process using a hybrid surrogate model is investigated for solving real-world design problems. The model constructs the local deviation using the kriging method and the global model using a radial basis function. The expected improvement is computed to decide additional samples that can improve the model. The approach was first investigated by solving mathematical test problems. The results were compared with optimization results from an ordinary kriging method and a co-kriging method, and the proposed method produced the best solution. The proposed method was also applied to aerodynamic design optimization of helicopter blades to obtain the maximum blade efficiency. The optimal shape obtained by the proposed method achieved performance almost equivalent to that obtained using the high-fidelity, evaluation-based single-fidelity optimization. Comparing all three methods, the proposed method required the lowest total number of high-fidelity evaluation runs to obtain a converged solution.

On a numerical solving of random generated hexamatrix games

NASA Astrophysics Data System (ADS)

Orlov, Andrei; Strekalovskiy, Alexander

2016-10-01

In this paper, we develop a global search method for finding a Nash equilibrium in a hexamatrix game (polymatrix game of three players). The method, on the one hand, is based on the equivalence theorem of the problem of finding a Nash equilibrium in the game and a special mathematical optimization problem, and, on the other hand, on the usage of Global Search Theory for solving the latter problem. The efficiency of this approach is demonstrated by the results of computational testing.

Students’ difficulties in probabilistic problem-solving

NASA Astrophysics Data System (ADS)

Arum, D. P.; Kusmayadi, T. A.; Pramudya, I.

2018-03-01

There are many errors can be identified when students solving mathematics problems, particularly in solving the probabilistic problem. This present study aims to investigate students’ difficulties in solving the probabilistic problem. It focuses on analyzing and describing students errors during solving the problem. This research used the qualitative method with case study strategy. The subjects in this research involve ten students of 9th grade that were selected by purposive sampling. Data in this research involve students’ probabilistic problem-solving result and recorded interview regarding students’ difficulties in solving the problem. Those data were analyzed descriptively using Miles and Huberman steps. The results show that students have difficulties in solving the probabilistic problem and can be divided into three categories. First difficulties relate to students’ difficulties in understanding the probabilistic problem. Second, students’ difficulties in choosing and using appropriate strategies for solving the problem. Third, students’ difficulties with the computational process in solving the problem. Based on the result seems that students still have difficulties in solving the probabilistic problem. It means that students have not able to use their knowledge and ability for responding probabilistic problem yet. Therefore, it is important for mathematics teachers to plan probabilistic learning which could optimize students probabilistic thinking ability.

I-STEM Ed Exemplar: Implementation of the PIRPOSAL Model

ERIC Educational Resources Information Center

Wells, John G.

2016-01-01

The opening pages of the first PIRPOSAL (Problem Identification, Ideation, Research, Potential Solutions, Optimization, Solution Evaluation, Alterations, and Learned Outcomes) article make the case that the instructional models currently used in K-12 Science, Technology, Engineering, and Mathematics (STEM) Education fall short of conveying their…

Price schedules coordination for electricity pool markets

NASA Astrophysics Data System (ADS)

Legbedji, Alexis Motto

2002-04-01

We consider the optimal coordination of a class of mathematical programs with equilibrium constraints, which is formally interpreted as a resource-allocation problem. Many decomposition techniques were proposed to circumvent the difficulty of solving large systems with limited computer resources. The considerable improvement in computer architecture has allowed the solution of large-scale problems with increasing speed. Consequently, interest in decomposition techniques has waned. Nonetheless, there is an important class of applications for which decomposition techniques will still be relevant, among others, distributed systems---the Internet, perhaps, being the most conspicuous example---and competitive economic systems. Conceptually, a competitive economic system is a collection of agents that have similar or different objectives while sharing the same system resources. In theory, constructing a large-scale mathematical program and solving it centrally, using currently available computing power can optimize such systems of agents. In practice, however, because agents are self-interested and not willing to reveal some sensitive corporate data, one cannot solve these kinds of coordination problems by simply maximizing the sum of agent's objective functions with respect to their constraints. An iterative price decomposition or Lagrangian dual method is considered best suited because it can operate with limited information. A price-directed strategy, however, can only work successfully when coordinating or equilibrium prices exist, which is not generally the case when a weak duality is unavoidable. Showing when such prices exist and how to compute them is the main subject of this thesis. Among our results, we show that, if the Lagrangian function of a primal program is additively separable, price schedules coordination may be attained. The prices are Lagrange multipliers, and are also the decision variables of a dual program. In addition, we propose a new form of augmented or nonlinear pricing, which is an example of the use of penalty functions in mathematical programming. Applications are drawn from mathematical programming problems of the form arising in electric power system scheduling under competition.

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

Discrete homotopy analysis for optimal trading execution with nonlinear transient market impact

NASA Astrophysics Data System (ADS)

Curato, Gianbiagio; Gatheral, Jim; Lillo, Fabrizio

2016-10-01

Optimal execution in financial markets is the problem of how to trade a large quantity of shares incrementally in time in order to minimize the expected cost. In this paper, we study the problem of the optimal execution in the presence of nonlinear transient market impact. Mathematically such problem is equivalent to solve a strongly nonlinear integral equation, which in our model is a weakly singular Urysohn equation of the first kind. We propose an approach based on Homotopy Analysis Method (HAM), whereby a well behaved initial trading strategy is continuously deformed to lower the expected execution cost. Specifically, we propose a discrete version of the HAM, i.e. the DHAM approach, in order to use the method when the integrals to compute have no closed form solution. We find that the optimal solution is front loaded for concave instantaneous impact even when the investor is risk neutral. More important we find that the expected cost of the DHAM strategy is significantly smaller than the cost of conventional strategies.

Comparison of optimal design methods in inverse problems

NASA Astrophysics Data System (ADS)

Banks, H. T.; Holm, K.; Kappel, F.

2011-07-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).

A problem of optimal control and observation for distributed homogeneous multi-agent system

NASA Astrophysics Data System (ADS)

Kruglikov, Sergey V.

2017-12-01

The paper considers the implementation of a algorithm for controlling a distributed complex of several mobile multi-robots. The concept of a unified information space of the controlling system is applied. The presented information and mathematical models of participants and obstacles, as real agents, and goals and scenarios, as virtual agents, create the base forming the algorithmic and software background for computer decision support system. The controlling scheme assumes the indirect management of the robotic team on the basis of optimal control and observation problem predicting intellectual behavior in a dynamic, hostile environment. A basic content problem is a compound cargo transportation by a group of participants in the case of a distributed control scheme in the terrain with multiple obstacles.

A Study on a Centralized Under-Voltage Load Shedding Scheme Considering the Load Characteristics

NASA Astrophysics Data System (ADS)

Deng, Jiyu; Liu, Junyong

Under-voltage load shedding is an important measure for maintaining voltage stability.Aiming at the optimal load shedding problem considering the load characteristics,firstly,the traditional under-voltage load shedding scheme based on a static load model may cause the analysis inaccurate is pointed out on the equivalent Thevenin circuit.Then,the dynamic voltage stability margin indicator is derived through local measurement.The derived indicator can reflect the voltage change of the key area in a myopia linear way.Dimensions of the optimal problem will be greatly simplified using this indicator.In the end,mathematical model of the centralized load shedding scheme is built with the indicator considering load characteristics.HSPPSO is introduced to slove the optimal problem.Simulation results on IEEE-39 system show that the proposed scheme display a good adaptability in solving the under-voltage load shedding considering dynamic load characteristics.

A quantile-based scenario analysis approach to biomass supply chain optimization under uncertainty

DOE PAGES

Zamar, David S.; Gopaluni, Bhushan; Sokhansanj, Shahab; ...

2016-11-21

Supply chain optimization for biomass-based power plants is an important research area due to greater emphasis on renewable power energy sources. Biomass supply chain design and operational planning models are often formulated and studied using deterministic mathematical models. While these models are beneficial for making decisions, their applicability to real world problems may be limited because they do not capture all the complexities in the supply chain, including uncertainties in the parameters. This study develops a statistically robust quantile-based approach for stochastic optimization under uncertainty, which builds upon scenario analysis. We apply and evaluate the performance of our approach tomore » address the problem of analyzing competing biomass supply chains subject to stochastic demand and supply. Finally, the proposed approach was found to outperform alternative methods in terms of computational efficiency and ability to meet the stochastic problem requirements.« less

A quantile-based scenario analysis approach to biomass supply chain optimization under uncertainty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zamar, David S.; Gopaluni, Bhushan; Sokhansanj, Shahab

Supply chain optimization for biomass-based power plants is an important research area due to greater emphasis on renewable power energy sources. Biomass supply chain design and operational planning models are often formulated and studied using deterministic mathematical models. While these models are beneficial for making decisions, their applicability to real world problems may be limited because they do not capture all the complexities in the supply chain, including uncertainties in the parameters. This study develops a statistically robust quantile-based approach for stochastic optimization under uncertainty, which builds upon scenario analysis. We apply and evaluate the performance of our approach tomore » address the problem of analyzing competing biomass supply chains subject to stochastic demand and supply. Finally, the proposed approach was found to outperform alternative methods in terms of computational efficiency and ability to meet the stochastic problem requirements.« less

An Optimization Code for Nonlinear Transient Problems of a Large Scale Multidisciplinary Mathematical Model

NASA Astrophysics Data System (ADS)

Takasaki, Koichi

This paper presents a program for the multidisciplinary optimization and identification problem of the nonlinear model of large aerospace vehicle structures. The program constructs the global matrix of the dynamic system in the time direction by the p-version finite element method (pFEM), and the basic matrix for each pFEM node in the time direction is described by a sparse matrix similarly to the static finite element problem. The algorithm used by the program does not require the Hessian matrix of the objective function and so has low memory requirements. It also has a relatively low computational cost, and is suited to parallel computation. The program was integrated as a solver module of the multidisciplinary analysis system CUMuLOUS (Computational Utility for Multidisciplinary Large scale Optimization of Undense System) which is under development by the Aerospace Research and Development Directorate (ARD) of the Japan Aerospace Exploration Agency (JAXA).

Mathematical simulation and optimization of cutting mode in turning of workpieces made of nickel-based heat-resistant alloy

NASA Astrophysics Data System (ADS)

Bogoljubova, M. N.; Afonasov, A. I.; Kozlov, B. N.; Shavdurov, D. E.

2018-05-01

A predictive simulation technique of optimal cutting modes in the turning of workpieces made of nickel-based heat-resistant alloys, different from the well-known ones, is proposed. The impact of various factors on the cutting process with the purpose of determining optimal parameters of machining in concordance with certain effectiveness criteria is analyzed in the paper. A mathematical model of optimization, algorithms and computer programmes, visual graphical forms reflecting dependences of the effectiveness criteria – productivity, net cost, and tool life on parameters of the technological process - have been worked out. A nonlinear model for multidimensional functions, “solution of the equation with multiple unknowns”, “a coordinate descent method” and heuristic algorithms are accepted to solve the problem of optimization of cutting mode parameters. Research shows that in machining of workpieces made from heat-resistant alloy AISI N07263, the highest possible productivity will be achieved with the following parameters: cutting speed v = 22.1 m/min., feed rate s=0.26 mm/rev; tool life T = 18 min.; net cost – 2.45 per hour.

Uncertainty reasoning in expert systems

NASA Technical Reports Server (NTRS)

Kreinovich, Vladik

1993-01-01

Intelligent control is a very successful way to transform the expert's knowledge of the type 'if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible' into an actual control. To apply this transformation, one must choose appropriate methods for reasoning with uncertainty, i.e., one must: (1) choose the representation for words like 'small', 'big'; (2) choose operations corresponding to 'and' and 'or'; (3) choose a method that transforms the resulting uncertain control recommendations into a precise control strategy. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From a mathematical viewpoint these choice problems correspond to non-linear optimization and are therefore extremely difficult. In this project, a new mathematical formalism (based on group theory) is developed that allows us to solve the problem of optimal choice and thus: (1) explain why the existing choices are really the best (in some situations); (2) explain a rather mysterious fact that fuzzy control (i.e., control based on the experts' knowledge) is often better than the control by these same experts; and (3) give choice recommendations for the cases when traditional choices do not work.

Mixed Integer Programming and Heuristic Scheduling for Space Communication

NASA Technical Reports Server (NTRS)

Lee, Charles H.; Cheung, Kar-Ming

2013-01-01

Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.

The Applied Mathematics for Power Systems (AMPS)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chertkov, Michael

2012-07-24

Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxesmore » for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.« less

Investigating the enhanced Best Performance Algorithm for Annual Crop Planning problem based on economic factors

PubMed Central

2017-01-01

The Annual Crop Planning (ACP) problem was a recently introduced problem in the literature. This study further expounds on this problem by presenting a new mathematical formulation, which is based on market economic factors. To determine solutions, a new local search metaheuristic algorithm is investigated which is called the enhanced Best Performance Algorithm (eBPA). eBPA’s results are compared against two well-known local search metaheuristic algorithms; these include Tabu Search and Simulated Annealing. The results show the potential of the eBPA for continuous optimization problems. PMID:28792495

Influence of Problem-Based Learning Model of Learning to the Mathematical Communication Ability of Students of Grade XI IPA SMAN 14 Padang

NASA Astrophysics Data System (ADS)

Nisa, I. M.

2018-04-01

The ability of mathematical communication is one of the goals of learning mathematics expected to be mastered by students. However, reality in the field found that the ability of mathematical communication the students of grade XI IPA SMA Negeri 14 Padang have not developed optimally. This is evident from the low test results of communication skills mathematically done. One of the factors that causes this happens is learning that has not been fully able to facilitate students to develop mathematical communication skills well. By therefore, to improve students' mathematical communication skills required a model in the learning activities. One of the models learning that can be used is Problem Based learning model Learning (PBL). The purpose of this study is to see whether the ability the students' mathematical communication using the PBL model better than the students' mathematical communication skills of the learning using conventional learning in Class XI IPA SMAN 14 Padang. This research type is quasi experiment with design Randomized Group Only Design. Population in this research that is student of class XI IPA SMAN 14 Padang with sample class XI IPA 3 and class XI IPA 4. Data retrieval is done by using communication skill test mathematically shaped essay. To test the hypothesis used U-Mann test Whitney. Based on the results of data analysis, it can be concluded that the ability mathematical communication of students whose learning apply more PBL model better than the students' mathematical communication skills of their learning apply conventional learning in class XI IPA SMA 14 Padang at α = 0.05. This indicates that the PBL learning model effect on students' mathematical communication ability.

Design optimization of steel frames using an enhanced firefly algorithm

NASA Astrophysics Data System (ADS)

Carbas, Serdar

2016-12-01

Mathematical modelling of real-world-sized steel frames under the Load and Resistance Factor Design-American Institute of Steel Construction (LRFD-AISC) steel design code provisions, where the steel profiles for the members are selected from a table of steel sections, turns out to be a discrete nonlinear programming problem. Finding the optimum design of such design optimization problems using classical optimization techniques is difficult. Metaheuristic algorithms provide an alternative way of solving such problems. The firefly algorithm (FFA) belongs to the swarm intelligence group of metaheuristics. The standard FFA has the drawback of being caught up in local optima in large-sized steel frame design problems. This study attempts to enhance the performance of the FFA by suggesting two new expressions for the attractiveness and randomness parameters of the algorithm. Two real-world-sized design examples are designed by the enhanced FFA and its performance is compared with standard FFA as well as with particle swarm and cuckoo search algorithms.

A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty

NASA Astrophysics Data System (ADS)

Tian, Wenli; Cao, Chengxuan

2017-03-01

A generalized interval fuzzy mixed integer programming model is proposed for the multimodal freight transportation problem under uncertainty, in which the optimal mode of transport and the optimal amount of each type of freight transported through each path need to be decided. For practical purposes, three mathematical methods, i.e. the interval ranking method, fuzzy linear programming method and linear weighted summation method, are applied to obtain equivalents of constraints and parameters, and then a fuzzy expected value model is presented. A heuristic algorithm based on a greedy criterion and the linear relaxation algorithm are designed to solve the model.

Mathematical logic as a mean of solving the problems of power supply for buildings and constructions

NASA Astrophysics Data System (ADS)

Pryadko, Igor; Nozdrina, Ekaterina; Boltaevsky, Andrey

2017-10-01

The article analyzes the questions of application of mathematical logic in engineering design associated with machinery and construction. The aim of the work is to study the logical working-out of Russian electrical engineer V.I. Shestakov. These elaborations are considered in connection with the problem of analysis and synthesis of relay contact circuits of the degenerate (A) class which the scientist solved. The article proposes to use Shestakov’s elaborations for optimization of buildings and constructions of modern high-tech. In the second part of the article the events are actualized in association with the development of problems of application of mathematical logic in the analysis and synthesis of electric circuits, relay and bridging. The arguments in favor of the priority of the authorship of the elaborations of Russian electrical engineer V. I. Shestakov, K. Shannon - one of the founders of computer science, and Japanese engineer A. Nakashima are discussed. The issue of contradiction between V. I. Shestakov and representatives of the school of M. A. Gavrilov is touched on.

Construction Method of Analytical Solutions to the Mathematical Physics Boundary Problems for Non-Canonical Domains

NASA Astrophysics Data System (ADS)

Mobarakeh, Pouyan Shakeri; Grinchenko, Victor T.

2015-06-01

The majority of practical cases of acoustics problems requires solving the boundary problems in non-canonical domains. Therefore construction of analytical solutions of mathematical physics boundary problems for non-canonical domains is both lucrative from the academic viewpoint, and very instrumental for elaboration of efficient algorithms of quantitative estimation of the field characteristics under study. One of the main solving ideologies for such problems is based on the superposition method that allows one to analyze a wide class of specific problems with domains which can be constructed as the union of canonically-shaped subdomains. It is also assumed that an analytical solution (or quasi-solution) can be constructed for each subdomain in one form or another. However, this case implies some difficulties in the construction of calculation algorithms, insofar as the boundary conditions are incompletely defined in the intervals, where the functions appearing in the general solution are orthogonal to each other. We discuss several typical examples of problems with such difficulties, we study their nature and identify the optimal methods to overcome them.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

PubMed Central

2011-01-01

Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520

Do Dogs Know Bifurcations?

ERIC Educational Resources Information Center

Minton, Roland; Pennings, Timothy J.

2007-01-01

When a dog (in this case, Tim Pennings' dog Elvis) is in the water and a ball is thrown downshore, it must choose to swim directly to the ball or first swim to shore. The mathematical analysis of this problem leads to the computation of bifurcation points at which the optimal strategy changes.

Valuing hydrological alteration in Multi-Objective reservoir management

NASA Astrophysics Data System (ADS)

Bizzi, S.; Pianosi, F.; Soncini-Sessa, R.

2012-04-01

Water management through dams and reservoirs is worldwide necessary to support key human-related activities ranging from hydropower production to water allocation for agricultural production, and flood risk mitigation. Advances in multi-objectives (MO) optimization techniques and ever growing computing power make it possible to design reservoir operating policies that represent Pareto-optimal tradeoffs between the multiple interests analysed. These progresses if on one hand are likely to enhance performances of commonly targeted objectives (such as hydropower production or water supply), on the other risk to strongly penalize all the interests not directly (i.e. mathematically) optimized within the MO algorithm. Alteration of hydrological regime, although is a well established cause of ecological degradation and its evaluation and rehabilitation are commonly required by recent legislation (as the Water Framework Directive in Europe), is rarely embedded as an objective in MO planning of optimal releases from reservoirs. Moreover, even when it is explicitly considered, the criteria adopted for its evaluation are doubted and not commonly trusted, undermining the possibility of real implementation of environmentally friendly policies. The main challenges in defining and assessing hydrological alterations are: how to define a reference state (referencing); how to define criteria upon which to build mathematical indicators of alteration (measuring); and finally how to aggregate the indicators in a single evaluation index that can be embedded in a MO optimization problem (valuing). This paper aims to address these issues by: i) discussing benefits and constrains of different approaches to referencing, measuring and valuing hydrological alteration; ii) testing two alternative indices of hydrological alteration in the context of MO problems, one based on the established framework of Indices of Hydrological Alteration (IHA, Richter et al., 1996), and a novel satisfying the mathematical properties required by widely used optimization methods based on dynamic programming; iii) discussing the ranking provided by the proposed indices for a case study in Italy where different operating policies were designed using a MO algorithm, taking into account hydropower production, irrigation supply and flood mitigation and imposing different type of minimum environmental flow; iv) providing a framework to effectively include hydrological alteration within MO problem of reservoir management. Richter, B.D., Baumgartner, J.V., Powell, J., Braun, D.P., 1996, A Method for Assessing Hydrologic Alteration within Ecosystems, Conservation Biology, 10(4), 1163-1174.

Quadratic Optimization in the Problems of Active Control of Sound

NASA Technical Reports Server (NTRS)

Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

H∞ robust fault-tolerant controller design for an autonomous underwater vehicle's navigation control system

NASA Astrophysics Data System (ADS)

Cheng, Xiang-Qin; Qu, Jing-Yuan; Yan, Zhe-Ping; Bian, Xin-Qian

2010-03-01

In order to improve the security and reliability for autonomous underwater vehicle (AUV) navigation, an H∞ robust fault-tolerant controller was designed after analyzing variations in state-feedback gain. Operating conditions and the design method were then analyzed so that the control problem could be expressed as a mathematical optimization problem. This permitted the use of linear matrix inequalities (LMI) to solve for the H∞ controller for the system. When considering different actuator failures, these conditions were then also mathematically expressed, allowing the H∞ robust controller to solve for these events and thus be fault-tolerant. Finally, simulation results showed that the H∞ robust fault-tolerant controller could provide precise AUV navigation control with strong robustness.

Optimization of structures undergoing harmonic or stochastic excitation. Ph.D. Thesis; [atmospheric turbulence and white noise

NASA Technical Reports Server (NTRS)

Johnson, E. H.

1975-01-01

The optimal design was investigated of simple structures subjected to dynamic loads, with constraints on the structures' responses. Optimal designs were examined for one dimensional structures excited by harmonically oscillating loads, similar structures excited by white noise, and a wing in the presence of continuous atmospheric turbulence. The first has constraints on the maximum allowable stress while the last two place bounds on the probability of failure of the structure. Approximations were made to replace the time parameter with a frequency parameter. For the first problem, this involved the steady state response, and in the remaining cases, power spectral techniques were employed to find the root mean square values of the responses. Optimal solutions were found by using computer algorithms which combined finite elements methods with optimization techniques based on mathematical programming. It was found that the inertial loads for these dynamic problems result in optimal structures that are radically different from those obtained for structures loaded statically by forces of comparable magnitude.

Improved multi-objective ant colony optimization algorithm and its application in complex reasoning

NASA Astrophysics Data System (ADS)

Wang, Xinqing; Zhao, Yang; Wang, Dong; Zhu, Huijie; Zhang, Qing

2013-09-01

The problem of fault reasoning has aroused great concern in scientific and engineering fields. However, fault investigation and reasoning of complex system is not a simple reasoning decision-making problem. It has become a typical multi-constraint and multi-objective reticulate optimization decision-making problem under many influencing factors and constraints. So far, little research has been carried out in this field. This paper transforms the fault reasoning problem of complex system into a paths-searching problem starting from known symptoms to fault causes. Three optimization objectives are considered simultaneously: maximum probability of average fault, maximum average importance, and minimum average complexity of test. Under the constraints of both known symptoms and the causal relationship among different components, a multi-objective optimization mathematical model is set up, taking minimizing cost of fault reasoning as the target function. Since the problem is non-deterministic polynomial-hard(NP-hard), a modified multi-objective ant colony algorithm is proposed, in which a reachability matrix is set up to constrain the feasible search nodes of the ants and a new pseudo-random-proportional rule and a pheromone adjustment mechinism are constructed to balance conflicts between the optimization objectives. At last, a Pareto optimal set is acquired. Evaluation functions based on validity and tendency of reasoning paths are defined to optimize noninferior set, through which the final fault causes can be identified according to decision-making demands, thus realize fault reasoning of the multi-constraint and multi-objective complex system. Reasoning results demonstrate that the improved multi-objective ant colony optimization(IMACO) can realize reasoning and locating fault positions precisely by solving the multi-objective fault diagnosis model, which provides a new method to solve the problem of multi-constraint and multi-objective fault diagnosis and reasoning of complex system.

Optimal policies of non-cross-resistant chemotherapy on Goldie and Coldman's cancer model.

PubMed

Chen, Jeng-Huei; Kuo, Ya-Hui; Luh, Hsing Paul

2013-10-01

Mathematical models can be used to study the chemotherapy on tumor cells. Especially, in 1979, Goldie and Coldman proposed the first mathematical model to relate the drug sensitivity of tumors to their mutation rates. Many scientists have since referred to this pioneering work because of its simplicity and elegance. Its original idea has also been extended and further investigated in massive follow-up studies of cancer modeling and optimal treatment. Goldie and Coldman, together with Guaduskas, later used their model to explain why an alternating non-cross-resistant chemotherapy is optimal with a simulation approach. Subsequently in 1983, Goldie and Coldman proposed an extended stochastic based model and provided a rigorous mathematical proof to their earlier simulation work when the extended model is approximated by its quasi-approximation. However, Goldie and Coldman's analytic study of optimal treatments majorly focused on a process with symmetrical parameter settings, and presented few theoretical results for asymmetrical settings. In this paper, we recast and restate Goldie, Coldman, and Guaduskas' model as a multi-stage optimization problem. Under an asymmetrical assumption, the conditions under which a treatment policy can be optimal are derived. The proposed framework enables us to consider some optimal policies on the model analytically. In addition, Goldie, Coldman and Guaduskas' work with symmetrical settings can be treated as a special case of our framework. Based on the derived conditions, this study provides an alternative proof to Goldie and Coldman's work. In addition to the theoretical derivation, numerical results are included to justify the correctness of our work. Copyright © 2013 Elsevier Inc. All rights reserved.

A Particle Swarm Optimization Algorithm for Optimal Operating Parameters of VMI Systems in a Two-Echelon Supply Chain

NASA Astrophysics Data System (ADS)

Sue-Ann, Goh; Ponnambalam, S. G.

This paper focuses on the operational issues of a Two-echelon Single-Vendor-Multiple-Buyers Supply chain (TSVMBSC) under vendor managed inventory (VMI) mode of operation. To determine the optimal sales quantity for each buyer in TSVMBC, a mathematical model is formulated. Based on the optimal sales quantity can be obtained and the optimal sales price that will determine the optimal channel profit and contract price between the vendor and buyer. All this parameters depends upon the understanding of the revenue sharing between the vendor and buyers. A Particle Swarm Optimization (PSO) is proposed for this problem. Solutions obtained from PSO is compared with the best known results reported in literature.

The Role of Hellinger Processes in Mathematical Finance

NASA Astrophysics Data System (ADS)

Choulli, T.; Hurd, T. R.

2001-09-01

This paper illustrates the natural role that Hellinger processes can play in solving problems from ¯nance. We propose an extension of the concept of Hellinger process applicable to entropy distance and f-divergence distances, where f is a convex logarithmic function or a convex power function with general order q, 0 6= q < 1. These concepts lead to a new approach to Merton's optimal portfolio problem and its dual in general L¶evy markets.

Applications of Sharp Interface Method for Flow Dynamics, Scattering and Control Problems

DTIC Science & Technology

2012-07-30

Reynolds number, Advances in Applied Mathematics and Mechanics, to appear. 17. K. Ito and K. Kunisch, Optimal Control of Parabolic Variational ...provides more precise and detailed sensitivity of the solution and describes the dynamical change due to the variation in the Reynolds number. The immersed... Inequalities , Journal de Math. Pures et Appl, 93 (2010), no. 4, 329-360. 18. K. Ito and K. Kunisch, Semi-smooth Newton Methods for Time-Optimal Control for a

Stochastic search in structural optimization - Genetic algorithms and simulated annealing

NASA Technical Reports Server (NTRS)

Hajela, Prabhat

1993-01-01

An account is given of illustrative applications of genetic algorithms and simulated annealing methods in structural optimization. The advantages of such stochastic search methods over traditional mathematical programming strategies are emphasized; it is noted that these methods offer a significantly higher probability of locating the global optimum in a multimodal design space. Both genetic-search and simulated annealing can be effectively used in problems with a mix of continuous, discrete, and integer design variables.

A multi-objective programming model for assessment the GHG emissions in MSW management

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mavrotas, George, E-mail: mavrotas@chemeng.ntua.gr; Skoulaxinou, Sotiria; Gakis, Nikos

2013-09-15

Highlights: • The multi-objective multi-period optimization model. • The solution approach for the generation of the Pareto front with mathematical programming. • The very detailed description of the model (decision variables, parameters, equations). • The use of IPCC 2006 guidelines for landfill emissions (first order decay model) in the mathematical programming formulation. - Abstract: In this study a multi-objective mathematical programming model is developed for taking into account GHG emissions for Municipal Solid Waste (MSW) management. Mathematical programming models are often used for structure, design and operational optimization of various systems (energy, supply chain, processes, etc.). The last twenty yearsmore » they are used all the more often in Municipal Solid Waste (MSW) management in order to provide optimal solutions with the cost objective being the usual driver of the optimization. In our work we consider the GHG emissions as an additional criterion, aiming at a multi-objective approach. The Pareto front (Cost vs. GHG emissions) of the system is generated using an appropriate multi-objective method. This information is essential to the decision maker because he can explore the trade-offs in the Pareto curve and select his most preferred among the Pareto optimal solutions. In the present work a detailed multi-objective, multi-period mathematical programming model is developed in order to describe the waste management problem. Apart from the bi-objective approach, the major innovations of the model are (1) the detailed modeling considering 34 materials and 42 technologies, (2) the detailed calculation of the energy content of the various streams based on the detailed material balances, and (3) the incorporation of the IPCC guidelines for the CH{sub 4} generated in the landfills (first order decay model). The equations of the model are described in full detail. Finally, the whole approach is illustrated with a case study referring to the application of the model in a Greek region.« less

Inference of Vohradský's Models of Genetic Networks by Solving Two-Dimensional Function Optimization Problems

PubMed Central

Kimura, Shuhei; Sato, Masanao; Okada-Hatakeyama, Mariko

2013-01-01

The inference of a genetic network is a problem in which mutual interactions among genes are inferred from time-series of gene expression levels. While a number of models have been proposed to describe genetic networks, this study focuses on a mathematical model proposed by Vohradský. Because of its advantageous features, several researchers have proposed the inference methods based on Vohradský's model. When trying to analyze large-scale networks consisting of dozens of genes, however, these methods must solve high-dimensional non-linear function optimization problems. In order to resolve the difficulty of estimating the parameters of the Vohradský's model, this study proposes a new method that defines the problem as several two-dimensional function optimization problems. Through numerical experiments on artificial genetic network inference problems, we showed that, although the computation time of the proposed method is not the shortest, the method has the ability to estimate parameters of Vohradský's models more effectively with sufficiently short computation times. This study then applied the proposed method to an actual inference problem of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. PMID:24386175

Mathematical Analysis and Optimization of Infiltration Processes

NASA Technical Reports Server (NTRS)

Chang, H.-C.; Gottlieb, D.; Marion, M.; Sheldon, B. W.

1997-01-01

A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, alpha and beta. The optimization problem associated with minimizing the infiltration time is also considered. Allowing alpha and beta to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where alpha and beta are treated as constants.

Sensitivity computation of the ell1 minimization problem and its application to dictionary design of ill-posed problems

NASA Astrophysics Data System (ADS)

Horesh, L.; Haber, E.

2009-09-01

The ell1 minimization problem has been studied extensively in the past few years. Recently, there has been a growing interest in its application for inverse problems. Most studies have concentrated in devising ways for sparse representation of a solution using a given prototype dictionary. Very few studies have addressed the more challenging problem of optimal dictionary construction, and even these were primarily devoted to the simplistic sparse coding application. In this paper, sensitivity analysis of the inverse solution with respect to the dictionary is presented. This analysis reveals some of the salient features and intrinsic difficulties which are associated with the dictionary design problem. Equipped with these insights, we propose an optimization strategy that alleviates these hurdles while utilizing the derived sensitivity relations for the design of a locally optimal dictionary. Our optimality criterion is based on local minimization of the Bayesian risk, given a set of training models. We present a mathematical formulation and an algorithmic framework to achieve this goal. The proposed framework offers the design of dictionaries for inverse problems that incorporate non-trivial, non-injective observation operators, where the data and the recovered parameters may reside in different spaces. We test our algorithm and show that it yields improved dictionaries for a diverse set of inverse problems in geophysics and medical imaging.

Optimization strategies based on sequential quadratic programming applied for a fermentation process for butanol production.

PubMed

Pinto Mariano, Adriano; Bastos Borba Costa, Caliane; de Franceschi de Angelis, Dejanira; Maugeri Filho, Francisco; Pires Atala, Daniel Ibraim; Wolf Maciel, Maria Regina; Maciel Filho, Rubens

2009-11-01

In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.

An opinion formation based binary optimization approach for feature selection

NASA Astrophysics Data System (ADS)

Hamedmoghadam, Homayoun; Jalili, Mahdi; Yu, Xinghuo

2018-02-01

This paper proposed a novel optimization method based on opinion formation in complex network systems. The proposed optimization technique mimics human-human interaction mechanism based on a mathematical model derived from social sciences. Our method encodes a subset of selected features to the opinion of an artificial agent and simulates the opinion formation process among a population of agents to solve the feature selection problem. The agents interact using an underlying interaction network structure and get into consensus in their opinions, while finding better solutions to the problem. A number of mechanisms are employed to avoid getting trapped in local minima. We compare the performance of the proposed method with a number of classical population-based optimization methods and a state-of-the-art opinion formation based method. Our experiments on a number of high dimensional datasets reveal outperformance of the proposed algorithm over others.

Modeling an integrated hospital management planning problem using integer optimization approach

NASA Astrophysics Data System (ADS)

Sitepu, Suryati; Mawengkang, Herman; Irvan

2017-09-01

Hospital is a very important institution to provide health care for people. It is not surprising that nowadays the people’s demands for hospital is increasing. However, due to the rising cost of healthcare services, hospitals need to consider efficiencies in order to overcome these two problems. This paper deals with an integrated strategy of staff capacity management and bed allocation planning to tackle these problems. Mathematically, the strategy can be modeled as an integer linear programming problem. We solve the model using a direct neighborhood search approach, based on the notion of superbasic variables.

Early stage response problem for post-disaster incidents

NASA Astrophysics Data System (ADS)

Kim, Sungwoo; Shin, Youngchul; Lee, Gyu M.; Moon, Ilkyeong

2018-07-01

Research on evacuation plans for reducing damages and casualties has been conducted to advise defenders against threats. However, despite the attention given to the research in the past, emergency response management, designed to neutralize hazards, has been undermined since planners frequently fail to apprehend the complexities and contexts of the emergency situation. Therefore, this study considers a response problem with unique characteristics for the duration of the emergency. An early stage response problem is identified to find the optimal routing and scheduling plan for responders to prevent further hazards. Due to the complexity of the proposed mathematical model, two algorithms are developed. Data from a high-rise building, called Central City in Seoul, Korea, are used to evaluate the algorithms. Results show that the proposed algorithms can procure near-optimal solutions within a reasonable time.

Optimal mistuning for enhanced aeroelastic stability of transonic fans

NASA Technical Reports Server (NTRS)

Hall, K. C.; Crawley, E. F.

1983-01-01

An inverse design procedure was developed for the design of a mistuned rotor. The design requirements are that the stability margin of the eigenvalues of the aeroelastic system be greater than or equal to some minimum stability margin, and that the mass added to each blade be positive. The objective was to achieve these requirements with a minimal amount of mistuning. Hence, the problem was posed as a constrained optimization problem. The constrained minimization problem was solved by the technique of mathematical programming via augmented Lagrangians. The unconstrained minimization phase of this technique was solved by the variable metric method. The bladed disk was modelled as being composed of a rigid disk mounted on a rigid shaft. Each of the blades were modelled with a single tosional degree of freedom.

Solving the infeasible trust-region problem using approximations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Renaud, John E.; Perez, Victor M.; Eldred, Michael Scott

2004-07-01

The use of optimization in engineering design has fueled the development of algorithms for specific engineering needs. When the simulations are expensive to evaluate or the outputs present some noise, the direct use of nonlinear optimizers is not advisable, since the optimization process will be expensive and may result in premature convergence. The use of approximations for both cases is an alternative investigated by many researchers including the authors. When approximations are present, a model management is required for proper convergence of the algorithm. In nonlinear programming, the use of trust-regions for globalization of a local algorithm has been provenmore » effective. The same approach has been used to manage the local move limits in sequential approximate optimization frameworks as in Alexandrov et al., Giunta and Eldred, Perez et al. , Rodriguez et al., etc. The experience in the mathematical community has shown that more effective algorithms can be obtained by the specific inclusion of the constraints (SQP type of algorithms) rather than by using a penalty function as in the augmented Lagrangian formulation. The presence of explicit constraints in the local problem bounded by the trust region, however, may have no feasible solution. In order to remedy this problem the mathematical community has developed different versions of a composite steps approach. This approach consists of a normal step to reduce the amount of constraint violation and a tangential step to minimize the objective function maintaining the level of constraint violation attained at the normal step. Two of the authors have developed a different approach for a sequential approximate optimization framework using homotopy ideas to relax the constraints. This algorithm called interior-point trust-region sequential approximate optimization (IPTRSAO) presents some similarities to the two normal-tangential steps algorithms. In this paper, a description of the similarities is presented and an expansion of the two steps algorithm is presented for the case of approximations.« less

Active stability augmentation of large space structures: A stochastic control problem

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1987-01-01

A problem in SCOLE is that of slewing an offset antenna on a long flexible beam-like truss attached to the space shuttle, with rather stringent pointing accuracy requirements. The relevant methodology aspects in robust feedback-control design for stability augmentation of the beam using on-board sensors is examined. It is framed as a stochastic control problem, boundary control of a distributed parameter system described by partial differential equations. While the framework is mathematical, the emphasis is still on an engineering solution. An abstract mathematical formulation is developed as a nonlinear wave equation in a Hilbert space. That the system is controllable is shown and a feedback control law that is robust in the sense that it does not require quantitative knowledge of system parameters is developed. The stochastic control problem that arises in instrumenting this law using appropriate sensors is treated. Using an engineering first approximation which is valid for small damping, formulas for optimal choice of the control gain are developed.

Analytical sizing methods for behind-the-meter battery storage

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Di; Kintner-Meyer, Michael; Yang, Tao

In behind-the-meter application, battery storage system (BSS) is utilized to reduce a commercial or industrial customer’s payment for electricity use, including energy charge and demand charge. The potential value of BSS in payment reduction and the most economic size can be determined by formulating and solving standard mathematical programming problems. In this method, users input system information such as load profiles, energy/demand charge rates, and battery characteristics to construct a standard programming problem that typically involve a large number of constraints and decision variables. Such a large scale programming problem is then solved by optimization solvers to obtain numerical solutions.more » Such a method cannot directly link the obtained optimal battery sizes to input parameters and requires case-by-case analysis. In this paper, we present an objective quantitative analysis of costs and benefits of customer-side energy storage, and thereby identify key factors that affect battery sizing. Based on the analysis, we then develop simple but effective guidelines that can be used to determine the most cost-effective battery size or guide utility rate design for stimulating energy storage development. The proposed analytical sizing methods are innovative, and offer engineering insights on how the optimal battery size varies with system characteristics. We illustrate the proposed methods using practical building load profile and utility rate. The obtained results are compared with the ones using mathematical programming based methods for validation.« less

Optimal Iterative Task Scheduling for Parallel Simulations.

DTIC Science & Technology

1991-03-01

State University, Pullman, Washington. November 1976. 19. Grimaldi , Ralph P . Discrete and Combinatorial Mathematics. Addison-Wesley. June 1989. 20...2 4.8.1 Problem Description .. .. .. .. ... .. ... .... 4-25 4.8.2 Reasons for Level-Strate- p Failure. .. .. .. .. ... 4-26...f- I CA A* overview................................ C-1 C .2 Sample A* r......................... .... C-I C-3 Evaluation P

Rugby and Mathematics: A Surprising Link among Geometry, the Conics, and Calculus.

ERIC Educational Resources Information Center

Jones, Troy; Jackson, Steven

2001-01-01

Describes a rugby problem designed to help students understand the maximum-minimum situation. Presents a series of explorations that locate an optimal place for kicking the ball to maximize the angle at the goalposts. Uses interactive geometry software to construct a model of the situation. Includes a sample student activity. (KHR)

Genetic Networks and Anticipation of Gene Expression Patterns

NASA Astrophysics Data System (ADS)

Gebert, J.; Lätsch, M.; Pickl, S. W.; Radde, N.; Weber, G.-W.; Wünschiers, R.

2004-08-01

An interesting problem for computational biology is the analysis of time-series expression data. Here, the application of modern methods from dynamical systems, optimization theory, numerical algorithms and the utilization of implicit discrete information lead to a deeper understanding. In [1], we suggested to represent the behavior of time-series gene expression patterns by a system of ordinary differential equations, which we analytically and algorithmically investigated under the parametrical aspect of stability or instability. Our algorithm strongly exploited combinatorial information. In this paper, we deepen, extend and exemplify this study from the viewpoint of underlying mathematical modelling. This modelling consists in evaluating DNA-microarray measurements as the basis of anticipatory prediction, in the choice of a smooth model given by differential equations, in an approach of the right-hand side with parametric matrices, and in a discrete approximation which is a least squares optimization problem. We give a mathematical and biological discussion, and pay attention to the special case of a linear system, where the matrices do not depend on the state of expressions. Here, we present first numerical examples.

A Heuristic Bioinspired for 8-Piece Puzzle

NASA Astrophysics Data System (ADS)

Machado, M. O.; Fabres, P. A.; Melo, J. C. L.

2017-10-01

This paper investigates a mathematical model inspired by nature, and presents a Meta-Heuristic that is efficient in improving the performance of an informed search, when using strategy A * using a General Search Tree as data structure. The work hypothesis suggests that the investigated meta-heuristic is optimal in nature and may be promising in minimizing the computational resources required by an objective-based agent in solving high computational complexity problems (n-part puzzle) as well as In the optimization of objective functions for local search agents. The objective of this work is to describe qualitatively the characteristics and properties of the mathematical model investigated, correlating the main concepts of the A * function with the significant variables of the metaheuristic used. The article shows that the amount of memory required to perform this search when using the metaheuristic is less than using the A * function to evaluate the nodes of a general search tree for the eight-piece puzzle. It is concluded that the meta-heuristic must be parameterized according to the chosen heuristic and the level of the tree that contains the possible solutions to the chosen problem.

A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry

NASA Astrophysics Data System (ADS)

Rusyda, N. A.; Kusnandi, K.; Suhendra, S.

2017-09-01

The purpose of this research is to analyze of mathematical problem solving ability of students in one of secondary school on geometry. This research was conducted by using quantitative approach with descriptive method. Population in this research was all students of that school and the sample was twenty five students that was chosen by purposive sampling technique. Data of mathematical problem solving were collected through essay test. The results showed the percentage of achievement of mathematical problem solving indicators of students were: 1) solve closed mathematical problems with context in math was 50%; 2) solve the closed mathematical problems with the context beyond mathematics was 24%; 3) solving open mathematical problems with contexts in mathematics was 35%; And 4) solving open mathematical problems with contexts outside mathematics was 44%. Based on the percentage, it can be concluded that the level of achievement of mathematical problem solving ability in geometry still low. This is because students are not used to solving problems that measure mathematical problem solving ability, weaknesses remember previous knowledge, and lack of problem solving framework. So the students’ ability of mathematical problems solving need to be improved with implement appropriate learning strategy.

Replica Approach for Minimal Investment Risk with Cost

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-06-01

In the present work, the optimal portfolio minimizing the investment risk with cost is discussed analytically, where an objective function is constructed in terms of two negative aspects of investment, the risk and cost. We note the mathematical similarity between the Hamiltonian in the mean-variance model and the Hamiltonians in the Hopfield model and the Sherrington-Kirkpatrick model, show that we can analyze this portfolio optimization problem by using replica analysis, and derive the minimal investment risk with cost and the investment concentration of the optimal portfolio. Furthermore, we validate our proposed method through numerical simulations.

Optimal control of first order distributed systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Johnson, T. L.

1972-01-01

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Domain decomposition method for the Baltic Sea based on theory of adjoint equation and inverse problem.

NASA Astrophysics Data System (ADS)

Lezina, Natalya; Agoshkov, Valery

2017-04-01

Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).

Automated parameterization of intermolecular pair potentials using global optimization techniques

NASA Astrophysics Data System (ADS)

Krämer, Andreas; Hülsmann, Marco; Köddermann, Thorsten; Reith, Dirk

2014-12-01

In this work, different global optimization techniques are assessed for the automated development of molecular force fields, as used in molecular dynamics and Monte Carlo simulations. The quest of finding suitable force field parameters is treated as a mathematical minimization problem. Intricate problem characteristics such as extremely costly and even abortive simulations, noisy simulation results, and especially multiple local minima naturally lead to the use of sophisticated global optimization algorithms. Five diverse algorithms (pure random search, recursive random search, CMA-ES, differential evolution, and taboo search) are compared to our own tailor-made solution named CoSMoS. CoSMoS is an automated workflow. It models the parameters' influence on the simulation observables to detect a globally optimal set of parameters. It is shown how and why this approach is superior to other algorithms. Applied to suitable test functions and simulations for phosgene, CoSMoS effectively reduces the number of required simulations and real time for the optimization task.

Integrated configurable equipment selection and line balancing for mass production with serial-parallel machining systems

NASA Astrophysics Data System (ADS)

Battaïa, Olga; Dolgui, Alexandre; Guschinsky, Nikolai; Levin, Genrikh

2014-10-01

Solving equipment selection and line balancing problems together allows better line configurations to be reached and avoids local optimal solutions. This article considers jointly these two decision problems for mass production lines with serial-parallel workplaces. This study was motivated by the design of production lines based on machines with rotary or mobile tables. Nevertheless, the results are more general and can be applied to assembly and production lines with similar structures. The designers' objectives and the constraints are studied in order to suggest a relevant mathematical model and an efficient optimization approach to solve it. A real case study is used to validate the model and the developed approach.

A Multi-Objective Optimization Technique to Model the Pareto Front of Organic Dielectric Polymers

NASA Astrophysics Data System (ADS)

Gubernatis, J. E.; Mannodi-Kanakkithodi, A.; Ramprasad, R.; Pilania, G.; Lookman, T.

Multi-objective optimization is an area of decision making that is concerned with mathematical optimization problems involving more than one objective simultaneously. Here we describe two new Monte Carlo methods for this type of optimization in the context of their application to the problem of designing polymers with more desirable dielectric and optical properties. We present results of applying these Monte Carlo methods to a two-objective problem (maximizing the total static band dielectric constant and energy gap) and a three objective problem (maximizing the ionic and electronic contributions to the static band dielectric constant and energy gap) of a 6-block organic polymer. Our objective functions were constructed from high throughput DFT calculations of 4-block polymers, following the method of Sharma et al., Nature Communications 5, 4845 (2014) and Mannodi-Kanakkithodi et al., Scientific Reports, submitted. Our high throughput and Monte Carlo methods of analysis extend to general N-block organic polymers. This work was supported in part by the LDRD DR program of the Los Alamos National Laboratory and in part by a Multidisciplinary University Research Initiative (MURI) Grant from the Office of Naval Research.

The role of optimization in the next generation of computer-based design tools

NASA Technical Reports Server (NTRS)

Rogan, J. Edward

1989-01-01

There is a close relationship between design optimization and the emerging new generation of computer-based tools for engineering design. With some notable exceptions, the development of these new tools has not taken full advantage of recent advances in numerical design optimization theory and practice. Recent work in the field of design process architecture has included an assessment of the impact of next-generation computer-based design tools on the design process. These results are summarized, and insights into the role of optimization in a design process based on these next-generation tools are presented. An example problem has been worked out to illustrate the application of this technique. The example problem - layout of an aircraft main landing gear - is one that is simple enough to be solved by many other techniques. Although the mathematical relationships describing the objective function and constraints for the landing gear layout problem can be written explicitly and are quite straightforward, an approximation technique has been used in the solution of this problem that can just as easily be applied to integrate supportability or producibility assessments using theory of measurement techniques into the design decision-making process.

Applications of fuzzy theories to multi-objective system optimization

NASA Technical Reports Server (NTRS)

Rao, S. S.; Dhingra, A. K.

1991-01-01

Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis.

From analytic inversion to contemporary IMRT optimization: Radiation therapy planning revisited from a mathematical perspective

PubMed Central

Censor, Yair; Unkelbach, Jan

2011-01-01

In this paper we look at the development of radiation therapy treatment planning from a mathematical point of view. Historically, planning for Intensity-Modulated Radiation Therapy (IMRT) has been considered as an inverse problem. We discuss first the two fundamental approaches that have been investigated to solve this inverse problem: Continuous analytic inversion techniques on one hand, and fully-discretized algebraic methods on the other hand. In the second part of the paper, we review another fundamental question which has been subject to debate from the beginning of IMRT until the present day: The rotation therapy approach versus fixed angle IMRT. This builds a bridge from historic work on IMRT planning to contemporary research in the context of Intensity-Modulated Arc Therapy (IMAT). PMID:21616694

Shakedown Analysis of Composite Steel-Concrete Frame Systems with Plastic and Brittle Elements Under Seismic Action

NASA Astrophysics Data System (ADS)

Alawdin, Piotr; Bulanov, George

2017-06-01

In this paper the earthquake analysis of composite steel-concrete frames is performed by finding solution of the optimization problem of shakedown analysis, which takes into account the nonlinear properties of materials. The constructions are equipped with systems bearing structures of various elastic-plastic and brittle elements absorbing energy of seismic actions. A mathematical model of this problem is presented on the base of limit analysis theory with partial redistribution of self-stressed internal forces. It is assumed that the load varies randomly within the specified limits. These limits are determined by the possible direction and magnitude of seismic loads. The illustrative example of such analysis of system is introduced. Some attention has been paid to the practical application of the proposed mathematical model.

MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys: A DIRECT-inspired optimization algorithm for experimentally accessible computational material design

DOE PAGES

Graf, Peter A.; Billups, Stephen

2017-07-24

Computational materials design has suffered from a lack of algorithms formulated in terms of experimentally accessible variables. Here we formulate the problem of (ternary) alloy optimization at the level of choice of atoms and their composition that is normal for synthesists. Mathematically, this is a mixed integer problem where a candidate solution consists of a choice of three elements, and how much of each of them to use. This space has the natural structure of a set of equilateral triangles. We solve this problem by introducing a novel version of the DIRECT algorithm that (1) operates on equilateral triangles insteadmore » of rectangles and (2) works across multiple triangles. We demonstrate on a test case that the algorithm is both robust and efficient. Lastly, we offer an explanation of the efficacy of DIRECT -- specifically, its balance of global and local search -- by showing that 'potentially optimal rectangles' of the original algorithm are akin to the Pareto front of the 'multi-component optimization' of global and local search.« less

MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys: A DIRECT-inspired optimization algorithm for experimentally accessible computational material design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Graf, Peter A.; Billups, Stephen

Computational materials design has suffered from a lack of algorithms formulated in terms of experimentally accessible variables. Here we formulate the problem of (ternary) alloy optimization at the level of choice of atoms and their composition that is normal for synthesists. Mathematically, this is a mixed integer problem where a candidate solution consists of a choice of three elements, and how much of each of them to use. This space has the natural structure of a set of equilateral triangles. We solve this problem by introducing a novel version of the DIRECT algorithm that (1) operates on equilateral triangles insteadmore » of rectangles and (2) works across multiple triangles. We demonstrate on a test case that the algorithm is both robust and efficient. Lastly, we offer an explanation of the efficacy of DIRECT -- specifically, its balance of global and local search -- by showing that 'potentially optimal rectangles' of the original algorithm are akin to the Pareto front of the 'multi-component optimization' of global and local search.« less

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

On the possibility of control restoration in some inverse problems of heat and mass transfer

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2016-11-01

The hypersonic aircraft permeable surfaces effective heat protection problems are considered. The physic-chemical processes (the dissociation and the ionization) in laminar boundary layer of compressible gas are appreciated in mathematical model. The statements of direct problems of heat and mass transfer are given: according to preset given controls it is necessary to compute the boundary layer mathematical model parameters and determinate the local and total heat flows and friction forces and the power of blowing system. The A.A.Dorodnicyn's generalized integral relations method has been used as calculation basis. The optimal control - the blowing into boundary layer (for continuous functions) was constructed as the solution of direct problem in extreme statement with the use of this approach. The statement of inverse problems are given: the control laws ensuring the preset given local heat flow and local tangent friction are restored. The differences between the interpolation and the approximation statements are discussed. The possibility of unique control restoration is established and proved (in the stagnation point). The computational experiments results are presented.

Solving a bi-objective mathematical model for location-routing problem with time windows in multi-echelon reverse logistics using metaheuristic procedure

NASA Astrophysics Data System (ADS)

Ghezavati, V. R.; Beigi, M.

2016-12-01

During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics (RL) network. The success of a logistics system may depend on the decisions of the facilities locations and vehicle routings. The location-routing problem (LRP) simultaneously locates the facilities and designs the travel routes for vehicles among established facilities and existing demand points. In this paper, the location-routing problem with time window (LRPTW) and homogeneous fleet type and designing a multi-echelon, and capacitated reverse logistics network, are considered which may arise in many real-life situations in logistics management. Our proposed RL network consists of hybrid collection/inspection centers, recovery centers and disposal centers. Here, we present a new bi-objective mathematical programming (BOMP) for LRPTW in reverse logistic. Since this type of problem is NP-hard, the non-dominated sorting genetic algorithm II (NSGA-II) is proposed to obtain the Pareto frontier for the given problem. Several numerical examples are presented to illustrate the effectiveness of the proposed model and algorithm. Also, the present work is an effort to effectively implement the ɛ-constraint method in GAMS software for producing the Pareto-optimal solutions in a BOMP. The results of the proposed algorithm have been compared with the ɛ-constraint method. The computational results show that the ɛ-constraint method is able to solve small-size instances to optimality within reasonable computing times, and for medium-to-large-sized problems, the proposed NSGA-II works better than the ɛ-constraint.

Finding optimal vaccination strategies under parameter uncertainty using stochastic programming.

PubMed

Tanner, Matthew W; Sattenspiel, Lisa; Ntaimo, Lewis

2008-10-01

We present a stochastic programming framework for finding the optimal vaccination policy for controlling infectious disease epidemics under parameter uncertainty. Stochastic programming is a popular framework for including the effects of parameter uncertainty in a mathematical optimization model. The problem is initially formulated to find the minimum cost vaccination policy under a chance-constraint. The chance-constraint requires that the probability that R(*)

Optimal Control via Self-Generated Stochasticity

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.

Perceptual support promotes strategy generation: Evidence from equation solving.

PubMed

Alibali, Martha W; Crooks, Noelle M; McNeil, Nicole M

2017-08-30

Over time, children shift from using less optimal strategies for solving mathematics problems to using better ones. But why do children generate new strategies? We argue that they do so when they begin to encode problems more accurately; therefore, we hypothesized that perceptual support for correct encoding would foster strategy generation. Fourth-grade students solved mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __) in a pre-test. They were then randomly assigned to one of three perceptual support conditions or to a Control condition. Participants in all conditions completed three mathematical equivalence problems with feedback about correctness. Participants in the experimental conditions received perceptual support (i.e., highlighting in red ink) for accurately encoding the equal sign, the right side of the equation, or the numbers that could be added to obtain the correct solution. Following this intervention, participants completed a problem-solving post-test. Among participants who solved the problems incorrectly at pre-test, those who received perceptual support for correctly encoding the equal sign were more likely to generate new, correct strategies for solving the problems than were those who received feedback only. Thus, perceptual support for accurate encoding of a key problem feature promoted generation of new, correct strategies. Statement of Contribution What is already known on this subject? With age and experience, children shift to using more effective strategies for solving math problems. Problem encoding also improves with age and experience. What the present study adds? Support for encoding the equal sign led children to generate correct strategies for solving equations. Improvements in problem encoding are one source of new strategies. © 2017 The British Psychological Society.

The Construction of Mathematical Literacy Problems for Geometry

NASA Astrophysics Data System (ADS)

Malasari, P. N.; Herman, T.; Jupri, A.

2017-09-01

The students of junior high school should have mathematical literacy ability to formulate, apply, and interpret mathematics in problem solving of daily life. Teaching these students are not enough by giving them ordinary mathematics problems. Teaching activities for these students brings consequence for teacher to construct mathematical literacy problems. Therefore, the aim of this study is to construct mathematical literacy problems to assess mathematical literacy ability. The steps of this study that consists of analysing, designing, theoretical validation, revising, limited testing to students, and evaluating. The data was collected with written test to 38 students of grade IX at one of state junior high school. Mathematical literacy problems consist of three essays with three indicators and three levels at polyhedron subject. The Indicators are formulating and employing mathematics. The results show that: (1) mathematical literacy problems which are constructed have been valid and practical, (2) mathematical literacy problems have good distinguishing characteristics and adequate distinguishing characteristics, (3) difficulty levels of problems are easy and moderate. The final conclusion is mathematical literacy problems which are constructed can be used to assess mathematical literacy ability.

Cost minimizing of cutting process for CNC thermal and water-jet machines

NASA Astrophysics Data System (ADS)

Tavaeva, Anastasia; Kurennov, Dmitry

2015-11-01

This paper deals with optimization problem of cutting process for CNC thermal and water-jet machines. The accuracy of objective function parameters calculation for optimization problem is investigated. This paper shows that working tool path speed is not constant value. One depends on some parameters that are described in this paper. The relations of working tool path speed depending on the numbers of NC programs frames, length of straight cut, configuration part are presented. Based on received results the correction coefficients for working tool speed are defined. Additionally the optimization problem may be solved by using mathematical model. Model takes into account the additional restrictions of thermal cutting (choice of piercing and output tool point, precedence condition, thermal deformations). At the second part of paper the non-standard cutting techniques are considered. Ones may lead to minimizing of cutting cost and time compared with standard cutting techniques. This paper considers the effectiveness of non-standard cutting techniques application. At the end of the paper the future research works are indicated.

Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

NASA Astrophysics Data System (ADS)

Takabe, Satoshi; Hukushima, Koji

2016-05-01

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.

MONSS: A multi-objective nonlinear simplex search approach

NASA Astrophysics Data System (ADS)

Zapotecas-Martínez, Saúl; Coello Coello, Carlos A.

2016-01-01

This article presents a novel methodology for dealing with continuous box-constrained multi-objective optimization problems (MOPs). The proposed algorithm adopts a nonlinear simplex search scheme in order to obtain multiple elements of the Pareto optimal set. The search is directed by a well-distributed set of weight vectors, each of which defines a scalarization problem that is solved by deforming a simplex according to the movements described by Nelder and Mead's method. Considering an MOP with n decision variables, the simplex is constructed using n+1 solutions which minimize different scalarization problems defined by n+1 neighbor weight vectors. All solutions found in the search are used to update a set of solutions considered to be the minima for each separate problem. In this way, the proposed algorithm collectively obtains multiple trade-offs among the different conflicting objectives, while maintaining a proper representation of the Pareto optimal front. In this article, it is shown that a well-designed strategy using just mathematical programming techniques can be competitive with respect to the state-of-the-art multi-objective evolutionary algorithms against which it was compared.

Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems.

PubMed

Takabe, Satoshi; Hukushima, Koji

2016-05-01

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.

Modeling and control of flexible space platforms with articulated payloads

NASA Technical Reports Server (NTRS)

Graves, Philip C.; Joshi, Suresh M.

1989-01-01

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

Analysis, approximation, and computation of a coupled solid/fluid temperature control problem

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Lee, Hyung C.

1993-01-01

An optimization problem is formulated motivated by the desire to remove temperature peaks, i.e., 'hot spots', along the bounding surfaces of containers of fluid flows. The heat equation of the solid container is coupled to the energy equations for the fluid. Heat sources can be located in the solid body, the fluid, or both. Control is effected by adjustments to the temperature of the fluid at the inflow boundary. Both mathematical analyses and computational experiments are given.

Maximizing the nurses' preferences in nurse scheduling problem: mathematical modeling and a meta-heuristic algorithm

NASA Astrophysics Data System (ADS)

Jafari, Hamed; Salmasi, Nasser

2015-09-01

The nurse scheduling problem (NSP) has received a great amount of attention in recent years. In the NSP, the goal is to assign shifts to the nurses in order to satisfy the hospital's demand during the planning horizon by considering different objective functions. In this research, we focus on maximizing the nurses' preferences for working shifts and weekends off by considering several important factors such as hospital's policies, labor laws, governmental regulations, and the status of nurses at the end of the previous planning horizon in one of the largest hospitals in Iran i.e., Milad Hospital. Due to the shortage of available nurses, at first, the minimum total number of required nurses is determined. Then, a mathematical programming model is proposed to solve the problem optimally. Since the proposed research problem is NP-hard, a meta-heuristic algorithm based on simulated annealing (SA) is applied to heuristically solve the problem in a reasonable time. An initial feasible solution generator and several novel neighborhood structures are applied to enhance performance of the SA algorithm. Inspired from our observations in Milad hospital, random test problems are generated to evaluate the performance of the SA algorithm. The results of computational experiments indicate that the applied SA algorithm provides solutions with average percentage gap of 5.49 % compared to the upper bounds obtained from the mathematical model. Moreover, the applied SA algorithm provides significantly better solutions in a reasonable time than the schedules provided by the head nurses.

Dialogue-Based Activities and Manipulatives to Engage Liberal Arts Majors in Mathematics

ERIC Educational Resources Information Center

Price, James C.

2015-01-01

This article presents four inquiry-based learning activities developed for a liberal arts math course. The activities cover four topics: the Pythagorean theorem, interest theory, optimization, and the Monty Hall problem. Each activity consists of a dialogue, with a theme and characters related to the topic, and a manipulative, that allow students…

An integer programming model to optimize resource allocation for wildfire containment.

Treesearch

Geoffrey H. Donovan; Douglas B. Rideout

2003-01-01

Determining the specific mix of fire-fighting resources for a given fire is a necessary condition for identifying the minimum of the Cost Plus Net Value Change (C+NVC) function. Current wildland fire management models may not reliably do so. The problem of identifying the most efficient wildland fire organization is characterized mathematically using integer-...

Optimal cure cycle design of a resin-fiber composite laminate

NASA Technical Reports Server (NTRS)

Hou, Jean W.; Sheen, Jeenson

1987-01-01

A unified computed aided design method was studied for the cure cycle design that incorporates an optimal design technique with the analytical model of a composite cure process. The preliminary results of using this proposed method for optimal cure cycle design are reported and discussed. The cure process of interest is the compression molding of a polyester which is described by a diffusion reaction system. The finite element method is employed to convert the initial boundary value problem into a set of first order differential equations which are solved simultaneously by the DE program. The equations for thermal design sensitivities are derived by using the direct differentiation method and are solved by the DE program. A recursive quadratic programming algorithm with an active set strategy called a linearization method is used to optimally design the cure cycle, subjected to the given design performance requirements. The difficulty of casting the cure cycle design process into a proper mathematical form is recognized. Various optimal design problems are formulated to address theses aspects. The optimal solutions of these formulations are compared and discussed.

Optimal design of reverse osmosis module networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maskan, F.; Wiley, D.E.; Johnston, L.P.M.

2000-05-01

The structure of individual reverse osmosis modules, the configuration of the module network, and the operating conditions were optimized for seawater and brackish water desalination. The system model included simple mathematical equations to predict the performance of the reverse osmosis modules. The optimization problem was formulated as a constrained multivariable nonlinear optimization. The objective function was the annual profit for the system, consisting of the profit obtained from the permeate, capital cost for the process units, and operating costs associated with energy consumption and maintenance. Optimization of several dual-stage reverse osmosis systems were investigated and compared. It was found thatmore » optimal network designs are the ones that produce the most permeate. It may be possible to achieve economic improvements by refining current membrane module designs and their operating pressures.« less

An Iterative Approach for the Optimization of Pavement Maintenance Management at the Network Level

PubMed Central

Torres-Machí, Cristina; Chamorro, Alondra; Videla, Carlos; Yepes, Víctor

2014-01-01

Pavement maintenance is one of the major issues of public agencies. Insufficient investment or inefficient maintenance strategies lead to high economic expenses in the long term. Under budgetary restrictions, the optimal allocation of resources becomes a crucial aspect. Two traditional approaches (sequential and holistic) and four classes of optimization methods (selection based on ranking, mathematical optimization, near optimization, and other methods) have been applied to solve this problem. They vary in the number of alternatives considered and how the selection process is performed. Therefore, a previous understanding of the problem is mandatory to identify the most suitable approach and method for a particular network. This study aims to assist highway agencies, researchers, and practitioners on when and how to apply available methods based on a comparative analysis of the current state of the practice. Holistic approach tackles the problem considering the overall network condition, while the sequential approach is easier to implement and understand, but may lead to solutions far from optimal. Scenarios defining the suitability of these approaches are defined. Finally, an iterative approach gathering the advantages of traditional approaches is proposed and applied in a case study. The proposed approach considers the overall network condition in a simpler and more intuitive manner than the holistic approach. PMID:24741352

An iterative approach for the optimization of pavement maintenance management at the network level.

PubMed

Torres-Machí, Cristina; Chamorro, Alondra; Videla, Carlos; Pellicer, Eugenio; Yepes, Víctor

2014-01-01

Pavement maintenance is one of the major issues of public agencies. Insufficient investment or inefficient maintenance strategies lead to high economic expenses in the long term. Under budgetary restrictions, the optimal allocation of resources becomes a crucial aspect. Two traditional approaches (sequential and holistic) and four classes of optimization methods (selection based on ranking, mathematical optimization, near optimization, and other methods) have been applied to solve this problem. They vary in the number of alternatives considered and how the selection process is performed. Therefore, a previous understanding of the problem is mandatory to identify the most suitable approach and method for a particular network. This study aims to assist highway agencies, researchers, and practitioners on when and how to apply available methods based on a comparative analysis of the current state of the practice. Holistic approach tackles the problem considering the overall network condition, while the sequential approach is easier to implement and understand, but may lead to solutions far from optimal. Scenarios defining the suitability of these approaches are defined. Finally, an iterative approach gathering the advantages of traditional approaches is proposed and applied in a case study. The proposed approach considers the overall network condition in a simpler and more intuitive manner than the holistic approach.

Aerodynamics of an airfoil with a jet issuing from its surface

NASA Technical Reports Server (NTRS)

Tavella, D. A.; Karamcheti, K.

1982-01-01

A simple, two dimensional, incompressible and inviscid model for the problem posed by a two dimensional wing with a jet issuing from its lower surface is considered and a parametric analysis is carried out to observe how the aerodynamic characteristics depend on the different parameters. The mathematical problem constitutes a boundary value problem where the position of part of the boundary is not known a priori. A nonlinear optimization approach was used to solve the problem, and the analysis reveals interesting characteristics that may help to better understand the physics involved in more complex situations in connection with high lift systems.

Optimization Model for Capacity Management and Bed Scheduling for Hospital

NASA Astrophysics Data System (ADS)

Sitepu, Suryati; Mawengkang, Herman; Husein, Ismail

2018-01-01

Hospital is a very important institution to provide health care for people. It is not surprising that nowadays the people’s demands for hospital is increasing.. However, due to the rising cost of healthcare services, hospitals need to consider efficiencies in order to overcome these two problems. This paper deals with an integrated strategy of staff capacity management and bed allocation planning to tackle these problems. Mathematically, the strategy can be modeled as an integer linear programming problem. We solve the model using a direct neighborhood search approach, based on the notion of superbasic variables.

Time-optimal control of the spacecraft trajectories in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Starinova, O. L.; Fain, M. K.; Materova, I. L.

2017-01-01

This paper outlines the multiparametric optimization of the L1-L2 and L2-L1 missions in the Earth-Moon system using electric propulsion. The optimal control laws are obtained using the Fedorenko successful linearization method to estimate the derivatives and the gradient method to optimize the control laws. The study of the transfers is based on the restricted circular three-body problem. The mathematical model of the missions is described within the barycentric system of coordinates. The optimization criterion is the total flight time. The perturbation from the Earth, the Moon and the Sun are taking into account. The impact of the shaded areas, induced by the Earth and the Moon, is also accounted. As the results of the optimization we obtained optimal control laws, corresponding trajectories and minimal total flight times.

Generalization of Water Pricing Model in Agriculture and Domestic Groundwater for Water Sustainability and Conservation

NASA Astrophysics Data System (ADS)

Hek, Tan Kim; Fadzli Ramli, Mohammad; Iryanto; Rohana Goh, Siti; Zaki, Mohd Faiz M.

2018-03-01

The water requirement greatly increased due to population growth, increased agricultural areas and industrial development, thus causing high water demand. The complex problems facing by country is water pricing is not designed optimally as a staple of human needs and on the other hand also cannot guarantee the maintenance and distribution of water effectively. The cheap water pricing caused increase of water use and unmanageable water resource. Therefore, the more optimal water pricing as an effective control of water policy is needed for the sake of ensuring water resources conservation and sustainability. This paper presents the review on problems, issues and mathematical modelling of water pricing based on agriculture and domestic groundwater for water sustainability and conservation.

Optimal Diet Planning for Eczema Patient Using Integer Programming

NASA Astrophysics Data System (ADS)

Zhen Sheng, Low; Sufahani, Suliadi

2018-04-01

Human diet planning is conducted by choosing appropriate food items that fulfill the nutritional requirements into the diet formulation. This paper discusses the application of integer programming to build the mathematical model of diet planning for eczema patients. The model developed is used to solve the diet problem of eczema patients from young age group. The integer programming is a scientific approach to select suitable food items, which seeks to minimize the costs, under conditions of meeting desired nutrient quantities, avoiding food allergens and getting certain foods into the diet that brings relief to the eczema conditions. This paper illustrates that the integer programming approach able to produce the optimal and feasible solution to deal with the diet problem of eczema patient.

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks.

PubMed

Deng, Zhimin; Tian, Tianhai

2014-07-29

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging. To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions. The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

A Mathematical Model and Algorithm for Routing Air Traffic Under Weather Uncertainty

NASA Technical Reports Server (NTRS)

Sadovsky, Alexander V.

2016-01-01

A central challenge in managing today's commercial en route air traffic is the task of routing the aircraft in the presence of adverse weather. Such weather can make regions of the airspace unusable, so all affected flights must be re-routed. Today this task is carried out by conference and negotiation between human air traffic controllers (ATC) responsible for the involved sectors of the airspace. One can argue that, in so doing, ATC try to solve an optimization problem without giving it a precise quantitative formulation. Such a formulation gives the mathematical machinery for constructing and verifying algorithms that are aimed at solving the problem. This paper contributes one such formulation and a corresponding algorithm. The algorithm addresses weather uncertainty and has closed form, which allows transparent analysis of correctness, realism, and computational costs.

Elaine Hale | NREL

Science.gov Websites

Analysis Center. Areas of Expertise Mathematical modeling, simulation, and optimization of complex Industrial and Applied Mathematics Mathematical Optimization Society Featured Publications Stoll, Brady

Use of multilevel modeling for determining optimal parameters of heat supply systems

NASA Astrophysics Data System (ADS)

Stennikov, V. A.; Barakhtenko, E. A.; Sokolov, D. V.

2017-07-01

The problem of finding optimal parameters of a heat-supply system (HSS) is in ensuring the required throughput capacity of a heat network by determining pipeline diameters and characteristics and location of pumping stations. Effective methods for solving this problem, i.e., the method of stepwise optimization based on the concept of dynamic programming and the method of multicircuit optimization, were proposed in the context of the hydraulic circuit theory developed at Melentiev Energy Systems Institute (Siberian Branch, Russian Academy of Sciences). These methods enable us to determine optimal parameters of various types of piping systems due to flexible adaptability of the calculation procedure to intricate nonlinear mathematical models describing features of used equipment items and methods of their construction and operation. The new and most significant results achieved in developing methodological support and software for finding optimal parameters of complex heat supply systems are presented: a new procedure for solving the problem based on multilevel decomposition of a heat network model that makes it possible to proceed from the initial problem to a set of interrelated, less cumbersome subproblems with reduced dimensionality; a new algorithm implementing the method of multicircuit optimization and focused on the calculation of a hierarchical model of a heat supply system; the SOSNA software system for determining optimum parameters of intricate heat-supply systems and implementing the developed methodological foundation. The proposed procedure and algorithm enable us to solve engineering problems of finding the optimal parameters of multicircuit heat supply systems having large (real) dimensionality, and are applied in solving urgent problems related to the optimal development and reconstruction of these systems. The developed methodological foundation and software can be used for designing heat supply systems in the Central and the Admiralty regions in St. Petersburg, the city of Bratsk, and the Magistral'nyi settlement.

Solving the Traveling Salesman's Problem Using the African Buffalo Optimization.

PubMed

Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam

2016-01-01

This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive.

Solving the Traveling Salesman's Problem Using the African Buffalo Optimization

PubMed Central

Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam

2016-01-01

This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive. PMID:26880872

An optimal analysis for Darcy-Forchheimer 3D flow of Carreau nanofluid with convectively heated surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2018-06-01

Darcy-Forchheimer three dimensional flow of Carreau nanoliquid induced by a linearly stretchable surface with convective boundary condition has been analyzed. Buongiorno model has been employed to elaborate thermophoresis and Brownian diffusion effects. Zero nanoparticles mass flux and convective surface conditions are implemented at the boundary. The governing problems are nonlinear. Optimal homotopic procedure has been used to tackle the governing mathematical system. Graphical results clearly depict the outcome of temperature and concentration fields. Surface drag coefficients and local Nusselt number are also plotted and discussed.

A model for dynamic allocation of human attention among multiple tasks

NASA Technical Reports Server (NTRS)

Sheridan, T. B.; Tulga, M. K.

1978-01-01

The problem of multi-task attention allocation with special reference to aircraft piloting is discussed with the experimental paradigm used to characterize this situation and the experimental results obtained in the first phase of the research. A qualitative description of an approach to mathematical modeling, and some results obtained with it are also presented to indicate what aspects of the model are most promising. Two appendices are given which (1) discuss the model in relation to graph theory and optimization and (2) specify the optimization algorithm of the model.

Power-limited low-thrust trajectory optimization with operation point detection

NASA Astrophysics Data System (ADS)

Chi, Zhemin; Li, Haiyang; Jiang, Fanghua; Li, Junfeng

2018-06-01

The power-limited solar electric propulsion system is considered more practical in mission design. An accurate mathematical model of the propulsion system, based on experimental data of the power generation system, is used in this paper. An indirect method is used to deal with the time-optimal and fuel-optimal control problems, in which the solar electric propulsion system is described using a finite number of operation points, which are characterized by different pairs of thruster input power. In order to guarantee the integral accuracy for the discrete power-limited problem, a power operation detection technique is embedded in the fourth-order Runge-Kutta algorithm with fixed step. Moreover, the logarithmic homotopy method and normalization technique are employed to overcome the difficulties caused by using indirect methods. Three numerical simulations with actual propulsion systems are given to substantiate the feasibility and efficiency of the proposed method.

Optimization of self-study room open problem based on green and low-carbon campus construction

NASA Astrophysics Data System (ADS)

Liu, Baoyou

2017-04-01

The optimization of self-study room open arrangement problem in colleges and universities is conducive to accelerate the fine management of the campus and promote green and low-carbon campus construction. Firstly, combined with the actual survey data, the self-study area and living area were divided into different blocks, and the electricity consumption in each self-study room and distance between different living and studying areas were normalized. Secondly, the minimum of total satisfaction index and the minimum of the total electricity consumption were selected as the optimization targets respectively. The mathematical models of linear programming were established and resolved by LINGO software. The results showed that the minimum of total satisfaction index was 4055.533 and the total minimum electricity consumption was 137216 W. Finally, some advice had been put forward on how to realize the high efficient administration of the study room.

Find the Dimensions: Students Solving a Tiling Problem

ERIC Educational Resources Information Center

Obara, Samuel

2018-01-01

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations

NASA Astrophysics Data System (ADS)

Podlipenko, Yu. K.; Shestopalov, Yu. V.

2017-09-01

We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

Experimental design for estimating unknown groundwater pumping using genetic algorithm and reduced order model

NASA Astrophysics Data System (ADS)

Ushijima, Timothy T.; Yeh, William W.-G.

2013-10-01

An optimal experimental design algorithm is developed to select locations for a network of observation wells that provide maximum information about unknown groundwater pumping in a confined, anisotropic aquifer. The design uses a maximal information criterion that chooses, among competing designs, the design that maximizes the sum of squared sensitivities while conforming to specified design constraints. The formulated optimization problem is non-convex and contains integer variables necessitating a combinatorial search. Given a realistic large-scale model, the size of the combinatorial search required can make the problem difficult, if not impossible, to solve using traditional mathematical programming techniques. Genetic algorithms (GAs) can be used to perform the global search; however, because a GA requires a large number of calls to a groundwater model, the formulated optimization problem still may be infeasible to solve. As a result, proper orthogonal decomposition (POD) is applied to the groundwater model to reduce its dimensionality. Then, the information matrix in the full model space can be searched without solving the full model. Results from a small-scale test case show identical optimal solutions among the GA, integer programming, and exhaustive search methods. This demonstrates the GA's ability to determine the optimal solution. In addition, the results show that a GA with POD model reduction is several orders of magnitude faster in finding the optimal solution than a GA using the full model. The proposed experimental design algorithm is applied to a realistic, two-dimensional, large-scale groundwater problem. The GA converged to a solution for this large-scale problem.

Novel Approach on the Optimisation of Mid-Course Corrections Along Interplanetary Trajectories

NASA Astrophysics Data System (ADS)

Iorfida, Elisabetta; Palmer, Phil; Roberts, Mark

The primer vector theory, firstly proposed by Lawden, defines a set of necessary conditions to characterise whether an impulsive thrust trajectory is optimal with respect to propellant usage, within a two-body problem context. If the conditions are not satisfied, one or more potential intermediate impulses are performed along the transfer arc, in order to lower the overall cost. The method is based on the propagation of the state transition matrix and on the solution of a boundary value problem, which leads to a mathematical and computational complexity.In this paper, a different approach is introduced. It is based on a polar coordinates transformation of the primer vector which allows the decoupling between its in-plane and out-of-plane components. The out-of-plane component is solved analytically while for the in-plane ones a Hamiltonian approximation is made.The novel procedure reduces the mathematical complexity and the computational cost of Lawden's problem and gives also a different perspective about the optimisation of a transfer trajectory.

Description of Student’s Metacognitive Ability in Understanding and Solving Mathematics Problem

NASA Astrophysics Data System (ADS)

Ahmad, Herlina; Febryanti, Fatimah; Febryanti, Fatimah; Muthmainnah

2018-01-01

This research was conducted qualitative which was aim to describe metacognitive ability to understand and solve the problems of mathematics. The subject of the research was the first year students at computer and networking department of SMK Mega Link Majene. The sample was taken by purposive sampling technique. The data obtained used the research instrument based on the form of students achievements were collected by using test of student’s achievement and interview guidance. The technique of collecting data researcher had observation to ascertain the model that used by teacher was teaching model of developing metacognitive. The technique of data analysis in this research was reduction data, presentation and conclusion. Based on the whole findings in this study it was shown that student’s metacognitive ability generally not develops optimally. It was because of limited scope of the materials, and cognitive teaching strategy handled by verbal presentation and trained continuously in facing cognitive tasks, such as understanding and solving problem.

What Makes a Problem Mathematically Interesting? Inviting Prospective Teachers to Pose Better Problems

ERIC Educational Resources Information Center

Crespo, Sandra; Sinclair, Nathalie

2008-01-01

School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics education reform vision that seeks to promote mathematics as an worthy intellectual…

DOE Office of Scientific and Technical Information (OSTI.GOV)

None, None

The Second SIAM Conference on Computational Science and Engineering was held in San Diego from February 10-12, 2003. Total conference attendance was 553. This is a 23% increase in attendance over the first conference. The focus of this conference was to draw attention to the tremendous range of major computational efforts on large problems in science and engineering, to promote the interdisciplinary culture required to meet these large-scale challenges, and to encourage the training of the next generation of computational scientists. Computational Science & Engineering (CS&E) is now widely accepted, along with theory and experiment, as a crucial third modemore » of scientific investigation and engineering design. Aerospace, automotive, biological, chemical, semiconductor, and other industrial sectors now rely on simulation for technical decision support. For federal agencies also, CS&E has become an essential support for decisions on resources, transportation, and defense. CS&E is, by nature, interdisciplinary. It grows out of physical applications and it depends on computer architecture, but at its heart are powerful numerical algorithms and sophisticated computer science techniques. From an applied mathematics perspective, much of CS&E has involved analysis, but the future surely includes optimization and design, especially in the presence of uncertainty. Another mathematical frontier is the assimilation of very large data sets through such techniques as adaptive multi-resolution, automated feature search, and low-dimensional parameterization. The themes of the 2003 conference included, but were not limited to: Advanced Discretization Methods; Computational Biology and Bioinformatics; Computational Chemistry and Chemical Engineering; Computational Earth and Atmospheric Sciences; Computational Electromagnetics; Computational Fluid Dynamics; Computational Medicine and Bioengineering; Computational Physics and Astrophysics; Computational Solid Mechanics and Materials; CS&E Education; Meshing and Adaptivity; Multiscale and Multiphysics Problems; Numerical Algorithms for CS&E; Discrete and Combinatorial Algorithms for CS&E; Inverse Problems; Optimal Design, Optimal Control, and Inverse Problems; Parallel and Distributed Computing; Problem-Solving Environments; Software and Wddleware Systems; Uncertainty Estimation and Sensitivity Analysis; and Visualization and Computer Graphics.« less

SURVIVABILITY THROUGH OPTIMIZING RESILIENT MECHANISMS (STORM)

DTIC Science & Technology

2017-04-01

STATEMENT Approved for Public Release; Distribution Unlimited. PA# 88ABW-2017-0894 Date Cleared: 07 Mar 2017 13. SUPPLEMENTARY NOTES 14. ABSTRACT Game ...quantitatively about cyber-attacks. Game theory is the branch of applied mathematics that formalizes strategic interaction among intelligent rational agents...mechanism based on game theory. This work has applied game theory to numerous cyber security problems: cloud security, cyber threat information sharing

A Framework for Supporting Survivability, Network Planning and Cross-Layer Optimization in Future Multi-Domain Terabit Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baldin, Ilya; Huang, Shu; Gopidi, Rajesh

This final project report describes the accomplishments, products and publications from the award. It includes the overview of the project goals to devise a framework for managing resources in multi-domain, multi-layer networks, as well the details of the mathematical problem formulation and the description of the prototype built to prove the concept.

Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Kim, Hongman; Ragon, Scott; Soremekun, Grant; Malone, Brett

2004-01-01

Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.

Valuing hydrological alteration in multi-objective water resources management

NASA Astrophysics Data System (ADS)

Bizzi, Simone; Pianosi, Francesca; Soncini-Sessa, Rodolfo

2012-11-01

SummaryThe management of water through the impoundment of rivers by dams and reservoirs is necessary to support key human activities such as hydropower production, agriculture and flood risk mitigation. Advances in multi-objective optimization techniques and ever growing computing power make it possible to design reservoir operating policies that represent Pareto-optimal tradeoffs between multiple interests. On the one hand, such optimization methods can enhance performances of commonly targeted objectives (such as hydropower production or water supply), on the other hand they risk strongly penalizing all the interests not directly (i.e. mathematically) included in the optimization algorithm. The alteration of the downstream hydrological regime is a well established cause of ecological degradation and its evaluation and rehabilitation is commonly required by recent legislation (as the Water Framework Directive in Europe). However, it is rarely embedded in reservoir optimization routines and, even when explicitly considered, the criteria adopted for its evaluation are doubted and not commonly trusted, undermining the possibility of real implementation of environmentally friendly policies. The main challenges in defining and assessing hydrological alterations are: how to define a reference state (referencing); how to define criteria upon which to build mathematical indicators of alteration (measuring); and finally how to aggregate the indicators in a single evaluation index (valuing) that can serve as objective function in the optimization problem. This paper aims to address these issues by: (i) discussing the benefits and constrains of different approaches to referencing, measuring and valuing hydrological alteration; (ii) testing two alternative indices of hydrological alteration, one based on the established framework of Indicators of Hydrological Alteration (Richter et al., 1996), and one satisfying the mathematical properties required by widely used optimization methods based on dynamic programming; (iii) demonstrating and discussing these indices by application River Ticino, in Italy; (iv) providing a framework to effectively include hydrological alteration within reservoir operation optimization.

Optimization of the Bridgman crystal growth process

NASA Astrophysics Data System (ADS)

Margulies, M.; Witomski, P.; Duffar, T.

2004-05-01

A numerical optimization method of the vertical Bridgman growth configuration is presented and developed. It permits to optimize the furnace temperature field and the pulling rate versus time in order to decrease the radial thermal gradients in the sample. Some constraints are also included in order to insure physically realistic results. The model includes the two classical non-linearities associated to crystal growth processes, the radiative thermal exchange and the release of latent heat at the solid-liquid interface. The mathematical analysis and development of the problem is shortly described. On some examples, it is shown that the method works in a satisfactory way; however the results are dependent on the numerical parameters. Improvements of the optimization model, on the physical and numerical point of view, are suggested.

Some unsolved problems in discrete mathematics and mathematical cybernetics

NASA Astrophysics Data System (ADS)

Korshunov, Aleksei D.

2009-10-01

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

The Increase of Critical Thinking Skills through Mathematical Investigation Approach

NASA Astrophysics Data System (ADS)

Sumarna, N.; Wahyudin; Herman, T.

2017-02-01

Some research findings on critical thinking skills of prospective elementary teachers, showed a response that is not optimal. On the other hand, critical thinking skills will lead a student in the process of analysis, evaluation and synthesis in solving a mathematical problem. This study attempts to perform an alternative solution with a focus on mathematics learning conditions that is held in the lecture room through mathematical investigation approach. This research method was Quasi-Experimental design with pre-test post-test design. Data analysis using a mixed method with Embedded design. Subjects were regular students enrolled in 2014 at the study program of education of primary school teachers. The number of research subjects were 111 students consisting of 56 students in the experimental group and 55 students in the control group. The results of the study showed that (1) there is a significant difference in the improvement of critical thinking ability of students who receive learning through mathematical investigation approach when compared with students studying through expository approach, and (2) there is no interaction effect between prior knowledge of mathematics and learning factors (mathematical investigation and expository) to increase of critical thinking skills of students.

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

DOE PAGES

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul; ...

2017-12-20

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent experimental, theoretical, and numerical investigations of problems in applied mechanics are discussed in reviews and reports. The fields covered include vibration and stability; the mechanics of elastic and plastic materials; fluid mechanics; the numerical treatment of differential equations; finite and boundary elements; optimization, decision theory, stochastics, and actuarial analysis; applied analysis and mathematical physics; and numerical analysis. Reviews are presented on mathematical applications of geometric-optics methods, biomechanics and implant technology, vibration theory in engineering, the stiffness and strength of damaged materials, and the existence of slow steady flows of viscoelastic fluids of integral type.

D-Optimal Experimental Design for Contaminant Source Identification

NASA Astrophysics Data System (ADS)

Sai Baba, A. K.; Alexanderian, A.

2016-12-01

Contaminant source identification seeks to estimate the release history of a conservative solute given point concentration measurements at some time after the release. This can be mathematically expressed as an inverse problem, with a linear observation operator or a parameter-to-observation map, which we tackle using a Bayesian approach. Acquisition of experimental data can be laborious and expensive. The goal is to control the experimental parameters - in our case, the sparsity of the sensors, to maximize the information gain subject to some physical or budget constraints. This is known as optimal experimental design (OED). D-optimal experimental design seeks to maximize the expected information gain, and has long been considered the gold standard in the statistics community. Our goal is to develop scalable methods for D-optimal experimental designs involving large-scale PDE constrained problems with high-dimensional parameter fields. A major challenge for the OED, is that a nonlinear optimization algorithm for the D-optimality criterion requires repeated evaluation of objective function and gradient involving the determinant of large and dense matrices - this cost can be prohibitively expensive for applications of interest. We propose novel randomized matrix techniques that bring down the computational costs of the objective function and gradient evaluations by several orders of magnitude compared to the naive approach. The effect of randomized estimators on the accuracy and the convergence of the optimization solver will be discussed. The features and benefits of our new approach will be demonstrated on a challenging model problem from contaminant source identification involving the inference of the initial condition from spatio-temporal observations in a time-dependent advection-diffusion problem.

A two-stage path planning approach for multiple car-like robots based on PH curves and a modified harmony search algorithm

NASA Astrophysics Data System (ADS)

Zeng, Wenhui; Yi, Jin; Rao, Xiao; Zheng, Yun

2017-11-01

In this article, collision-avoidance path planning for multiple car-like robots with variable motion is formulated as a two-stage objective optimization problem minimizing both the total length of all paths and the task's completion time. Accordingly, a new approach based on Pythagorean Hodograph (PH) curves and Modified Harmony Search algorithm is proposed to solve the two-stage path-planning problem subject to kinematic constraints such as velocity, acceleration, and minimum turning radius. First, a method of path planning based on PH curves for a single robot is proposed. Second, a mathematical model of the two-stage path-planning problem for multiple car-like robots with variable motion subject to kinematic constraints is constructed that the first-stage minimizes the total length of all paths and the second-stage minimizes the task's completion time. Finally, a modified harmony search algorithm is applied to solve the two-stage optimization problem. A set of experiments demonstrate the effectiveness of the proposed approach.

On designing for quality

NASA Technical Reports Server (NTRS)

Vajingortin, L. D.; Roisman, W. P.

1991-01-01

The problem of ensuring the required quality of products and/or technological processes often becomes more difficult due to the fact that there is not general theory of determining the optimal sets of value of the primary factors, i.e., of the output parameters of the parts and units comprising an object and ensuring the correspondence of the object's parameters to the quality requirements. This is the main reason for the amount of time taken to finish complex vital article. To create this theory, one has to overcome a number of difficulties and to solve the following tasks: the creation of reliable and stable mathematical models showing the influence of the primary factors on the output parameters; finding a new technique of assigning tolerances for primary factors with regard to economical, technological, and other criteria, the technique being based on the solution of the main problem; well reasoned assignment of nominal values for primary factors which serve as the basis for creating tolerances. Each of the above listed tasks is of independent importance. An attempt is made to give solutions for this problem. The above problem dealing with quality ensuring an mathematically formalized aspect is called the multiple inverse problem.

The problem-solving approach in the teaching of number theory

NASA Astrophysics Data System (ADS)

Toh, Pee Choon; Hoong Leong, Yew; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Guan Tay, Eng; Him Ho, Foo

2014-02-01

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to adopt a Pólya-style approach in learning mathematics. The Practical Worksheet is an instructional scaffold we adopted to help our pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. The Worksheet was initially used in a design experiment aimed at teaching problem solving in a secondary school. In this paper, we describe an application and adaptation of the MProSE (Mathematical Problem Solving for Everyone) design experiment to a university level number theory course for pre-service mathematics teachers. The goal of the enterprise was to help the pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. Our analysis of the pre-service mathematics teachers' work shows that the MProSE design holds promise for mathematics courses at the tertiary level.

Optimisation by hierarchical search

NASA Astrophysics Data System (ADS)

Zintchenko, Ilia; Hastings, Matthew; Troyer, Matthias

2015-03-01

Finding optimal values for a set of variables relative to a cost function gives rise to some of the hardest problems in physics, computer science and applied mathematics. Although often very simple in their formulation, these problems have a complex cost function landscape which prevents currently known algorithms from efficiently finding the global optimum. Countless techniques have been proposed to partially circumvent this problem, but an efficient method is yet to be found. We present a heuristic, general purpose approach to potentially improve the performance of conventional algorithms or special purpose hardware devices by optimising groups of variables in a hierarchical way. We apply this approach to problems in combinatorial optimisation, machine learning and other fields.

Transitions in optimal adaptive strategies for populations in fluctuating environments

NASA Astrophysics Data System (ADS)

Mayer, Andreas; Mora, Thierry; Rivoire, Olivier; Walczak, Aleksandra M.

2017-09-01

Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist phenotype that compromises between conditions, or population-wise diversification (bet hedging). Which strategy provides the largest selective advantage in the long run depends on the range of accessible phenotypes and the statistics of the environmental fluctuations. Here, we analyze this problem in a simple mathematical model of population growth. First, we review and extend a graphical method to identify the nature of the optimal strategy when the environmental fluctuations are uncorrelated. Temporal correlations in environmental fluctuations open up new strategies that rely on memory but are mathematically challenging to study: We present analytical results to address this challenge. We illustrate our general approach by analyzing optimal adaptive strategies in the presence of trade-offs that constrain the range of accessible phenotypes. Our results extend several previous studies and have applications to a variety of biological phenomena, from antibiotic resistance in bacteria to immune responses in vertebrates.

A mathematical model for the generation and control of a pH gradient in an immobilized enzyme system involving acid generation.

PubMed

Chen, G; Fournier, R L; Varanasi, S

1998-02-20

An optimal pH control technique has been developed for multistep enzymatic synthesis reactions where the optimal pH differs by several units for each step. This technique separates an acidic environment from a basic environment by the hydrolysis of urea within a thin layer of immobilized urease. With this technique, a two-step enzymatic reaction can take place simultaneously, in proximity to each other, and at their respective optimal pH. Because a reaction system involving an acid generation represents a more challenging test of this pH control technique, a number of factors that affect the generation of such a pH gradient are considered in this study. The mathematical model proposed is based on several simplifying assumptions and represents a first attempt to provide an analysis of this complex problem. The results show that, by choosing appropriate parameters, the pH control technique still can generate the desired pH gradient even if there is an acid-generating reaction in the system. Copyright 1998 John Wiley & Sons, Inc.

Problem Solving: How Do In-Service Secondary School Teachers of Mathematics Make Sense of a Non-Routine Problem Context?

ERIC Educational Resources Information Center

Mwei, Philip K.

2017-01-01

The concept of mathematical problem solving is an important mathematical process in mathematics curricula of education systems worldwide. These math curricula demand that learners are exposed to authentic problems that foster successful problem solving. To attain this very important goal, there must be mathematics teachers well versed in content…

Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

Students’ Mathematical Problem-Solving Abilities Through The Application of Learning Models Problem Based Learning

NASA Astrophysics Data System (ADS)

Nasution, M. L.; Yerizon, Y.; Gusmiyanti, R.

2018-04-01

One of the purpose mathematic learning is to develop problem solving abilities. Problem solving is obtained through experience in questioning non-routine. Improving students’ mathematical problem-solving abilities required an appropriate strategy in learning activities one of them is models problem based learning (PBL). Thus, the purpose of this research is to determine whether the problem solving abilities of mathematical students’ who learn to use PBL better than on the ability of students’ mathematical problem solving by applying conventional learning. This research included quasi experiment with static group design and population is students class XI MIA SMAN 1 Lubuk Alung. Class experiment in the class XI MIA 5 and class control in the class XI MIA 6. The instrument of final test students’ mathematical problem solving used essay form. The result of data final test in analyzed with t-test. The result is students’ mathematical problem solving abilities with PBL better then on the ability of students’ mathematical problem solving by applying conventional learning. It’s seen from the high percentage achieved by the group of students who learn to use PBL for each indicator of students’ mathematical problem solving.

PROBABILISTIC CROSS-IDENTIFICATION IN CROWDED FIELDS AS AN ASSIGNMENT PROBLEM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Budavári, Tamás; Basu, Amitabh, E-mail: budavari@jhu.edu, E-mail: basu.amitabh@jhu.edu

2016-10-01

One of the outstanding challenges of cross-identification is multiplicity: detections in crowded regions of the sky are often linked to more than one candidate associations of similar likelihoods. We map the resulting maximum likelihood partitioning to the fundamental assignment problem of discrete mathematics and efficiently solve the two-way catalog-level matching in the realm of combinatorial optimization using the so-called Hungarian algorithm. We introduce the method, demonstrate its performance in a mock universe where the true associations are known, and discuss the applicability of the new procedure to large surveys.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Technische Universitaet Berlin, Berlin, West Germany, April 8-11, 1980, Reports. Parts 1 & 2

NASA Astrophysics Data System (ADS)

1981-04-01

The main topics discussed were related to nonparametric statistics, plane and antiplane states in finite elasticity, free-boundary-variational inequalities, the numerical solution of free boundary-value problems, discrete and combinatorial optimization, mathematical modelling in fluid mechanics, a survey and comparison regarding thermodynamic theories, invariant and almost invariant subspaces in linear systems with applications to disturbance isolation, nonlinear acoustics, and methods of function theory in the case of partial differential equations, giving particular attention to elliptic problems in the plane.

Probabilistic Cross-identification in Crowded Fields as an Assignment Problem

NASA Astrophysics Data System (ADS)

Budavári, Tamás; Basu, Amitabh

2016-10-01

One of the outstanding challenges of cross-identification is multiplicity: detections in crowded regions of the sky are often linked to more than one candidate associations of similar likelihoods. We map the resulting maximum likelihood partitioning to the fundamental assignment problem of discrete mathematics and efficiently solve the two-way catalog-level matching in the realm of combinatorial optimization using the so-called Hungarian algorithm. We introduce the method, demonstrate its performance in a mock universe where the true associations are known, and discuss the applicability of the new procedure to large surveys.

Automated design optimization of supersonic airplane wing structures under dynamic constraints

NASA Technical Reports Server (NTRS)

Fox, R. L.; Miura, H.; Rao, S. S.

1972-01-01

The problems of the preliminary and first level detail design of supersonic aircraft wings are stated as mathematical programs and solved using automated optimum design techniques. The problem is approached in two phases: the first is a simplified equivalent plate model in which the envelope, planform and structural parameters are varied to produce a design, the second is a finite element model with fixed configuration in which the material distribution is varied. Constraints include flutter, aeroelastically computed stresses and deflections, natural frequency and a variety of geometric limitations.

Can hydro-economic river basin models simulate water shadow prices under asymmetric access?

PubMed

Kuhn, A; Britz, W

2012-01-01

Hydro-economic river basin models (HERBM) based on mathematical programming are conventionally formulated as explicit 'aggregate optimization' problems with a single, aggregate objective function. Often unintended, this format implicitly assumes that decisions on water allocation are made via central planning or functioning markets such as to maximize social welfare. In the absence of perfect water markets, however, individually optimal decisions by water users will differ from the social optimum. Classical aggregate HERBMs cannot simulate that situation and thus might be unable to describe existing institutions governing access to water and might produce biased results for alternative ones. We propose a new solution format for HERBMs, based on the format of the mixed complementarity problem (MCP), where modified shadow price relations express spatial externalities resulting from asymmetric access to water use. This new problem format, as opposed to commonly used linear (LP) or non-linear programming (NLP) approaches, enables the simultaneous simulation of numerous 'independent optimization' decisions by multiple water users while maintaining physical interdependences based on water use and flow in the river basin. We show that the alternative problem format allows the formulation HERBMs that yield more realistic results when comparing different water management institutions.

Optimal Down Regulation of mRNA Translation

NASA Astrophysics Data System (ADS)

Zarai, Yoram; Margaliot, Michael; Tuller, Tamir

2017-01-01

Down regulation of mRNA translation is an important problem in various bio-medical domains ranging from developing effective medicines for tumors and for viral diseases to developing attenuated virus strains that can be used for vaccination. Here, we study the problem of down regulation of mRNA translation using a mathematical model called the ribosome flow model (RFM). In the RFM, the mRNA molecule is modeled as a chain of n sites. The flow of ribosomes between consecutive sites is regulated by n + 1 transition rates. Given a set of feasible transition rates, that models the outcome of all possible mutations, we consider the problem of maximally down regulating protein production by altering the rates within this set of feasible rates. Under certain conditions on the feasible set, we show that an optimal solution can be determined efficiently. We also rigorously analyze two special cases of the down regulation optimization problem. Our results suggest that one must focus on the position along the mRNA molecule where the transition rate has the strongest effect on the protein production rate. However, this rate is not necessarily the slowest transition rate along the mRNA molecule. We discuss some of the biological implications of these results.

An algorithm for the optimal collection of wet waste.

PubMed

Laureri, Federica; Minciardi, Riccardo; Robba, Michela

2016-02-01

This work refers to the development of an approach for planning wet waste (food waste and other) collection at a metropolitan scale. Some specific modeling features distinguish this specific waste collection problem from the other ones. For instance, there may be significant differences as regards the values of the parameters (such as weight and volume) characterizing the various collection points. As it happens for classical waste collection planning, even in the case of wet waste, one has to deal with difficult combinatorial problems, where the determination of an optimal solution may require a very large computational effort, in the case of problem instances having a noticeable dimensionality. For this reason, in this work, a heuristic procedure for the optimal planning of wet waste is developed and applied to problem instances drawn from a real case study. The performances that can be obtained by applying such a procedure are evaluated by a comparison with those obtainable via a general-purpose mathematical programming software package, as well as those obtained by applying very simple decision rules commonly used in practice. The considered case study consists in an area corresponding to the historical center of the Municipality of Genoa. Copyright © 2015 Elsevier Ltd. All rights reserved.

Robust Airfoil Optimization to Achieve Consistent Drag Reduction Over a Mach Range

NASA Technical Reports Server (NTRS)

Li, Wu; Huyse, Luc; Padula, Sharon; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

We prove mathematically that in order to avoid point-optimization at the sampled design points for multipoint airfoil optimization, the number of design points must be greater than the number of free-design variables. To overcome point-optimization at the sampled design points, a robust airfoil optimization method (called the profile optimization method) is developed and analyzed. This optimization method aims at a consistent drag reduction over a given Mach range and has three advantages: (a) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (b) there is no random airfoil shape distortion for any iterate it generates, and (c) it allows a designer to make a trade-off between a truly optimized airfoil and the amount of computing time consumed. For illustration purposes, we use the profile optimization method to solve a lift-constrained drag minimization problem for 2-D airfoil in Euler flow with 20 free-design variables. A comparison with other airfoil optimization methods is also included.

A tabu search evalutionary algorithm for multiobjective optimization: Application to a bi-criterion aircraft structural reliability problem

NASA Astrophysics Data System (ADS)

Long, Kim Chenming

Real-world engineering optimization problems often require the consideration of multiple conflicting and noncommensurate objectives, subject to nonconvex constraint regions in a high-dimensional decision space. Further challenges occur for combinatorial multiobjective problems in which the decision variables are not continuous. Traditional multiobjective optimization methods of operations research, such as weighting and epsilon constraint methods, are ill-suited to solving these complex, multiobjective problems. This has given rise to the application of a wide range of metaheuristic optimization algorithms, such as evolutionary, particle swarm, simulated annealing, and ant colony methods, to multiobjective optimization. Several multiobjective evolutionary algorithms have been developed, including the strength Pareto evolutionary algorithm (SPEA) and the non-dominated sorting genetic algorithm (NSGA), for determining the Pareto-optimal set of non-dominated solutions. Although numerous researchers have developed a wide range of multiobjective optimization algorithms, there is a continuing need to construct computationally efficient algorithms with an improved ability to converge to globally non-dominated solutions along the Pareto-optimal front for complex, large-scale, multiobjective engineering optimization problems. This is particularly important when the multiple objective functions and constraints of the real-world system cannot be expressed in explicit mathematical representations. This research presents a novel metaheuristic evolutionary algorithm for complex multiobjective optimization problems, which combines the metaheuristic tabu search algorithm with the evolutionary algorithm (TSEA), as embodied in genetic algorithms. TSEA is successfully applied to bicriteria (i.e., structural reliability and retrofit cost) optimization of the aircraft tail structure fatigue life, which increases its reliability by prolonging fatigue life. A comparison for this application of the proposed algorithm, TSEA, with several state-of-the-art multiobjective optimization algorithms reveals that TSEA outperforms these algorithms by providing retrofit solutions with greater reliability for the same costs (i.e., closer to the Pareto-optimal front) after the algorithms are executed for the same number of generations. This research also demonstrates that TSEA competes with and, in some situations, outperforms state-of-the-art multiobjective optimization algorithms such as NSGA II and SPEA 2 when applied to classic bicriteria test problems in the technical literature and other complex, sizable real-world applications. The successful implementation of TSEA contributes to the safety of aeronautical structures by providing a systematic way to guide aircraft structural retrofitting efforts, as well as a potentially useful algorithm for a wide range of multiobjective optimization problems in engineering and other fields.

Modelling mid-course corrections for optimality conditions along interplanetary transfers

NASA Astrophysics Data System (ADS)

Iorfida, Elisabetta; Palmer, Phil; Roberts, Mark

2014-12-01

Within the field of trajectory optimisation, Lawden developed the primer vector theory, which defines a set of necessary conditions to characterise whether a transfer trajectory, in the two-body problem context, is optimum with respect to propellant usage. If the conditions are not satisfied, a region of the transfer trajectory is identified in which one or more potential intermediate impulses are performed in order to lower the overall cost. The method is computationally complex owing to having to solve a boundary value problem. In this paper is presented a new propagator that reduces the mathematical complexity and the computational cost of the problem, in particular it exploits a separation between the in-plane and out-of-plane components of the primer vector along the transfer trajectory. Using this propagator, the optimality of the transfer arc has been investigated, varying the departure and arrival orbits. In particular, keeping fixed the transfer trajectory, the optimality has been extensively analysed varying both the initial and final positions on the orbit, together with the directions of the initial and final thrust impulses.

The Deterministic Information Bottleneck

NASA Astrophysics Data System (ADS)

Strouse, D. J.; Schwab, David

2015-03-01

A fundamental and ubiquitous task that all organisms face is prediction of the future based on past sensory experience. Since an individual's memory resources are limited and costly, however, there is a tradeoff between memory cost and predictive payoff. The information bottleneck (IB) method (Tishby, Pereira, & Bialek 2000) formulates this tradeoff as a mathematical optimization problem using an information theoretic cost function. IB encourages storing as few bits of past sensory input as possible while selectively preserving the bits that are most predictive of the future. Here we introduce an alternative formulation of the IB method, which we call the deterministic information bottleneck (DIB). First, we argue for an alternative cost function, which better represents the biologically-motivated goal of minimizing required memory resources. Then, we show that this seemingly minor change has the dramatic effect of converting the optimal memory encoder from stochastic to deterministic. Next, we propose an iterative algorithm for solving the DIB problem. Additionally, we compare the IB and DIB methods on a variety of synthetic datasets, and examine the performance of retinal ganglion cell populations relative to the optimal encoding strategy for each problem.

From analytic inversion to contemporary IMRT optimization: radiation therapy planning revisited from a mathematical perspective.

PubMed

Censor, Yair; Unkelbach, Jan

2012-04-01

In this paper we look at the development of radiation therapy treatment planning from a mathematical point of view. Historically, planning for Intensity-Modulated Radiation Therapy (IMRT) has been considered as an inverse problem. We discuss first the two fundamental approaches that have been investigated to solve this inverse problem: Continuous analytic inversion techniques on one hand, and fully-discretized algebraic methods on the other hand. In the second part of the paper, we review another fundamental question which has been subject to debate from the beginning of IMRT until the present day: The rotation therapy approach versus fixed angle IMRT. This builds a bridge from historic work on IMRT planning to contemporary research in the context of Intensity-Modulated Arc Therapy (IMAT). Copyright © 2011 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Model correlation and damage location for large space truss structures: Secant method development and evaluation

NASA Technical Reports Server (NTRS)

Smith, Suzanne Weaver; Beattie, Christopher A.

1991-01-01

On-orbit testing of a large space structure will be required to complete the certification of any mathematical model for the structure dynamic response. The process of establishing a mathematical model that matches measured structure response is referred to as model correlation. Most model correlation approaches have an identification technique to determine structural characteristics from the measurements of the structure response. This problem is approached with one particular class of identification techniques - matrix adjustment methods - which use measured data to produce an optimal update of the structure property matrix, often the stiffness matrix. New methods were developed for identification to handle problems of the size and complexity expected for large space structures. Further development and refinement of these secant-method identification algorithms were undertaken. Also, evaluation of these techniques is an approach for model correlation and damage location was initiated.

The Music of Mathematics: Toward a New Problem Typology

NASA Astrophysics Data System (ADS)

Quarfoot, David

Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking about that world. Most importantly, this work highlights and names the panoply of problems that exist, expanding the myopic vision of contemporary mathematical problem solving.

Nonnegative constraint quadratic program technique to enhance the resolution of γ spectra

NASA Astrophysics Data System (ADS)

Li, Jinglun; Xiao, Wuyun; Ai, Xianyun; Chen, Ye

2018-04-01

Two concepts of the nonnegative least squares problem (NNLS) and the linear complementarity problem (LCP) are introduced for the resolution enhancement of the γ spectra. The respective algorithms such as the active set method and the primal-dual interior point method are applied to solve the above two problems. In mathematics, the nonnegative constraint results in the sparsity of the optimal solution of the deconvolution, and it is this sparsity that enhances the resolution. Finally, a comparison in the peak position accuracy and the computation time is made between these two methods and the boosted L_R and Gold methods.

Engineering tradeoff problems viewed as multiple objective optimizations and the VODCA methodology

NASA Astrophysics Data System (ADS)

Morgan, T. W.; Thurgood, R. L.

1984-05-01

This paper summarizes a rational model for making engineering tradeoff decisions. The model is a hybrid from the fields of social welfare economics, communications, and operations research. A solution methodology (Vector Optimization Decision Convergence Algorithm - VODCA) firmly grounded in the economic model is developed both conceptually and mathematically. The primary objective for developing the VODCA methodology was to improve the process for extracting relative value information about the objectives from the appropriate decision makers. This objective was accomplished by employing data filtering techniques to increase the consistency of the relative value information and decrease the amount of information required. VODCA is applied to a simplified hypothetical tradeoff decision problem. Possible use of multiple objective analysis concepts and the VODCA methodology in product-line development and market research are discussed.

Analysis and design of a capsule landing system and surface vehicle control system for Mars exploration

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Sandor, G. N.; Shen, C. N.; Smith, E. V.; Yerazunis, S. W.

1973-01-01

Problems related to the design and control of a mobile planetary vehicle to implement a systematic plan for the exploration of Mars are reported. Problem areas include: vehicle configuration, control, dynamics, systems and propulsion; systems analysis, terrain modeling and path selection; and chemical analysis of specimens. These tasks are summarized: vehicle model design, mathematical model of vehicle dynamics, experimental vehicle dynamics, obstacle negotiation, electrochemical controls, remote control, collapsibility and deployment, construction of a wheel tester, wheel analysis, payload design, system design optimization, effect of design assumptions, accessory optimal design, on-board computer subsystem, laser range measurement, discrete obstacle detection, obstacle detection systems, terrain modeling, path selection system simulation and evaluation, gas chromatograph/mass spectrometer system concepts, and chromatograph model evaluation and improvement.

Numerical algebraic geometry for model selection and its application to the life sciences

PubMed Central

Gross, Elizabeth; Davis, Brent; Ho, Kenneth L.; Bates, Daniel J.

2016-01-01

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology. PMID:27733697

Advanced Computational Methods for Security Constrained Financial Transmission Rights

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalsi, Karanjit; Elbert, Stephen T.; Vlachopoulou, Maria

Financial Transmission Rights (FTRs) are financial insurance tools to help power market participants reduce price risks associated with transmission congestion. FTRs are issued based on a process of solving a constrained optimization problem with the objective to maximize the FTR social welfare under power flow security constraints. Security constraints for different FTR categories (monthly, seasonal or annual) are usually coupled and the number of constraints increases exponentially with the number of categories. Commercial software for FTR calculation can only provide limited categories of FTRs due to the inherent computational challenges mentioned above. In this paper, first an innovative mathematical reformulationmore » of the FTR problem is presented which dramatically improves the computational efficiency of optimization problem. After having re-formulated the problem, a novel non-linear dynamic system (NDS) approach is proposed to solve the optimization problem. The new formulation and performance of the NDS solver is benchmarked against widely used linear programming (LP) solvers like CPLEX™ and tested on both standard IEEE test systems and large-scale systems using data from the Western Electricity Coordinating Council (WECC). The performance of the NDS is demonstrated to be comparable and in some cases is shown to outperform the widely used CPLEX algorithms. The proposed formulation and NDS based solver is also easily parallelizable enabling further computational improvement.« less

Solving fuzzy shortest path problem by genetic algorithm

NASA Astrophysics Data System (ADS)

Syarif, A.; Muludi, K.; Adrian, R.; Gen, M.

2018-03-01

Shortest Path Problem (SPP) is known as one of well-studied fields in the area Operations Research and Mathematical Optimization. It has been applied for many engineering and management designs. The objective is usually to determine path(s) in the network with minimum total cost or traveling time. In the past, the cost value for each arc was usually assigned or estimated as a deteministic value. For some specific real world applications, however, it is often difficult to determine the cost value properly. One way of handling such uncertainty in decision making is by introducing fuzzy approach. With this situation, it will become difficult to solve the problem optimally. This paper presents the investigations on the application of Genetic Algorithm (GA) to a new SPP model in which the cost values are represented as Triangular Fuzzy Number (TFN). We adopts the concept of ranking fuzzy numbers to determine how good the solutions. Here, by giving his/her degree value, the decision maker can determine the range of objective value. This would be very valuable for decision support system in the real world applications.Simulation experiments were carried out by modifying several test problems with 10-25 nodes. It is noted that the proposed approach is capable attaining a good solution with different degree of optimism for the tested problems.

Problem Posing with the Multiplication Table

ERIC Educational Resources Information Center

Dickman, Benjamin

2014-01-01

Mathematical problem posing is an important skill for teachers of mathematics, and relates readily to mathematical creativity. This article gives a bit of background information on mathematical problem posing, lists further references to connect problem posing and creativity, and then provides 20 problems based on the multiplication table to be…

Unraveling the Mystery of the Origin of Mathematical Problems: Using a Problem-Posing Framework with Prospective Mathematics Teachers

ERIC Educational Resources Information Center

Contreras, Jose

2007-01-01

In this article, I model how a problem-posing framework can be used to enhance our abilities to systematically generate mathematical problems by modifying the attributes of a given problem. The problem-posing model calls for the application of the following fundamental mathematical processes: proving, reversing, specializing, generalizing, and…

River bathymetry estimation based on the floodplains topography.

NASA Astrophysics Data System (ADS)

Bureš, Luděk; Máca, Petr; Roub, Radek; Pech, Pavel; Hejduk, Tomáš; Novák, Pavel

2017-04-01

Topographic model including River bathymetry (bed topography) is required for hydrodynamic simulation, water quality modelling, flood inundation mapping, sediment transport, ecological and geomorphologic assessments. The most common way to create the river bathymetry is to use of the spatial interpolation of discrete points or cross sections data. The quality of the generated bathymetry is dependent on the quality of the measurements, on the used technology and on the size of input dataset. Extensive measurements are often time consuming and expensive. Other option for creating of the river bathymetry is to use the methods of mathematical modelling. In the presented contribution we created the river bathymetry model. Model is based on the analytical curves. The curves are bent into shape of the cross sections. For the best description of the river bathymetry we need to know the values of the model parameters. For finding these parameters we use of the global optimization methods. The global optimization schemes is based on heuristics inspired by the natural processes. We use new type of DE (differential evolution) for finding the solutions of inverse problems, related to the parameters of mathematical model of river bed surfaces. The presented analysis discuss the dependence of model parameters on the selected characteristics. Selected characteristics are: (1) Topographic characteristics (slope and curvature in the left and right floodplains) determined on the base of DTM 5G (digital terrain model). (2) Optimization scheme. (3) Type of used analytical curves. The novel approach is applied on the three parts of Vltava river in Czech Republic. Each part of the river is described on the base of the point field. The point fields was measured with ADCP probe River surveyor M9. This work was supported by the Technology Agency of the Czech Republic, programme Alpha (project TA04020042 - New technologies bathymetry of rivers and reservoirs to determine their storage capacity and monitor the amount and dynamics of sediments) and Internal Grant Agency of Faculty of Environmental Sciences (CULS) (IGA/20164233). Keywords: bathymetry, global optimization, bed topography References: Merwade, Venkatesh. "Effect of spatial trends on interpolation of river bathymetry." Journal of Hydrology, 371.1, 169-181, 2009. Legleiter, Carl J., and Phaedon C. Kyriakidis. Spatial prediction of river channel topography by kriging. Earth Surface Processes and Landforms, 33.6 , 841-867, 2008. P. Maca and P. Pech and and J. Pavlasek. Comparing the Selected Transfer Functions and Local Optimization Methods for Neural Network Flood Runoff Forecast. Mathematical Problems in Engineering, vol. 2014, Article ID 782351, 10 pages, 2014. M. Jakubcova and P. Maca and and P. Pech. A Comparison of Selected Modifications of the Particle Swarm Optimization Algorithm. Journal of Applied Mathematics, vol. 2014, Article ID 293087, 10 pages, 2014.

Storage assignment optimization in a multi-tier shuttle warehousing system

NASA Astrophysics Data System (ADS)

Wang, Yanyan; Mou, Shandong; Wu, Yaohua

2016-03-01

The current mathematical models for the storage assignment problem are generally established based on the traveling salesman problem(TSP), which has been widely applied in the conventional automated storage and retrieval system(AS/RS). However, the previous mathematical models in conventional AS/RS do not match multi-tier shuttle warehousing systems(MSWS) because the characteristics of parallel retrieval in multiple tiers and progressive vertical movement destroy the foundation of TSP. In this study, a two-stage open queuing network model in which shuttles and a lift are regarded as servers at different stages is proposed to analyze system performance in the terms of shuttle waiting period (SWP) and lift idle period (LIP) during transaction cycle time. A mean arrival time difference matrix for pairwise stock keeping units(SKUs) is presented to determine the mean waiting time and queue length to optimize the storage assignment problem on the basis of SKU correlation. The decomposition method is applied to analyze the interactions among outbound task time, SWP, and LIP. The ant colony clustering algorithm is designed to determine storage partitions using clustering items. In addition, goods are assigned for storage according to the rearranging permutation and the combination of storage partitions in a 2D plane. This combination is derived based on the analysis results of the queuing network model and on three basic principles. The storage assignment method and its entire optimization algorithm method as applied in a MSWS are verified through a practical engineering project conducted in the tobacco industry. The applying results show that the total SWP and LIP can be reduced effectively to improve the utilization rates of all devices and to increase the throughput of the distribution center.

OTIS 3.2 Software Released

NASA Technical Reports Server (NTRS)

Riehl, John P.; Sjauw, Waldy K.

2004-01-01

Trajectory, mission, and vehicle engineers concern themselves with finding the best way for an object to get from one place to another. These engineers rely upon special software to assist them in this. For a number of years, many engineers have used the OTIS program for this assistance. With OTIS, an engineer can fully optimize trajectories for airplanes, launch vehicles like the space shuttle, interplanetary spacecraft, and orbital transfer vehicles. OTIS provides four modes of operation, with each mode providing successively stronger optimization capability. The most powerful mode uses a mathematical method called implicit integration to solve what engineers and mathematicians call the optimal control problem. OTIS 3.2, which was developed at the NASA Glenn Research Center, is the latest release of this industry workhorse and features new capabilities for parameter optimization and mission design. OTIS stands for Optimal Control by Implicit Simulation, and it is implicit integration that makes OTIS so powerful at solving trajectory optimization problems. Why is this so important? The optimization process not only determines how to get from point A to point B, but it can also determine how to do this with the least amount of propellant, with the lightest starting weight, or in the fastest time possible while avoiding certain obstacles along the way. There are numerous conditions that engineers can use to define optimal, or best. OTIS provides a framework for defining the starting and ending points of the trajectory (point A and point B), the constraints on the trajectory (requirements like "avoid these regions where obstacles occur"), and what is being optimized (e.g., minimize propellant). The implicit integration method can find solutions to very complicated problems when there is not a lot of information available about what the optimal trajectory might be. The method was first developed for solving two-point boundary value problems and was adapted for use in OTIS. Implicit integration usually allows OTIS to find solutions to problems much faster than programs that use explicit integration and parametric methods. Consequently, OTIS is best suited to solving very complicated and highly constrained problems.

Dynamic cellular manufacturing system considering machine failure and workload balance

NASA Astrophysics Data System (ADS)

Rabbani, Masoud; Farrokhi-Asl, Hamed; Ravanbakhsh, Mohammad

2018-02-01

Machines are a key element in the production system and their failure causes irreparable effects in terms of cost and time. In this paper, a new multi-objective mathematical model for dynamic cellular manufacturing system (DCMS) is provided with consideration of machine reliability and alternative process routes. In this dynamic model, we attempt to resolve the problem of integrated family (part/machine cell) formation as well as the operators' assignment to the cells. The first objective minimizes the costs associated with the DCMS. The second objective optimizes the labor utilization and, finally, a minimum value of the variance of workload between different cells is obtained by the third objective function. Due to the NP-hard nature of the cellular manufacturing problem, the problem is initially validated by the GAMS software in small-sized problems, and then the model is solved by two well-known meta-heuristic methods including non-dominated sorting genetic algorithm and multi-objective particle swarm optimization in large-scaled problems. Finally, the results of the two algorithms are compared with respect to five different comparison metrics.

Stochastic search, optimization and regression with energy applications

NASA Astrophysics Data System (ADS)

Hannah, Lauren A.

Designing clean energy systems will be an important task over the next few decades. One of the major roadblocks is a lack of mathematical tools to economically evaluate those energy systems. However, solutions to these mathematical problems are also of interest to the operations research and statistical communities in general. This thesis studies three problems that are of interest to the energy community itself or provide support for solution methods: R&D portfolio optimization, nonparametric regression and stochastic search with an observable state variable. First, we consider the one stage R&D portfolio optimization problem to avoid the sequential decision process associated with the multi-stage. The one stage problem is still difficult because of a non-convex, combinatorial decision space and a non-convex objective function. We propose a heuristic solution method that uses marginal project values---which depend on the selected portfolio---to create a linear objective function. In conjunction with the 0-1 decision space, this new problem can be solved as a knapsack linear program. This method scales well to large decision spaces. We also propose an alternate, provably convergent algorithm that does not exploit problem structure. These methods are compared on a solid oxide fuel cell R&D portfolio problem. Next, we propose Dirichlet Process mixtures of Generalized Linear Models (DPGLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression models. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression like CART, Bayesian trees and Gaussian processes. Compared to existing techniques, the DP-GLM provides a single model (and corresponding inference algorithms) that performs well in many regression settings. Finally, we study convex stochastic search problems where a noisy objective function value is observed after a decision is made. There are many stochastic search problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation to take observations from the joint state-outcome distribution and use them to infer the optimal decision for a given query state. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We examine two weighting schemes, kernel-based weights and Dirichlet process-based weights, for use with the solution methods. The weights and solution methods are tested on a synthetic multi-product newsvendor problem and the hour-ahead wind commitment problem. Our results show that in some cases Dirichlet process weights offer substantial benefits over kernel based weights and more generally that nonparametric estimation methods provide good solutions to otherwise intractable problems.

Problem solving in the borderland between mathematics and physics

NASA Astrophysics Data System (ADS)

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization.

Discrete bacteria foraging optimization algorithm for graph based problems - a transition from continuous to discrete

NASA Astrophysics Data System (ADS)

Sur, Chiranjib; Shukla, Anupam

2018-03-01

Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.

Superstructure-based Design and Optimization of Batch Biodiesel Production Using Heterogeneous Catalysts

NASA Astrophysics Data System (ADS)

Nuh, M. Z.; Nasir, N. F.

2017-08-01

Biodiesel as a fuel comprised of mono alkyl esters of long chain fatty acids derived from renewable lipid feedstock, such as vegetable oil and animal fat. Biodiesel production is complex process which need systematic design and optimization. However, no case study using the process system engineering (PSE) elements which are superstructure optimization of batch process, it involves complex problems and uses mixed-integer nonlinear programming (MINLP). The PSE offers a solution to complex engineering system by enabling the use of viable tools and techniques to better manage and comprehend the complexity of the system. This study is aimed to apply the PSE tools for the simulation of biodiesel process and optimization and to develop mathematical models for component of the plant for case A, B, C by using published kinetic data. Secondly, to determine economic analysis for biodiesel production, focusing on heterogeneous catalyst. Finally, the objective of this study is to develop the superstructure for biodiesel production by using heterogeneous catalyst. The mathematical models are developed by the superstructure and solving the resulting mixed integer non-linear model and estimation economic analysis by using MATLAB software. The results of the optimization process with the objective function of minimizing the annual production cost by batch process from case C is 23.2587 million USD. Overall, the implementation a study of process system engineering (PSE) has optimized the process of modelling, design and cost estimation. By optimizing the process, it results in solving the complex production and processing of biodiesel by batch.

The influence of the free space environment on the superlight-weight thermal protection system: conception, methods, and risk analysis

NASA Astrophysics Data System (ADS)

Yatsenko, Vitaliy; Falchenko, Iurii; Fedorchuk, Viktor; Petrushynets, Lidiia

2016-07-01

This report focuses on the results of the EU project "Superlight-weight thermal protection system for space application (LIGHT-TPS)". The bottom line is an analysis of influence of the free space environment on the superlight-weight thermal protection system (TPS). This report focuses on new methods that based on the following models: synergetic, physical, and computational. This report concentrates on four approaches. The first concerns the synergetic approach. The synergetic approach to the solution of problems of self-controlled synthesis of structures and creation of self-organizing technologies is considered in connection with the super-problem of creation of materials with new functional properties. Synergetics methods and mathematical design are considered according to actual problems of material science. The second approach describes how the optimization methods can be used to determine material microstructures with optimized or targeted properties. This technique enables one to find unexpected microstructures with exotic behavior (e.g., negative thermal expansion coefficients). The third approach concerns the dynamic probabilistic risk analysis of TPS l elements with complex characterizations for damages using a physical model of TPS system and a predictable level of ionizing radiation and space weather. Focusing is given mainly on the TPS model, mathematical models for dynamic probabilistic risk assessment and software for the modeling and prediction of the influence of the free space environment. The probabilistic risk assessment method for TPS is presented considering some deterministic and stochastic factors. The last approach concerns results of experimental research of the temperature distribution on the surface of the honeycomb sandwich panel size 150 x 150 x 20 mm at the diffusion welding in vacuum are considered. An equipment, which provides alignment of temperature fields in a product for the formation of equal strength of welded joints is considered. Many tasks in computational materials science can be posed as optimization problems. This technique enables one to find unexpected microstructures with exotic behavior (e.g., negative thermal expansion coefficients). The last approach is concerned with the generation of realizations of materials with specified but limited microstructural information: an intriguing inverse problem of both fundamental and practical importance. Computational models based upon the theories of molecular dynamics or quantum mechanics would enable the prediction and modification of fundamental materials properties. This problem is solved using deterministic and stochastic optimization techniques. The main optimization approaches in the frame of the EU project "Superlight-weight thermal protection system for space application" are discussed. Optimization approach to the alloys for obtaining materials with required properties using modeling techniques and experimental data will be also considered. This report is supported by the EU project "Superlight-weight thermal protection system for space application (LIGHT-TPS)"

Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment

NASA Astrophysics Data System (ADS)

Khan, Muhammad Altaf; Khan, Yasir; Islam, Saeed

2018-03-01

In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R0 < 1. The model is locally as well as globally asymptotically stable at endemic equilibrium when R0 > 1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results.

Optimal solutions for a bio mathematical model for the evolution of smoking habit

NASA Astrophysics Data System (ADS)

Sikander, Waseem; Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tauseef

In this study, we apply Variation of Parameter Method (VPM) coupled with an auxiliary parameter to obtain the approximate solutions for the epidemic model for the evolution of smoking habit in a constant population. Convergence of the developed algorithm, namely VPM with an auxiliary parameter is studied. Furthermore, a simple way is considered for obtaining an optimal value of auxiliary parameter via minimizing the total residual error over the domain of problem. Comparison of the obtained results with standard VPM shows that an auxiliary parameter is very feasible and reliable in controlling the convergence of approximate solutions.

Optimization in modeling the ribs-bounded contour from computer tomography scan

NASA Astrophysics Data System (ADS)

Bilinskas, M. J.; Dzemyda, G.

2016-10-01

In this paper a method for analyzing transversal plane images from computer tomography scans is presented. A mathematical model that describes the ribs-bounded contour was created and the problem of approximation is solved by finding out the optimal parameters of the model in the least-squares sense. Such model would be useful in registration of images independently on the patient position on the bed and on the radio-contrast agent injection. We consider the slices, where ribs are visible, because many important internal organs are located here: liver, heart, stomach, pancreas, lung, etc.

Sizing of complex structure by the integration of several different optimal design algorithms

NASA Technical Reports Server (NTRS)

Sobieszczanski, J.

1974-01-01

Practical design of large-scale structures can be accomplished with the aid of the digital computer by bringing together in one computer program algorithms of nonlinear mathematical programing and optimality criteria with weight-strength and other so-called engineering methods. Applications of this approach to aviation structures are discussed with a detailed description of how the total problem of structural sizing can be broken down into subproblems for best utilization of each algorithm and for efficient organization of the program into iterative loops. Typical results are examined for a number of examples.

Airborne data measurement system errors reduction through state estimation and control optimization

NASA Astrophysics Data System (ADS)

Sebryakov, G. G.; Muzhichek, S. M.; Pavlov, V. I.; Ermolin, O. V.; Skrinnikov, A. A.

2018-02-01

The paper discusses the problem of airborne data measurement system errors reduction through state estimation and control optimization. The approaches are proposed based on the methods of experiment design and the theory of systems with random abrupt structure variation. The paper considers various control criteria as applied to an aircraft data measurement system. The physics of criteria is explained, the mathematical description and the sequence of steps for each criterion application is shown. The formula is given for airborne data measurement system state vector posterior estimation based for systems with structure variations.

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

Optimal back-to-front airplane boarding.

PubMed

Bachmat, Eitan; Khachaturov, Vassilii; Kuperman, Ran

2013-06-01

The problem of finding an optimal back-to-front airplane boarding policy is explored, using a mathematical model that is related to the 1+1 polynuclear growth model with concave boundary conditions and to causal sets in gravity. We study all airplane configurations and boarding group sizes. Optimal boarding policies for various airplane configurations are presented. Detailed calculations are provided along with simulations that support the main conclusions of the theory. We show that the effectiveness of back-to-front policies undergoes a phase transition when passing from lightly congested airplanes to heavily congested airplanes. The phase transition also affects the nature of the optimal or near-optimal policies. Under what we consider to be realistic conditions, optimal back-to-front policies lead to a modest 8-12% improvement in boarding time over random (no policy) boarding, using two boarding groups. Having more than two groups is not effective.

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

NASA Astrophysics Data System (ADS)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

Optimization of numerical weather/wave prediction models based on information geometry and computational techniques

NASA Astrophysics Data System (ADS)

Galanis, George; Famelis, Ioannis; Kalogeri, Christina

2014-10-01

The last years a new highly demanding framework has been set for environmental sciences and applied mathematics as a result of the needs posed by issues that are of interest not only of the scientific community but of today's society in general: global warming, renewable resources of energy, natural hazards can be listed among them. Two are the main directions that the research community follows today in order to address the above problems: The utilization of environmental observations obtained from in situ or remote sensing sources and the meteorological-oceanographic simulations based on physical-mathematical models. In particular, trying to reach credible local forecasts the two previous data sources are combined by algorithms that are essentially based on optimization processes. The conventional approaches in this framework usually neglect the topological-geometrical properties of the space of the data under study by adopting least square methods based on classical Euclidean geometry tools. In the present work new optimization techniques are discussed making use of methodologies from a rapidly advancing branch of applied Mathematics, the Information Geometry. The latter prove that the distributions of data sets are elements of non-Euclidean structures in which the underlying geometry may differ significantly from the classical one. Geometrical entities like Riemannian metrics, distances, curvature and affine connections are utilized in order to define the optimum distributions fitting to the environmental data at specific areas and to form differential systems that describes the optimization procedures. The methodology proposed is clarified by an application for wind speed forecasts in the Kefaloniaisland, Greece.

Policy Gradient Adaptive Dynamic Programming for Data-Based Optimal Control.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning; Wang, Ding; Lewis, Frank L

2017-10-01

The model-free optimal control problem of general discrete-time nonlinear systems is considered in this paper, and a data-based policy gradient adaptive dynamic programming (PGADP) algorithm is developed to design an adaptive optimal controller method. By using offline and online data rather than the mathematical system model, the PGADP algorithm improves control policy with a gradient descent scheme. The convergence of the PGADP algorithm is proved by demonstrating that the constructed Q -function sequence converges to the optimal Q -function. Based on the PGADP algorithm, the adaptive control method is developed with an actor-critic structure and the method of weighted residuals. Its convergence properties are analyzed, where the approximate Q -function converges to its optimum. Computer simulation results demonstrate the effectiveness of the PGADP-based adaptive control method.

Writing in Groups as a Tool for Non-Routine Problem Solving in First Year University Mathematics

ERIC Educational Resources Information Center

Taylor, J. A.; McDonald, C.

2007-01-01

Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design…

Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

NASA Astrophysics Data System (ADS)

E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

2017-02-01

This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

Pre-service mathematics teachers’ ability in solving well-structured problem

NASA Astrophysics Data System (ADS)

Paradesa, R.

2018-01-01

This study aimed to describe the mathematical problem-solving ability of undergraduate students of mathematics education in solving the well-structured problem. The type of this study was qualitative descriptive. The subjects in this study were 100 undergraduate students of Mathematics Education at one of the private universities in Palembang city. The data in this study was collected through two test items with essay form. The results of this study showed that, from the first problem, only 8% students can solve it, but do not check back again to validate the process. Based on a scoring rubric that follows Polya strategy, their answer satisfied 2 4 2 0 patterns. But, from the second problem, 45% students satisfied it. This is because the second problem imitated from the example that was given in learning process. The average score of undergraduate students mathematical problem-solving ability in solving well-structured problems showed 56.00 with standard deviation was 13.22. It means that, from 0 - 100 scale, undergraduate students mathematical problem-solving ability can be categorized low. From this result, the conclusion was undergraduate students of mathematics education in Palembang still have a problem in solving mathematics well-structured problem.

Research Mathematicians' Practices in Selecting Mathematical Problems

ERIC Educational Resources Information Center

Misfeldt, Morten; Johansen, Mikkel Willum

2015-01-01

Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how mathematicians select and pose problems and discuss to…

Development of a Composite Tailoring Procedure for Airplane Wings

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi

2000-01-01

The quest for finding optimum solutions to engineering problems has existed for a long time. In modern times, the development of optimization as a branch of applied mathematics is regarded to have originated in the works of Newton, Bernoulli and Euler. Venkayya has presented a historical perspective on optimization in [1]. The term 'optimization' is defined by Ashley [2] as a procedure "...which attempts to choose the variables in a design process so as formally to achieve the best value of some performance index while not violating any of the associated conditions or constraints". Ashley presented an extensive review of practical applications of optimization in the aeronautical field till about 1980 [2]. It was noted that there existed an enormous amount of published literature in the field of optimization, but its practical applications in industry were very limited. Over the past 15 years, though, optimization has been widely applied to address practical problems in aerospace design [3-5]. The design of high performance aerospace systems is a complex task. It involves the integration of several disciplines such as aerodynamics, structural analysis, dynamics, and aeroelasticity. The problem involves multiple objectives and constraints pertaining to the design criteria associated with each of these disciplines. Many important trade-offs exist between the parameters involved which are used to define the different disciplines. Therefore, the development of multidisciplinary design optimization (MDO) techniques, in which different disciplines and design parameters are coupled into a closed loop numerical procedure, seems appropriate to address such a complex problem. The importance of MDO in successful design of aerospace systems has been long recognized. Recent developments in this field have been surveyed by Sobieszczanski-Sobieski and Haftka [6].

A new multi-objective optimization model for preventive maintenance and replacement scheduling of multi-component systems

NASA Astrophysics Data System (ADS)

Moghaddam, Kamran S.; Usher, John S.

2011-07-01

In this article, a new multi-objective optimization model is developed to determine the optimal preventive maintenance and replacement schedules in a repairable and maintainable multi-component system. In this model, the planning horizon is divided into discrete and equally-sized periods in which three possible actions must be planned for each component, namely maintenance, replacement, or do nothing. The objective is to determine a plan of actions for each component in the system while minimizing the total cost and maximizing overall system reliability simultaneously over the planning horizon. Because of the complexity, combinatorial and highly nonlinear structure of the mathematical model, two metaheuristic solution methods, generational genetic algorithm, and a simulated annealing are applied to tackle the problem. The Pareto optimal solutions that provide good tradeoffs between the total cost and the overall reliability of the system can be obtained by the solution approach. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.

Pre-Service Teachers' Free and Structured Mathematical Problem Posing

ERIC Educational Resources Information Center

Silber, Steven; Cai, Jinfa

2017-01-01

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

The Role of Expository Writing in Mathematical Problem Solving

ERIC Educational Resources Information Center

Craig, Tracy S.

2016-01-01

Mathematical problem-solving is notoriously difficult to teach in a standard university mathematics classroom. The project on which this article reports aimed to investigate the effect of the writing of explanatory strategies in the context of mathematical problem solving on problem-solving behaviour. This article serves to describe the…

Using Diagrams as Tools for the Solution of Non-Routine Mathematical Problems

ERIC Educational Resources Information Center

Pantziara, Marilena; Gagatsis, Athanasios; Elia, Iliada

2009-01-01

The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…

The Problem-Solving Approach in the Teaching of Number Theory

ERIC Educational Resources Information Center

Toh, Pee Choon; Leong, Yew Hoong; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Tay, Eng Guan; Ho, Foo Him

2014-01-01

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

How Students Process Equations in Solving Quantitative Synthesis Problems? Role of Mathematical Complexity in Students' Mathematical Performance

ERIC Educational Resources Information Center

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-01-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking,…

Multicriteria hierarchical iterative interactive algorithm for organizing operational modes of large heat supply systems

NASA Astrophysics Data System (ADS)

Korotkova, T. I.; Popova, V. I.

2017-11-01

The generalized mathematical model of decision-making in the problem of planning and mode selection providing required heat loads in a large heat supply system is considered. The system is multilevel, decomposed into levels of main and distribution heating networks with intermediate control stages. Evaluation of the effectiveness, reliability and safety of such a complex system is carried out immediately according to several indicators, in particular pressure, flow, temperature. This global multicriteria optimization problem with constraints is decomposed into a number of local optimization problems and the coordination problem. An agreed solution of local problems provides a solution to the global multicriterion problem of decision making in a complex system. The choice of the optimum operational mode of operation of a complex heat supply system is made on the basis of the iterative coordination process, which converges to the coordinated solution of local optimization tasks. The interactive principle of multicriteria task decision-making includes, in particular, periodic adjustment adjustments, if necessary, guaranteeing optimal safety, reliability and efficiency of the system as a whole in the process of operation. The degree of accuracy of the solution, for example, the degree of deviation of the internal air temperature from the required value, can also be changed interactively. This allows to carry out adjustment activities in the best way and to improve the quality of heat supply to consumers. At the same time, an energy-saving task is being solved to determine the minimum required values of heads at sources and pumping stations.

Dual methods and approximation concepts in structural synthesis

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins.

Compressed modes for variational problems in mathematical physics and compactly supported multiresolution basis for the Laplace operator

NASA Astrophysics Data System (ADS)

Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2014-03-01

We will describe a general formalism for obtaining spatially localized (``sparse'') solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an L1 regularization term to the variational principle, which is shown to yield solutions with compact support (``compressed modes''). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. In addition, we introduce an L1 regularized variational framework for developing a spatially localized basis, compressed plane waves (CPWs), that spans the eigenspace of a differential operator, for instance, the Laplace operator. Our approach generalizes the concept of plane waves to an orthogonal real-space basis with multiresolution capabilities. Supported by NSF Award DMR-1106024 (VO), DOE Contract No. DE-FG02-05ER25710 (RC) and ONR Grant No. N00014-11-1-719 (SO).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burchett, Deon L.; Chen, Richard Li-Yang; Phillips, Cynthia A.

This report summarizes the work performed under the project project Next-Generation Algo- rithms for Assessing Infrastructure Vulnerability and Optimizing System Resilience. The goal of the project was to improve mathematical programming-based optimization technology for in- frastructure protection. In general, the owner of a network wishes to design a network a network that can perform well when certain transportation channels are inhibited (e.g. destroyed) by an adversary. These are typically bi-level problems where the owner designs a system, an adversary optimally attacks it, and then the owner can recover by optimally using the remaining network. This project funded three years ofmore » Deon Burchett's graduate research. Deon's graduate advisor, Professor Jean-Philippe Richard, and his Sandia advisors, Richard Chen and Cynthia Phillips, supported Deon on other funds or volunteer time. This report is, therefore. essentially a replication of the Ph.D. dissertation it funded [12] in a format required for project documentation. The thesis had some general polyhedral research. This is the study of the structure of the feasi- ble region of mathematical programs, such as integer programs. For example, an integer program optimizes a linear objective function subject to linear constraints, and (nonlinear) integrality con- straints on the variables. The feasible region without the integrality constraints is a convex polygon. Careful study of additional valid constraints can significantly improve computational performance. Here is the abstract from the dissertation: We perform a polyhedral study of a multi-commodity generalization of variable upper bound flow models. In particular, we establish some relations between facets of single- and multi- commodity models. We then introduce a new family of inequalities, which generalizes traditional flow cover inequalities to the multi-commodity context. We present encouraging numerical results. We also consider the directed edge-failure resilient network design problem (DRNDP). This problem entails the design of a directed multi-commodity flow network that is capable of fulfilling a specified percentage of demands in the event that any G arcs are destroyed, where G is a constant parameter. We present a formulation of DRNDP and solve it in a branch-column-cut framework. We present computational results.« less

Modeling and Reduction With Applications to Semiconductor Processing

DTIC Science & Technology

1999-01-01

smoothies ,” as they kept my energy level high without resorting to coffee (the beverage of choice, it seems, for graduate students). My advisor gave me all...with POC data, and balancing approach. . . . . . . . . . . . . . . . 312 xii LIST OF FIGURES 1.1 General state-space model reduction methodology ...reduction problem, then, is one of finding a systematic methodology within a given mathematical framework to produce an efficient or optimal trade-off of

Multi-Criteria Optimization of the Deployment of a Grid for Rural Electrification Based on a Heuristic Method

NASA Astrophysics Data System (ADS)

Ortiz-Matos, L.; Aguila-Tellez, A.; Hincapié-Reyes, R. C.; González-Sanchez, J. W.

2017-07-01

In order to design electrification systems, recent mathematical models solve the problem of location, type of electrification components, and the design of possible distribution microgrids. However, due to the amount of points to be electrified increases, the solution to these models require high computational times, thereby becoming unviable practice models. This study posed a new heuristic method for the electrification of rural areas in order to solve the problem. This heuristic algorithm presents the deployment of rural electrification microgrids in the world, by finding routes for optimal placement lines and transformers in transmission and distribution microgrids. The challenge is to obtain a display with equity in losses, considering the capacity constraints of the devices and topology of the land at minimal economic cost. An optimal scenario ensures the electrification of all neighbourhoods to a minimum investment cost in terms of the distance between electric conductors and the amount of transformation devices.

Optimizing Cellular Networks Enabled with Renewal Energy via Strategic Learning.

PubMed

Sohn, Insoo; Liu, Huaping; Ansari, Nirwan

2015-01-01

An important issue in the cellular industry is the rising energy cost and carbon footprint due to the rapid expansion of the cellular infrastructure. Greening cellular networks has thus attracted attention. Among the promising green cellular network techniques, the renewable energy-powered cellular network has drawn increasing attention as a critical element towards reducing carbon emissions due to massive energy consumption in the base stations deployed in cellular networks. Game theory is a branch of mathematics that is used to evaluate and optimize systems with multiple players with conflicting objectives and has been successfully used to solve various problems in cellular networks. In this paper, we model the green energy utilization and power consumption optimization problem of a green cellular network as a pilot power selection strategic game and propose a novel distributed algorithm based on a strategic learning method. The simulation results indicate that the proposed algorithm achieves correlated equilibrium of the pilot power selection game, resulting in optimum green energy utilization and power consumption reduction.

Effective algorithm for solving complex problems of production control and of material flows control of industrial enterprise

NASA Astrophysics Data System (ADS)

Mezentsev, Yu A.; Baranova, N. V.

2018-05-01

A universal economical and mathematical model designed for determination of optimal strategies for managing subsystems (components of subsystems) of production and logistics of enterprises is considered. Declared universality allows taking into account on the system level both production components, including limitations on the ways of converting raw materials and components into sold goods, as well as resource and logical restrictions on input and output material flows. The presented model and generated control problems are developed within the framework of the unified approach that allows one to implement logical conditions of any complexity and to define corresponding formal optimization tasks. Conceptual meaning of used criteria and limitations are explained. The belonging of the generated tasks of the mixed programming with the class of NP is shown. An approximate polynomial algorithm for solving the posed optimization tasks for mixed programming of real dimension with high computational complexity is proposed. Results of testing the algorithm on the tasks in a wide range of dimensions are presented.

Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment

NASA Technical Reports Server (NTRS)

Braun, R. D.; Kroo, I. M.

1995-01-01

Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for large-scale distributed analysis applications. In this approach, a complex problem is hierarchically de- composed along disciplinary boundaries into a number of subproblems which are brought into multidisciplinary agreement by a system-level coordination process. When applied to problems in a multidisciplinary design environment, this scheme has several advantages over traditional solution strategies. These advantageous features include reducing the amount of information transferred between disciplines, the removal of large iteration-loops, allowing the use of different subspace optimizers among the various analysis groups, an analysis framework which is easily parallelized and can operate on heterogenous equipment, and a structural framework that is well-suited for conventional disciplinary organizations. In this article, the collaborative architecture is developed and its mathematical foundation is presented. An example application is also presented which highlights the potential of this method for use in large-scale design applications.

A New Conflict Resolution Method for Multiple Mobile Robots in Cluttered Environments With Motion-Liveness.

PubMed

Shahriari, Mohammadali; Biglarbegian, Mohammad

2018-01-01

This paper presents a new conflict resolution methodology for multiple mobile robots while ensuring their motion-liveness, especially for cluttered and dynamic environments. Our method constructs a mathematical formulation in a form of an optimization problem by minimizing the overall travel times of the robots subject to resolving all the conflicts in their motion. This optimization problem can be easily solved through coordinating only the robots' speeds. To overcome the computational cost in executing the algorithm for very cluttered environments, we develop an innovative method through clustering the environment into independent subproblems that can be solved using parallel programming techniques. We demonstrate the scalability of our approach through performing extensive simulations. Simulation results showed that our proposed method is capable of resolving the conflicts of 100 robots in less than 1.23 s in a cluttered environment that has 4357 intersections in the paths of the robots. We also developed an experimental testbed and demonstrated that our approach can be implemented in real time. We finally compared our approach with other existing methods in the literature both quantitatively and qualitatively. This comparison shows while our approach is mathematically sound, it is more computationally efficient, scalable for very large number of robots, and guarantees the live and smooth motion of robots.

Fuel optimal maneuvers for spacecraft with fixed thrusters

NASA Technical Reports Server (NTRS)

Carter, T. C.

1982-01-01

Several mathematical models, including a minimum integral square criterion problem, were used for the qualitative investigation of fuel optimal maneuvers for spacecraft with fixed thrusters. The solutions consist of intervals of "full thrust" and "coast" indicating that thrusters do not need to be designed as "throttleable" for fuel optimal performance. For the primary model considered, singular solutions occur only if the optimal solution is "pure translation". "Time optimal" singular solutions can be found which consist of intervals of "coast" and "full thrust". The shape of the optimal fuel consumption curve as a function of flight time was found to depend on whether or not the initial state is in the region admitting singular solutions. Comparisons of fuel optimal maneuvers in deep space with those relative to a point in circular orbit indicate that qualitative differences in the solutions can occur. Computation of fuel consumption for certain "pure translation" cases indicates that considerable savings in fuel can result from the fuel optimal maneuvers.

How do open-ended problems promote mathematical creativity? A reflection of bare mathematics problem and contextual problem

NASA Astrophysics Data System (ADS)

Wijaya, A.

2018-03-01

Creativity is often seen as one of the fundamental aspects of character education. As one of the 21st century skills, creativity has also been considered as an important goal of education across the world. This paper reports a study on promoting mathematical creativity through the use of open-ended mathematics problems. A total of 53 undergraduate students participated in the study. These students worked on open-ended problems in two types, i.e. bare mathematics problem and contextual problem. The contextual problem was presented in the form of paper-based and Geogebra-based. The students’ works were analysed qualitatively in order to describe how students’ mathematical creativity developed. It was found that the open-ended problems successfully promote students’ creativity as indicated by various solutions or strategies that were used by students to solve the problems. The analysis of students’ works show that students’ creativity developed through three kinds of exploration, i. e. (1) exploration of contexts, (2) exploration of software features, and (3) exploration of mathematics concepts. The use of metacognitive questioning was found to be helpful to develop the first two explorations into mathematical exploration.

Product modular design incorporating preventive maintenance issues

NASA Astrophysics Data System (ADS)

Gao, Yicong; Feng, Yixiong; Tan, Jianrong

2016-03-01

Traditional modular design methods lead to product maintenance problems, because the module form of a system is created according to either the function requirements or the manufacturing considerations. For solving these problems, a new modular design method is proposed with the considerations of not only the traditional function related attributes, but also the maintenance related ones. First, modularity parameters and modularity scenarios for product modularity are defined. Then the reliability and economic assessment models of product modularity strategies are formulated with the introduction of the effective working age of modules. A mathematical model used to evaluate the difference among the modules of the product so that the optimal module of the product can be established. After that, a multi-objective optimization problem based on metrics for preventive maintenance interval different degrees and preventive maintenance economics is formulated for modular optimization. Multi-objective GA is utilized to rapidly approximate the Pareto set of optimal modularity strategy trade-offs between preventive maintenance cost and preventive maintenance interval difference degree. Finally, a coordinate CNC boring machine is adopted to depict the process of product modularity. In addition, two factorial design experiments based on the modularity parameters are constructed and analyzed. These experiments investigate the impacts of these parameters on the optimal modularity strategies and the structure of module. The research proposes a new modular design method, which may help to improve the maintainability of product in modular design.

Cuckoo search via Levy flights applied to uncapacitated facility location problem

NASA Astrophysics Data System (ADS)

Mesa, Armacheska; Castromayor, Kris; Garillos-Manliguez, Cinmayii; Calag, Vicente

2017-11-01

Facility location problem (FLP) is a mathematical way to optimally locate facilities within a set of candidates to satisfy the requirements of a given set of clients. This study addressed the uncapacitated FLP as it assures that the capacity of every selected facility is finite. Thus, even if the demand is not known, which often is the case, in reality, organizations may still be able to take strategic decisions such as locating the facilities. There are different approaches relevant to the uncapacitated FLP. Here, the cuckoo search via Lévy flight (CS-LF) was used to solve the problem. Though hybrid methods produce better results, this study employed CS-LF to determine first its potential in finding solutions for the problem, particularly when applied to a real-world problem. The method was applied to the data set obtained from a department store in Davao City, Philippines. Results showed that applying CS-LF yielded better facility locations compared to particle swarm optimization and other existing algorithms. Although these results showed that CS-LF is a promising method to solve this particular problem, further studies on other FLP are recommended to establish a strong foundation of the capability of CS-LF in solving FLP.

Optimal planning for the sustainable utilization of municipal solid waste.

PubMed

Santibañez-Aguilar, José Ezequiel; Ponce-Ortega, José María; Betzabe González-Campos, J; Serna-González, Medardo; El-Halwagi, Mahmoud M

2013-12-01

The increasing generation of municipal solid waste (MSW) is a major problem particularly for large urban areas with insufficient landfill capacities and inefficient waste management systems. Several options associated to the supply chain for implementing a MSW management system are available, however to determine the optimal solution several technical, economic, environmental and social aspects must be considered. Therefore, this paper proposes a mathematical programming model for the optimal planning of the supply chain associated to the MSW management system to maximize the economic benefit while accounting for technical and environmental issues. The optimization model simultaneously selects the processing technologies and their location, the distribution of wastes from cities as well as the distribution of products to markets. The problem was formulated as a multi-objective mixed-integer linear programing problem to maximize the profit of the supply chain and the amount of recycled wastes, where the results are showed through Pareto curves that tradeoff economic and environmental aspects. The proposed approach is applied to a case study for the west-central part of Mexico to consider the integration of MSW from several cities to yield useful products. The results show that an integrated utilization of MSW can provide economic, environmental and social benefits. Copyright © 2013 Elsevier Ltd. All rights reserved.

Inferring neural activity from BOLD signals through nonlinear optimization.

PubMed

Vakorin, Vasily A; Krakovska, Olga O; Borowsky, Ron; Sarty, Gordon E

2007-11-01

The blood oxygen level-dependent (BOLD) fMRI signal does not measure neuronal activity directly. This fact is a key concern for interpreting functional imaging data based on BOLD. Mathematical models describing the path from neural activity to the BOLD response allow us to numerically solve the inverse problem of estimating the timing and amplitude of the neuronal activity underlying the BOLD signal. In fact, these models can be viewed as an advanced substitute for the impulse response function. In this work, the issue of estimating the dynamics of neuronal activity from the observed BOLD signal is considered within the framework of optimization problems. The model is based on the extended "balloon" model and describes the conversion of neuronal signals into the BOLD response through the transitional dynamics of the blood flow-inducing signal, cerebral blood flow, cerebral blood volume and deoxyhemoglobin concentration. Global optimization techniques are applied to find a control input (the neuronal activity and/or the biophysical parameters in the model) that causes the system to follow an admissible solution to minimize discrepancy between model and experimental data. As an alternative to a local linearization (LL) filtering scheme, the optimization method escapes the linearization of the transition system and provides a possibility to search for the global optimum, avoiding spurious local minima. We have found that the dynamics of the neural signals and the physiological variables as well as the biophysical parameters can be robustly reconstructed from the BOLD responses. Furthermore, it is shown that spiking off/on dynamics of the neural activity is the natural mathematical solution of the model. Incorporating, in addition, the expansion of the neural input by smooth basis functions, representing a low-pass filtering, allows us to model local field potential (LFP) solutions instead of spiking solutions.

Analysis and design of a capsule landing system and surface vehicle control system for Mars exporation

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Sandor, G. N.; Shen, C. N.; Smith, E. J.; Yerazunis, S. W.

1972-01-01

The problems related to the design and control of a mobile planetary vehicle to implement a systematic plan for the exploration of Mars were investigated. Problem areas receiving attention include: vehicle configuration, control, dynamics, systems and propulsion; systems analysis; navigation, terrain modeling and path selection; and chemical analysis of specimens. The following specific tasks were studied: vehicle model design, mathematical modeling of dynamic vehicle, experimental vehicle dynamics, obstacle negotiation, electromechanical controls, collapsibility and deployment, construction of a wheel tester, wheel analysis, payload design, system design optimization, effect of design assumptions, accessory optimal design, on-board computer subsystem, laser range measurement, discrete obstacle detection, obstacle detection systems, terrain modeling, path selection system simulation and evaluation, gas chromatograph/mass spectrometer system concepts, chromatograph model evaluation and improvement and transport parameter evaluation.

Analysis and design of a capsule landing system and surface vehicle control system for Mars exploration

NASA Technical Reports Server (NTRS)

Frederick, D. K.; Lashmet, P. K.; Sandor, G. N.; Shen, C. N.; Smith, E. J.; Yerazunis, S. W.

1972-01-01

Investigation of problems related to the design and control of a mobile planetary vehicle to implement a systematic plan for the exploration of Mars has been undertaken. Problem areas receiving attention include: vehicle configuration, control, dynamics, systems and propulsion; systems analysis; terrain modeling and path selection; and chemical analysis of specimens. The following specific tasks have been under study: vehicle model design, mathematical modeling of a dynamic vehicle, experimental vehicle dynamics, obstacle negotiation, electromechanical controls, collapsibility and deployment, construction of a wheel tester, wheel analysis, payload design, system design optimization, effect of design assumptions, accessory optimal design, on-board computer sybsystem, laser range measurement, discrete obstacle detection, obstacle detection systems, terrain modeling, path selection system simulation and evaluation, gas chromatograph/mass spectrometer system concepts, chromatograph model evaluation and improvement.

Game theory and extremal optimization for community detection in complex dynamic networks.

PubMed

Lung, Rodica Ioana; Chira, Camelia; Andreica, Anca

2014-01-01

The detection of evolving communities in dynamic complex networks is a challenging problem that recently received attention from the research community. Dynamics clearly add another complexity dimension to the difficult task of community detection. Methods should be able to detect changes in the network structure and produce a set of community structures corresponding to different timestamps and reflecting the evolution in time of network data. We propose a novel approach based on game theory elements and extremal optimization to address dynamic communities detection. Thus, the problem is formulated as a mathematical game in which nodes take the role of players that seek to choose a community that maximizes their profit viewed as a fitness function. Numerical results obtained for both synthetic and real-world networks illustrate the competitive performance of this game theoretical approach.

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

The semantic system is involved in mathematical problem solving.

PubMed

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

Stochastic modelling of slow-progressing tumors: Analysis and applications to the cell interplay and control of low grade gliomas

NASA Astrophysics Data System (ADS)

Rodríguez, Clara Rojas; Fernández Calvo, Gabriel; Ramis-Conde, Ignacio; Belmonte-Beitia, Juan

2017-08-01

Tumor-normal cell interplay defines the course of a neoplastic malignancy. The outcome of this dual relation is the ultimate prevailing of one of the cells and the death or retreat of the other. In this paper we study the mathematical principles that underlay one important scenario: that of slow-progressing cancers. For this, we develop, within a stochastic framework, a mathematical model to account for tumor-normal cell interaction in such a clinically relevant situation and derive a number of deterministic approximations from the stochastic model. We consider in detail the existence and uniqueness of the solutions of the deterministic model and study the stability analysis. We then focus our model to the specific case of low grade gliomas, where we introduce an optimal control problem for different objective functionals under the administration of chemotherapy. We derive the conditions for which singular and bang-bang control exist and calculate the optimal control and states.

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

What Is the Problem in Problem-Based Learning in Higher Education Mathematics

ERIC Educational Resources Information Center

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

Learning to Solve Story Problems--Supporting Transitions between Reality and Mathematics

ERIC Educational Resources Information Center

Große, Cornelia S.

2014-01-01

Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical…

Modeling human target acquisition in ground-to-air weapon systems

NASA Technical Reports Server (NTRS)

Phatak, A. V.; Mohr, R. L.; Vikmanis, M.; Wei, K. C.

1982-01-01

The problems associated with formulating and validating mathematical models for describing and predicting human target acquisition response are considered. In particular, the extension of the human observer model to include the acquisition phase as well as the tracking segment is presented. Relationship of the Observer model structure to the more complex Standard Optimal Control model formulation and to the simpler Transfer Function/Noise representation is discussed. Problems pertinent to structural identifiability and the form of the parameterization are elucidated. A systematic approach toward the identification of the observer acquisition model parameters from ensemble tracking error data is presented.

Method of Harmonic Balance in Full-Scale-Model Tests of Electrical Devices

NASA Astrophysics Data System (ADS)

Gorbatenko, N. I.; Lankin, A. M.; Lankin, M. V.

2017-01-01

Methods for determining the weber-ampere characteristics of electrical devices, one of which is based on solution of direct problem of harmonic balance and the other on solution of inverse problem of harmonic balance by the method of full-scale-model tests, are suggested. The mathematical model of the device is constructed using the describing function and simplex optimization methods. The presented results of experimental applications of the method show its efficiency. The advantage of the method is the possibility of application for nondestructive inspection of electrical devices in the processes of their production and operation.

Toward integration of in vivo molecular computing devices: successes and challenges

PubMed Central

Hayat, Sikander; Hinze, Thomas

2008-01-01

The computing power unleashed by biomolecule based massively parallel computational units has been the focus of many interdisciplinary studies that couple state of the art ideas from mathematical logic, theoretical computer science, bioengineering, and nanotechnology to fulfill some computational task. The output can influence, for instance, release of a drug at a specific target, gene expression, cell population, or be a purely mathematical entity. Analysis of the results of several studies has led to the emergence of a general set of rules concerning the implementation and optimization of in vivo computational units. Taking two recent studies on in vivo computing as examples, we discuss the impact of mathematical modeling and simulation in the field of synthetic biology and on in vivo computing. The impact of the emergence of gene regulatory networks and the potential of proteins acting as “circuit wires” on the problem of interconnecting molecular computing device subunits is also highlighted. PMID:19404433

Optimal insecticide-treated bed-net coverage and malaria treatment in a malaria-HIV co-infection model.

PubMed

Mohammed-Awel, Jemal; Numfor, Eric

2017-03-01

We propose and study a mathematical model for malaria-HIV co-infection transmission and control, in which malaria treatment and insecticide-treated nets are incorporated. The existence of a backward bifurcation is established analytically, and the occurrence of such backward bifurcation is influenced by disease-induced mortality, insecticide-treated bed-net coverage and malaria treatment parameters. To further assess the impact of malaria treatment and insecticide-treated bed-net coverage, we formulate an optimal control problem with malaria treatment and insecticide-treated nets as control functions. Using reasonable parameter values, numerical simulations of the optimal control suggest the possibility of eliminating malaria and reducing HIV prevalence significantly, within a short time horizon.

Fuzzy Energy and Reserve Co-optimization With High Penetration of Renewable Energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Cong; Botterud, Audun; Zhou, Zhi

In this study, we propose a fuzzy-based energy and reserve co-optimization model with consideration of high penetration of renewable energy. Under the assumption of a fixed uncertainty set of renewables, a two-stage robust model is proposed for clearing energy and reserves in the first stage and checking the feasibility and robustness of re-dispatches in the second stage. Fuzzy sets and their membership functions are introduced into the optimization model to represent the satisfaction degree of the variable uncertainty sets. The lower bound of the uncertainty set is expressed as fuzzy membership functions. The solutions are obtained by transforming the fuzzymore » mathematical programming formulation into traditional mixed integer linear programming problems.« less

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Xu; Tuo, Rui; Jeff Wu, C. F.

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi- delity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. Here, from simulation results and a real example using finite element analysis,more » our method out-performs the expected improvement (EI) criterion which works for single-accuracy experiments.« less

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

DOE PAGES

He, Xu; Tuo, Rui; Jeff Wu, C. F.

2017-01-31

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi- delity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. Here, from simulation results and a real example using finite element analysis,more » our method out-performs the expected improvement (EI) criterion which works for single-accuracy experiments.« less

Fuzzy Energy and Reserve Co-optimization With High Penetration of Renewable Energy

DOE PAGES

Liu, Cong; Botterud, Audun; Zhou, Zhi; ...

2016-10-21

In this study, we propose a fuzzy-based energy and reserve co-optimization model with consideration of high penetration of renewable energy. Under the assumption of a fixed uncertainty set of renewables, a two-stage robust model is proposed for clearing energy and reserves in the first stage and checking the feasibility and robustness of re-dispatches in the second stage. Fuzzy sets and their membership functions are introduced into the optimization model to represent the satisfaction degree of the variable uncertainty sets. The lower bound of the uncertainty set is expressed as fuzzy membership functions. The solutions are obtained by transforming the fuzzymore » mathematical programming formulation into traditional mixed integer linear programming problems.« less

Simple Example of Backtest Overfitting (SEBO)

DOE Office of Scientific and Technical Information (OSTI.GOV)

In the field of mathematical finance, a "backtest" is the usage of historical market data to assess the performance of a proposed trading strategy. It is a relatively simple matter for a present-day computer system to explore thousands, millions or even billions of variations of a proposed strategy, and pick the best performing variant as the "optimal" strategy "in sample" (i.e., on the input dataset). Unfortunately, such an "optimal" strategy often performs very poorly "out of sample" (i.e. on another dataset), because the parameters of the invest strategy have been oversit to the in-sample data, a situation known as "backtestmore » overfitting". While the mathematics of backtest overfitting has been examined in several recent theoretical studies, here we pursue a more tangible analysis of this problem, in the form of an online simulator tool. Given a input random walk time series, the tool develops an "optimal" variant of a simple strategy by exhaustively exploring all integer parameter values among a handful of parameters. That "optimal" strategy is overfit, since by definition a random walk is unpredictable. Then the tool tests the resulting "optimal" strategy on a second random walk time series. In most runs using our online tool, the "optimal" strategy derived from the first time series performs poorly on the second time series, demonstrating how hard it is not to overfit a backtest. We offer this online tool, "Simple Example of Backtest Overfitting (SEBO)", to facilitate further research in this area.« less

The role of under-determined approximations in engineering and science application

NASA Technical Reports Server (NTRS)

Carpenter, William C.

1992-01-01

There is currently a great deal of interest in using response surfaces in the optimization of aircraft performance. The objective function and/or constraint equations involved in these optimization problems may come from numerous disciplines such as structures, aerodynamics, environmental engineering, etc. In each of these disciplines, the mathematical complexity of the governing equations usually dictates that numerical results be obtained from large computer programs such as a finite element method program. Thus, when performing optimization studies, response surfaces are a convenient way of transferring information from the various disciplines to the optimization algorithm as opposed to bringing all the sundry computer programs together in a massive computer code. Response surfaces offer another advantage in the optimization of aircraft structures. A characteristic of these types of optimization problems is that evaluation of the objective function and response equations (referred to as a functional evaluation) can be very expensive in a computational sense. Because of the computational expense in obtaining functional evaluations, the present study was undertaken to investigate under-determinined approximations. An under-determined approximation is one in which there are fewer training pairs (pieces of information about a function) than there are undetermined parameters (coefficients or weights) associated with the approximation. Both polynomial approximations and neural net approximations were examined. Three main example problems were investigated: (1) a function of one design variable was considered; (2) a function of two design variables was considered; and (3) a 35 bar truss with 4 design variables was considered.

Individualized Math Problems in Percent. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume includes problems concerned with computing percents.…

Individualized Math Problems in Algebra. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic, and contains problems related to diverse vocations. Solutions are provided for all problems. Problems presented in this package concern ratios used in food…

Individualized Math Problems in Fractions. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This package contains problems involving computation with common…

Individualized Math Problems in Geometry. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. The volume contains problems in applied geometry. Measurement of…

Individualized Math Problems in Measurement and Conversion. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume includes problems involving measurement, computation of…

Individualized Math Problems in Integers. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume presents problems involving operations with positive and…

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biros, George

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. Thesemore » include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.« less

Heuristic for Critical Machine Based a Lot Streaming for Two-Stage Hybrid Production Environment

NASA Astrophysics Data System (ADS)

Vivek, P.; Saravanan, R.; Chandrasekaran, M.; Pugazhenthi, R.

2017-03-01

Lot streaming in Hybrid flowshop [HFS] is encountered in many real world problems. This paper deals with a heuristic approach for Lot streaming based on critical machine consideration for a two stage Hybrid Flowshop. The first stage has two identical parallel machines and the second stage has only one machine. In the second stage machine is considered as a critical by valid reasons these kind of problems is known as NP hard. A mathematical model developed for the selected problem. The simulation modelling and analysis were carried out in Extend V6 software. The heuristic developed for obtaining optimal lot streaming schedule. The eleven cases of lot streaming were considered. The proposed heuristic was verified and validated by real time simulation experiments. All possible lot streaming strategies and possible sequence under each lot streaming strategy were simulated and examined. The heuristic consistently yielded optimal schedule consistently in all eleven cases. The identification procedure for select best lot streaming strategy was suggested.

Experimental Design for Estimating Unknown Hydraulic Conductivity in a Confined Aquifer using a Genetic Algorithm and a Reduced Order Model

NASA Astrophysics Data System (ADS)

Ushijima, T.; Yeh, W.

2013-12-01

An optimal experimental design algorithm is developed to select locations for a network of observation wells that provides the maximum information about unknown hydraulic conductivity in a confined, anisotropic aquifer. The design employs a maximal information criterion that chooses, among competing designs, the design that maximizes the sum of squared sensitivities while conforming to specified design constraints. Because that the formulated problem is non-convex and contains integer variables (necessitating a combinatorial search), for a realistically-scaled model, the problem may be difficult, if not impossible, to solve through traditional mathematical programming techniques. Genetic Algorithms (GAs) are designed to search out the global optimum; however because a GA requires a large number of calls to a groundwater model, the formulated optimization problem may still be infeasible to solve. To overcome this, Proper Orthogonal Decomposition (POD) is applied to the groundwater model to reduce its dimension. The information matrix in the full model space can then be searched without solving the full model.

A modular approach to large-scale design optimization of aerospace systems

NASA Astrophysics Data System (ADS)

Hwang, John T.

Gradient-based optimization and the adjoint method form a synergistic combination that enables the efficient solution of large-scale optimization problems. Though the gradient-based approach struggles with non-smooth or multi-modal problems, the capability to efficiently optimize up to tens of thousands of design variables provides a valuable design tool for exploring complex tradeoffs and finding unintuitive designs. However, the widespread adoption of gradient-based optimization is limited by the implementation challenges for computing derivatives efficiently and accurately, particularly in multidisciplinary and shape design problems. This thesis addresses these difficulties in two ways. First, to deal with the heterogeneity and integration challenges of multidisciplinary problems, this thesis presents a computational modeling framework that solves multidisciplinary systems and computes their derivatives in a semi-automated fashion. This framework is built upon a new mathematical formulation developed in this thesis that expresses any computational model as a system of algebraic equations and unifies all methods for computing derivatives using a single equation. The framework is applied to two engineering problems: the optimization of a nanosatellite with 7 disciplines and over 25,000 design variables; and simultaneous allocation and mission optimization for commercial aircraft involving 330 design variables, 12 of which are integer variables handled using the branch-and-bound method. In both cases, the framework makes large-scale optimization possible by reducing the implementation effort and code complexity. The second half of this thesis presents a differentiable parametrization of aircraft geometries and structures for high-fidelity shape optimization. Existing geometry parametrizations are not differentiable, or they are limited in the types of shape changes they allow. This is addressed by a novel parametrization that smoothly interpolates aircraft components, providing differentiability. An unstructured quadrilateral mesh generation algorithm is also developed to automate the creation of detailed meshes for aircraft structures, and a mesh convergence study is performed to verify that the quality of the mesh is maintained as it is refined. As a demonstration, high-fidelity aerostructural analysis is performed for two unconventional configurations with detailed structures included, and aerodynamic shape optimization is applied to the truss-braced wing, which finds and eliminates a shock in the region bounded by the struts and the wing.

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

What is the problem in problem-based learning in higher education mathematics

NASA Astrophysics Data System (ADS)

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

Protocol Analysis of Group Problem Solving in Mathematics: A Cognitive-Metacognitive Framework for Assessment.

ERIC Educational Resources Information Center

Artzt, Alice F.; Armour-Thomas, Eleanor

The roles of cognition and metacognition were examined in the mathematical problem-solving behaviors of students as they worked in small groups. As an outcome, a framework that links the literature of cognitive science and mathematical problem solving was developed for protocol analysis of mathematical problem solving. Within this framework, each…

Mathematical Profiles and Problem Solving Abilities of Mathematically Promising Students

ERIC Educational Resources Information Center

Budak, Ibrahim

2012-01-01

Mathematically promising students are defined as those who have the potential to become the leaders and problem solvers of the future. The purpose of this research is to reveal what problem solving abilities mathematically promising students show in solving non-routine problems and type of profiles they present in the classroom and during problem…

Engaging Future Teachers in Problem-Based Learning with the Park City Mathematics Institute Problems

ERIC Educational Resources Information Center

Pilgrim, Mary E.

2014-01-01

Problem-based learning (PBL) is a pedagogical technique recommended for K-12 mathematics classrooms. However, the mathematics courses in future teachers' degree programs are often lecture based. Students typically learn about problem-based learning in theory, but rarely get to experience it first-hand in their mathematics courses. The premise…

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

ERIC Educational Resources Information Center

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-01-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

2017-01-01

The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

Developing Instruction Materials Based on Joyful PBL to Improve Students Mathematical Representation Ability

ERIC Educational Resources Information Center

Minarni, Ani; Napitupulu, E. Elvis

2017-01-01

Solving problem either within mathematics or beyond is one of the ultimate goal students learn mathematics. It is since mathematics takes role tool as well as vehicle to develop problem solving ability. One of the supporting components to problem solving is mathematical representation ability (MRA). Nowadays, many teachers and researchers find out…

Using the Wonder of Inequalities between Averages for Mathematics Problems Solving

ERIC Educational Resources Information Center

Shaanan, Rachel Mogilevsky; Gordon, Moshe Stupel

2016-01-01

The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…

A Critical Discourse Analysis of Practical Problems in a Foundation Mathematics Course at a South African University

ERIC Educational Resources Information Center

le Roux, Kate; Adler, Jill

2016-01-01

Mathematical problems that make links to the everyday and to disciplines other than mathematics--variously referred to as practical, realistic, real-world or applied problems in the literature--feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this…

An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

A mathematical model of sentimental dynamics accounting for marital dissolution.

PubMed

Rey, José-Manuel

2010-03-31

Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.

Designing a multistage supply chain in cross-stage reverse logistics environments: application of particle swarm optimization algorithms.

PubMed

Chiang, Tzu-An; Che, Z H; Cui, Zhihua

2014-01-01

This study designed a cross-stage reverse logistics course for defective products so that damaged products generated in downstream partners can be directly returned to upstream partners throughout the stages of a supply chain for rework and maintenance. To solve this reverse supply chain design problem, an optimal cross-stage reverse logistics mathematical model was developed. In addition, we developed a genetic algorithm (GA) and three particle swarm optimization (PSO) algorithms: the inertia weight method (PSOA_IWM), V(Max) method (PSOA_VMM), and constriction factor method (PSOA_CFM), which we employed to find solutions to support this mathematical model. Finally, a real case and five simulative cases with different scopes were used to compare the execution times, convergence times, and objective function values of the four algorithms used to validate the model proposed in this study. Regarding system execution time, the GA consumed more time than the other three PSOs did. Regarding objective function value, the GA, PSOA_IWM, and PSOA_CFM could obtain a lower convergence value than PSOA_VMM could. Finally, PSOA_IWM demonstrated a faster convergence speed than PSOA_VMM, PSOA_CFM, and the GA did.

Designing a Multistage Supply Chain in Cross-Stage Reverse Logistics Environments: Application of Particle Swarm Optimization Algorithms

PubMed Central

Chiang, Tzu-An; Che, Z. H.

2014-01-01

This study designed a cross-stage reverse logistics course for defective products so that damaged products generated in downstream partners can be directly returned to upstream partners throughout the stages of a supply chain for rework and maintenance. To solve this reverse supply chain design problem, an optimal cross-stage reverse logistics mathematical model was developed. In addition, we developed a genetic algorithm (GA) and three particle swarm optimization (PSO) algorithms: the inertia weight method (PSOA_IWM), V Max method (PSOA_VMM), and constriction factor method (PSOA_CFM), which we employed to find solutions to support this mathematical model. Finally, a real case and five simulative cases with different scopes were used to compare the execution times, convergence times, and objective function values of the four algorithms used to validate the model proposed in this study. Regarding system execution time, the GA consumed more time than the other three PSOs did. Regarding objective function value, the GA, PSOA_IWM, and PSOA_CFM could obtain a lower convergence value than PSOA_VMM could. Finally, PSOA_IWM demonstrated a faster convergence speed than PSOA_VMM, PSOA_CFM, and the GA did. PMID:24772026

A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution

PubMed Central

Rey, José-Manuel

2010-01-01

Background Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. Methodology/Principal Findings Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. Conclusions/Significance These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law. PMID:20360987

A network-based approach for resistance transmission in bacterial populations.

PubMed

Gehring, Ronette; Schumm, Phillip; Youssef, Mina; Scoglio, Caterina

2010-01-07

Horizontal transfer of mobile genetic elements (conjugation) is an important mechanism whereby resistance is spread through bacterial populations. The aim of our work is to develop a mathematical model that quantitatively describes this process, and to use this model to optimize antimicrobial dosage regimens to minimize resistance development. The bacterial population is conceptualized as a compartmental mathematical model to describe changes in susceptible, resistant, and transconjugant bacteria over time. This model is combined with a compartmental pharmacokinetic model to explore the effect of different plasma drug concentration profiles. An agent-based simulation tool is used to account for resistance transfer occurring when two bacteria are adjacent or in close proximity. In addition, a non-linear programming optimal control problem is introduced to minimize bacterial populations as well as the drug dose. Simulation and optimization results suggest that the rapid death of susceptible individuals in the population is pivotal in minimizing the number of transconjugants in a population. This supports the use of potent antimicrobials that rapidly kill susceptible individuals and development of dosage regimens that maintain effective antimicrobial drug concentrations for as long as needed to kill off the susceptible population. Suggestions are made for experiments to test the hypotheses generated by these simulations.

Modern meta-heuristics based on nonlinear physics processes: A review of models and design procedures

NASA Astrophysics Data System (ADS)

Salcedo-Sanz, S.

2016-10-01

Meta-heuristic algorithms are problem-solving methods which try to find good-enough solutions to very hard optimization problems, at a reasonable computation time, where classical approaches fail, or cannot even been applied. Many existing meta-heuristics approaches are nature-inspired techniques, which work by simulating or modeling different natural processes in a computer. Historically, many of the most successful meta-heuristic approaches have had a biological inspiration, such as evolutionary computation or swarm intelligence paradigms, but in the last few years new approaches based on nonlinear physics processes modeling have been proposed and applied with success. Non-linear physics processes, modeled as optimization algorithms, are able to produce completely new search procedures, with extremely effective exploration capabilities in many cases, which are able to outperform existing optimization approaches. In this paper we review the most important optimization algorithms based on nonlinear physics, how they have been constructed from specific modeling of a real phenomena, and also their novelty in terms of comparison with alternative existing algorithms for optimization. We first review important concepts on optimization problems, search spaces and problems' difficulty. Then, the usefulness of heuristics and meta-heuristics approaches to face hard optimization problems is introduced, and some of the main existing classical versions of these algorithms are reviewed. The mathematical framework of different nonlinear physics processes is then introduced as a preparatory step to review in detail the most important meta-heuristics based on them. A discussion on the novelty of these approaches, their main computational implementation and design issues, and the evaluation of a novel meta-heuristic based on Strange Attractors mutation will be carried out to complete the review of these techniques. We also describe some of the most important application areas, in broad sense, of meta-heuristics, and describe free-accessible software frameworks which can be used to make easier the implementation of these algorithms.

Can Television Enhance Children's Mathematical Problem Solving?

ERIC Educational Resources Information Center

Fisch, Shalom M.; And Others

1994-01-01

A summative evaluation of "Square One TV," an educational mathematics series produced by the Children's Television Workshop, shows that children who regularly viewed the program showed significant improvement in solving unfamiliar, complex mathematical problems, and viewers showed improvement in their mathematical problem-solving ability…

Automatic computation for optimum height planning of apartment buildings to improve solar access

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seong, Yoon-Bok; Kim, Yong-Yee; Seok, Ho-Tae

2011-01-15

The objective of this study is to suggest a mathematical model and an optimal algorithm for determining the height of apartment buildings to satisfy the solar rights of survey buildings or survey housing units. The objective is also to develop an automatic computation model for the optimum height of apartment buildings and then to clarify the performance and expected effects. To accomplish the objective of this study, the following procedures were followed: (1) The necessity of the height planning of obstruction buildings to satisfy the solar rights of survey buildings or survey housing units is demonstrated by analyzing through amore » literature review the recent trend of disputes related to solar rights and to examining the social requirements in terms of solar rights. In addition, the necessity of the automatic computation system for height planning of apartment buildings is demonstrated and a suitable analysis method for this system is chosen by investigating the characteristics of analysis methods for solar rights assessment. (2) A case study on the process of height planning of apartment buildings will be briefly described and the problems occurring in this process will then be examined carefully. (3) To develop an automatic computation model for height planning of apartment buildings, geometrical elements forming apartment buildings are defined by analyzing the geometrical characteristics of apartment buildings. In addition, design factors and regulations required in height planning of apartment buildings are investigated. Based on this knowledge, the methodology and mathematical algorithm to adjust the height of apartment buildings by automatic computation are suggested and probable problems and the ways to resolve these problems are discussed. Finally, the methodology and algorithm for the optimization are suggested. (4) Based on the suggested methodology and mathematical algorithm, the automatic computation model for optimum height of apartment buildings is developed and the developed system is verified through the application of some cases. The effects of the suggested model are then demonstrated quantitatively and qualitatively. (author)« less

A Strategy for Improving US Middle School Student Mathematics Word Problem Solving Performance

NASA Technical Reports Server (NTRS)

Thomas, Valerie L.

2004-01-01

U.S. middle school students have difficulty understanding and solving mathematics word problems. Their mathematics performance on the Third International Mathematics and Science Study (TIMMS) is far below their international peers, and minority students are less likely than high socioeconomic status (SES) White/Asian students to be exposed to higher-level mathematics concepts. Research literature also indicates that when students use both In-School and Out-of-School knowledge and experiences to create authentic mathematics word problems, student achievement improves. This researcher developed a Strategy for improving mathematics problem solving performance and a Professional Development Model (PDM) to effectively implement the Strategy.

An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

NASA Astrophysics Data System (ADS)

Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

2016-02-01

Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

Non Linear Programming (NLP) Formulation for Quantitative Modeling of Protein Signal Transduction Pathways

PubMed Central

Morris, Melody K.; Saez-Rodriguez, Julio; Lauffenburger, Douglas A.; Alexopoulos, Leonidas G.

2012-01-01

Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms. PMID:23226239

Non Linear Programming (NLP) formulation for quantitative modeling of protein signal transduction pathways.

PubMed

Mitsos, Alexander; Melas, Ioannis N; Morris, Melody K; Saez-Rodriguez, Julio; Lauffenburger, Douglas A; Alexopoulos, Leonidas G

2012-01-01

Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms.

Generation of structural topologies using efficient technique based on sorted compliances

NASA Astrophysics Data System (ADS)

Mazur, Monika; Tajs-Zielińska, Katarzyna; Bochenek, Bogdan

2018-01-01

Topology optimization, although well recognized is still widely developed. It has gained recently more attention since large computational ability become available for designers. This process is stimulated simultaneously by variety of emerging, innovative optimization methods. It is observed that traditional gradient-based mathematical programming algorithms, in many cases, are replaced by novel and e cient heuristic methods inspired by biological, chemical or physical phenomena. These methods become useful tools for structural optimization because of their versatility and easy numerical implementation. In this paper engineering implementation of a novel heuristic algorithm for minimum compliance topology optimization is discussed. The performance of the topology generator is based on implementation of a special function utilizing information of compliance distribution within the design space. With a view to cope with engineering problems the algorithm has been combined with structural analysis system Ansys.

Combinatorial Optimization in Project Selection Using Genetic Algorithm

NASA Astrophysics Data System (ADS)

Dewi, Sari; Sawaluddin

2018-01-01

This paper discusses the problem of project selection in the presence of two objective functions that maximize profit and minimize cost and the existence of some limitations is limited resources availability and time available so that there is need allocation of resources in each project. These resources are human resources, machine resources, raw material resources. This is treated as a consideration to not exceed the budget that has been determined. So that can be formulated mathematics for objective function (multi-objective) with boundaries that fulfilled. To assist the project selection process, a multi-objective combinatorial optimization approach is used to obtain an optimal solution for the selection of the right project. It then described a multi-objective method of genetic algorithm as one method of multi-objective combinatorial optimization approach to simplify the project selection process in a large scope.

Impact of structural optimization with aeroelastic/multidisciplinary constraints on helicopter rotor design

NASA Technical Reports Server (NTRS)

Friedmann, Peretz P.

1992-01-01

This paper presents a review of the state-of-the-art in the field of structural optimization when applied to vibration reduction of helicopters in forward flight with aeroelastic and multidisciplinary constraints. It emphasizes the application of the modern approach where the optimization is formulated as a mathematical programming problem and the objective function consists of the vibration levels at the hub and behavior constraints are imposed on the blade frequencies, aeroelastic stability margins as well as on a number of additional ingredients which can have a significant effect on the overall performance and flight mechanics of the helicopter. It is shown that the integrated multidisciplinary optimization of rotorcraft offers the potential for substantial improvements which can be achieved by careful preliminary design and analysis without requiring additional hardware such as rotor vibration absorbers or isolation systems.

Helicopter vibration reduction using structural optimization with aeroelastic/multidisciplinary constraints - A survey

NASA Technical Reports Server (NTRS)

Friedmann, Peretz P.

1991-01-01

This paper presents a survey of the state-of-the-art in the field of structural optimization when applied to vibration reduction of helicopters in forward flight with aeroelastic and multidisciplinary constraints. It emphasizes the application of the modern approach where the optimization is formulated as a mathematical programming problem, the objective function consists of the vibration levels at the hub, and behavior constraints are imposed on the blade frequencies and aeroelastic stability margins, as well as on a number of additional ingredients that can have a significant effect on the overall performance and flight mechanics of the helicopter. It is shown that the integrated multidisciplinary optimization of rotorcraft offers the potential for substantial improvements, which can be achieved by careful preliminary design and analysis without requiring additional hardware such as rotor vibration absorbers of isolation systems.

Optimal pricing and marketing planning for deteriorating items.

PubMed

Moosavi Tabatabaei, Seyed Reza; Sadjadi, Seyed Jafar; Makui, Ahmad

2017-01-01

Optimal pricing and marketing planning plays an essential role in production decisions on deteriorating items. This paper presents a mathematical model for a three-level supply chain, which includes one producer, one distributor and one retailer. The proposed study considers the production of a deteriorating item where demand is influenced by price, marketing expenditure, quality of product and after-sales service expenditures. The proposed model is formulated as a geometric programming with 5 degrees of difficulty and the problem is solved using the recent advances in optimization techniques. The study is supported by several numerical examples and sensitivity analysis is performed to analyze the effects of the changes in different parameters on the optimal solution. The preliminary results indicate that with the change in parameters influencing on demand, inventory holding, inventory deteriorating and set-up costs change and also significantly affect total revenue.

Resolving the multiple sequence alignment problem using biogeography-based optimization with multiple populations.

PubMed

Zemali, El-Amine; Boukra, Abdelmadjid

2015-08-01

The multiple sequence alignment (MSA) is one of the most challenging problems in bioinformatics, it involves discovering similarity between a set of protein or DNA sequences. This paper introduces a new method for the MSA problem called biogeography-based optimization with multiple populations (BBOMP). It is based on a recent metaheuristic inspired from the mathematics of biogeography named biogeography-based optimization (BBO). To improve the exploration ability of BBO, we have introduced a new concept allowing better exploration of the search space. It consists of manipulating multiple populations having each one its own parameters. These parameters are used to build up progressive alignments allowing more diversity. At each iteration, the best found solution is injected in each population. Moreover, to improve solution quality, six operators are defined. These operators are selected with a dynamic probability which changes according to the operators efficiency. In order to test proposed approach performance, we have considered a set of datasets from Balibase 2.0 and compared it with many recent algorithms such as GAPAM, MSA-GA, QEAMSA and RBT-GA. The results show that the proposed approach achieves better average score than the previously cited methods.

An Improved Multi-Objective Programming with Augmented ε-Constraint Method for Hazardous Waste Location-Routing Problems

PubMed Central

Yu, Hao; Solvang, Wei Deng

2016-01-01

Hazardous waste location-routing problems are of importance due to the potential risk for nearby residents and the environment. In this paper, an improved mathematical formulation is developed based upon a multi-objective mixed integer programming approach. The model aims at assisting decision makers in selecting locations for different facilities including treatment plants, recycling plants and disposal sites, providing appropriate technologies for hazardous waste treatment, and routing transportation. In the model, two critical factors are taken into account: system operating costs and risk imposed on local residents, and a compensation factor is introduced to the risk objective function in order to account for the fact that the risk level imposed by one type of hazardous waste or treatment technology may significantly vary from that of other types. Besides, the policy instruments for promoting waste recycling are considered, and their influence on the costs and risk of hazardous waste management is also discussed. The model is coded and calculated in Lingo optimization solver, and the augmented ε-constraint method is employed to generate the Pareto optimal curve of the multi-objective optimization problem. The trade-off between different objectives is illustrated in the numerical experiment. PMID:27258293

An Improved Multi-Objective Programming with Augmented ε-Constraint Method for Hazardous Waste Location-Routing Problems.

PubMed

Yu, Hao; Solvang, Wei Deng

2016-05-31

Hazardous waste location-routing problems are of importance due to the potential risk for nearby residents and the environment. In this paper, an improved mathematical formulation is developed based upon a multi-objective mixed integer programming approach. The model aims at assisting decision makers in selecting locations for different facilities including treatment plants, recycling plants and disposal sites, providing appropriate technologies for hazardous waste treatment, and routing transportation. In the model, two critical factors are taken into account: system operating costs and risk imposed on local residents, and a compensation factor is introduced to the risk objective function in order to account for the fact that the risk level imposed by one type of hazardous waste or treatment technology may significantly vary from that of other types. Besides, the policy instruments for promoting waste recycling are considered, and their influence on the costs and risk of hazardous waste management is also discussed. The model is coded and calculated in Lingo optimization solver, and the augmented ε-constraint method is employed to generate the Pareto optimal curve of the multi-objective optimization problem. The trade-off between different objectives is illustrated in the numerical experiment.

Individualized Math Problems in Ratio and Proportion. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume contains problems involving ratio and proportion. Some…

Individualized Math Problems in Whole Numbers. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this set require computations involving whole numbers.…

Individualized Math Problems in Graphs and Tables. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems involving the construction and interpretation of graphs and…

Individualized Math Problems in Simple Equations. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require solution of linear equations, systems…

Individualized Math Problems in Trigonometry. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require the use of trigonometric and inverse…

Individualized Math Problems in Decimals. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

THis is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume concern use of decimals and are related to the…

Individualized Math Problems in Volume. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this booklet require the computation of volumes of solids,…

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

Multi-objective optimal design of magnetorheological engine mount based on an improved non-dominated sorting genetic algorithm

NASA Astrophysics Data System (ADS)

Zheng, Ling; Duan, Xuwei; Deng, Zhaoxue; Li, Yinong

2014-03-01

A novel flow-mode magneto-rheological (MR) engine mount integrated a diaphragm de-coupler and the spoiler plate is designed and developed to isolate engine and the transmission from the chassis in a wide frequency range and overcome the stiffness in high frequency. A lumped parameter model of the MR engine mount in single degree of freedom system is further developed based on bond graph method to predict the performance of the MR engine mount accurately. The optimization mathematical model is established to minimize the total of force transmissibility over several frequency ranges addressed. In this mathematical model, the lumped parameters are considered as design variables. The maximum of force transmissibility and the corresponding frequency in low frequency range as well as individual lumped parameter are limited as constraints. The multiple interval sensitivity analysis method is developed to select the optimized variables and improve the efficiency of optimization process. An improved non-dominated sorting genetic algorithm (NSGA-II) is used to solve the multi-objective optimization problem. The synthesized distance between the individual in Pareto set and the individual in possible set in engineering is defined and calculated. A set of real design parameters is thus obtained by the internal relationship between the optimal lumped parameters and practical design parameters for the MR engine mount. The program flowchart for the improved non-dominated sorting genetic algorithm (NSGA-II) is given. The obtained results demonstrate the effectiveness of the proposed optimization approach in minimizing the total of force transmissibility over several frequency ranges addressed.

Modelling and Optimizing Mathematics Learning in Children

ERIC Educational Resources Information Center

Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus

2013-01-01

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

Energy-efficient approach to minimizing the energy consumption in an extended job-shop scheduling problem

NASA Astrophysics Data System (ADS)

Tang, Dunbing; Dai, Min

2015-09-01

The traditional production planning and scheduling problems consider performance indicators like time, cost and quality as optimization objectives in manufacturing processes. However, environmentally-friendly factors like energy consumption of production have not been completely taken into consideration. Against this background, this paper addresses an approach to modify a given schedule generated by a production planning and scheduling system in a job shop floor, where machine tools can work at different cutting speeds. It can adjust the cutting speeds of the operations while keeping the original assignment and processing sequence of operations of each job fixed in order to obtain energy savings. First, the proposed approach, based on a mixed integer programming mathematical model, changes the total idle time of the given schedule to minimize energy consumption in the job shop floor while accepting the optimal solution of the scheduling objective, makespan. Then, a genetic-simulated annealing algorithm is used to explore the optimal solution due to the fact that the problem is strongly NP-hard. Finally, the effectiveness of the approach is performed smalland large-size instances, respectively. The experimental results show that the approach can save 5%-10% of the average energy consumption while accepting the optimal solution of the makespan in small-size instances. In addition, the average maximum energy saving ratio can reach to 13%. And it can save approximately 1%-4% of the average energy consumption and approximately 2.4% of the average maximum energy while accepting the near-optimal solution of the makespan in large-size instances. The proposed research provides an interesting point to explore an energy-aware schedule optimization for a traditional production planning and scheduling problem.

A model for the submarine depthkeeping team

NASA Technical Reports Server (NTRS)

Ware, J. R.; Best, J. F.; Bozzi, P. J.; Kleinman, D. W.

1981-01-01

The most difficult task the depthkeeping team must face occurs during periscope-depth operations during which they may be required to maintain a submarine several hundred feet long within a foot of ordered depth and within one-half degree of ordered pitch. The difficulty is compounded by the facts that wave generated forces are extremely high, depth and pitch signals are very noisy and submarine speed is such that overall dynamics are slow. A mathematical simulation of the depthkeeping team based on the optimal control models is described. A solution of the optimal team control problem with an output control restriction (limited display to each controller) is presented.

Application of three controls optimally in a vector-borne disease - a mathematical study

NASA Astrophysics Data System (ADS)

Kar, T. K.; Jana, Soovoojeet

2013-10-01

We have proposed and analyzed a vector-borne disease model with three types of controls for the eradication of the disease. Four different classes for the human population namely susceptible, infected, recovered and vaccinated and two different classes for the vector populations namely susceptible and infected are considered. In the first part of our analysis the disease dynamics are described for fixed controls and some inferences have been drawn regarding the spread of the disease. Next the optimal control problem is formulated and solved considering control parameters as time dependent. Different possible combination of controls are used and their effectiveness are compared by numerical simulation.

WINDOWAC (Wing Design Optimization With Aeroelastic Constraints): Program manual

NASA Technical Reports Server (NTRS)

Haftka, R. T.; Starnes, J. H., Jr.

1974-01-01

User and programer documentation for the WIDOWAC programs is given. WIDOWAC may be used for the design of minimum mass wing structures subjected to flutter, strength, and minimum gage constraints. The wing structure is modeled by finite elements, flutter conditions may be both subsonic and supersonic, and mathematical programing methods are used for the optimization procedure. The user documentation gives general directions on how the programs may be used and describes their limitations; in addition, program input and output are described, and example problems are presented. A discussion of computational algorithms and flow charts of the WIDOWAC programs and major subroutines is also given.

An application of different dioids in public key cryptography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Durcheva, Mariana I., E-mail: mdurcheva66@gmail.com

2014-11-18

Dioids provide a natural framework for analyzing a broad class of discrete event dynamical systems such as the design and analysis of bus and railway timetables, scheduling of high-throughput industrial processes, solution of combinatorial optimization problems, the analysis and improvement of flow systems in communication networks. They have appeared in several branches of mathematics such as functional analysis, optimization, stochastic systems and dynamic programming, tropical geometry, fuzzy logic. In this paper we show how to involve dioids in public key cryptography. The main goal is to create key – exchange protocols based on dioids. Additionally the digital signature scheme ismore » presented.« less

An optimal brain can be composed of conflicting agents

PubMed Central

Livnat, Adi; Pippenger, Nicholas

2006-01-01

Many behaviors have been attributed to internal conflict within the animal and human mind. However, internal conflict has not been reconciled with evolutionary principles, in that it appears maladaptive relative to a seamless decision-making process. We study this problem through a mathematical analysis of decision-making structures. We find that, under natural physiological limitations, an optimal decision-making system can involve “selfish” agents that are in conflict with one another, even though the system is designed for a single purpose. It follows that conflict can emerge within a collective even when natural selection acts on the level of the collective only. PMID:16492775

Building a Career Mathematics File: Challenging Students to Find the Importance of Mathematics in a Variety of Occupations

ERIC Educational Resources Information Center

Keleher, Lori A.

2006-01-01

The Career Mathematics file is an occupational problem-solving system, which includes a wide range of mathematical problems and solutions, collected from various resources and helps students establish connections between mathematics and their environment. The study shows that the problems given can be used as realistic examples to study and…

An Investigation of Relationships between Students' Mathematical Problem-Posing Abilities and Their Mathematical Content Knowledge

ERIC Educational Resources Information Center

Van Harpen, Xianwei Y.; Presmeg, Norma C.

2013-01-01

The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly…

Creativity and Mathematical Problem Posing: An Analysis of High School Students' Mathematical Problem Posing in China and the USA

ERIC Educational Resources Information Center

Van Harpen, Xianwei Y.; Sriraman, Bharath

2013-01-01

In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in…

Recent Trends in Japanese Mathematics Textbooks for Elementary Grades: Supporting Teachers to Teach Mathematics through Problem Solving

ERIC Educational Resources Information Center

Takahashi, Akihiko

2016-01-01

Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

The way adults with orientation to mathematics teaching cope with the solution of everyday real-world problems

NASA Astrophysics Data System (ADS)

Gazit, Avikam; Patkin, Dorit

2012-03-01

The article aims to check the way adults, some who are practicing mathematics teachers at elementary school, some who are academicians making a career change to mathematics teachers at junior high school and the rest who are pre-service mathematics teachers at elementary school, cope with the solution of everyday real-world problems of buying and selling. The findings show that even adults with mathematical background tend to make mistakes in solving everyday real-world problems. Only about 70% of the adults who have an orientation to mathematics solved the sample problem correctly. The lowest percentage of success was demonstrated by the academicians making a career change to junior high school mathematics teachers whereas the highest percentage of success was manifested by pre-service elementary school mathematics teachers. Moreover, the findings illustrate that life experience of the practicing mathematics teachers and, mainly, of the academicians making a career change, who were older than the pre-service teachers, did not facilitate the solution of such a real-world problem. Perhaps the reason resides in the process of mathematics teaching at school, which does not put an emphasis on the solution of everyday real-world problems.

Optimization Parameters of Air-conditioning and Heat Insulation Systems of a Pressurized Cabins of Long-distance Airplanes

NASA Astrophysics Data System (ADS)

Gusev, Sergey A.; Nikolaev, Vladimir N.

2018-01-01

The method for determination of an aircraft compartment thermal condition, based on a mathematical model of a compartment thermal condition was developed. Development of solution techniques for solving heat exchange direct and inverse problems and for determining confidence intervals of parametric identification estimations was carried out. The required performance of air-conditioning, ventilation systems and heat insulation depth of crew and passenger cabins were received.

A new mathematical modeling approach for the energy of threonine molecule

NASA Astrophysics Data System (ADS)

Sahiner, Ahmet; Kapusuz, Gulden; Yilmaz, Nurullah

2017-07-01

In this paper, we propose an improved new methodology in energy conformation problems for finding optimum energy values. First, we construct the Bezier surfaces near local minimizers based on the data obtained from Density Functional Theory (DFT) calculations. Second, we blend the constructed surfaces in order to obtain a single smooth model. Finally, we apply the global optimization algorithm to find two torsion angles those make the energy of the molecule minimum.

Towards a formal semantics for Ada 9X

NASA Technical Reports Server (NTRS)

Guaspari, David; Mchugh, John; Wolfgang, Polak; Saaltink, Mark

1995-01-01

The Ada 9X language precision team was formed during the revisions of Ada 83, with the goal of analyzing the proposed design, identifying problems, and suggesting improvements, through the use of mathematical models. This report defines a framework for formally describing Ada 9X, based on Kahn's 'natural semantics', and applies the framework to portions of the language. The proposals for exceptions and optimization freedoms are also analyzed, using a different technique.

An Analysis of Mathematical Models to Improve Counter-Drug Smuggling Operations

DTIC Science & Technology

2014-09-01

users. The target input file for the optimization algorithm has one segment of one target path on each row. Thus, if a target travels along a path...organization TOS time on station TSP Travelling Salesperson Problem USCG United States Coast Guard USN United States Navy UCONN University...of Connecticut UNCLOS United Nations Convention on Law of the Sea xv EXECUTIVE SUMMARY This research is motivated by the ongoing efforts of the

The influence of optimism and pessimism on student achievement in mathematics

NASA Astrophysics Data System (ADS)

Yates, Shirley M.

2002-11-01

Students' causal attributions are not only fundamental motivational variables but are also critical motivators of their persistence in learning. Optimism, pessimism, and achievement in mathematics were measured in a sample of primary and lower secondary students on two occasions. Although achievement in mathematics was most strongly related to prior achievement and grade level, optimism and pessimism were significant factors. In particular, students with a more generally pessimistic outlook on life had a lower level of achievement in mathematics over time. Gender was not a significant factor in achievement. The implications of these findings are discussed.

A cooperative strategy for parameter estimation in large scale systems biology models.

PubMed

Villaverde, Alejandro F; Egea, Jose A; Banga, Julio R

2012-06-22

Mathematical models play a key role in systems biology: they summarize the currently available knowledge in a way that allows to make experimentally verifiable predictions. Model calibration consists of finding the parameters that give the best fit to a set of experimental data, which entails minimizing a cost function that measures the goodness of this fit. Most mathematical models in systems biology present three characteristics which make this problem very difficult to solve: they are highly non-linear, they have a large number of parameters to be estimated, and the information content of the available experimental data is frequently scarce. Hence, there is a need for global optimization methods capable of solving this problem efficiently. A new approach for parameter estimation of large scale models, called Cooperative Enhanced Scatter Search (CeSS), is presented. Its key feature is the cooperation between different programs ("threads") that run in parallel in different processors. Each thread implements a state of the art metaheuristic, the enhanced Scatter Search algorithm (eSS). Cooperation, meaning information sharing between threads, modifies the systemic properties of the algorithm and allows to speed up performance. Two parameter estimation problems involving models related with the central carbon metabolism of E. coli which include different regulatory levels (metabolic and transcriptional) are used as case studies. The performance and capabilities of the method are also evaluated using benchmark problems of large-scale global optimization, with excellent results. The cooperative CeSS strategy is a general purpose technique that can be applied to any model calibration problem. Its capability has been demonstrated by calibrating two large-scale models of different characteristics, improving the performance of previously existing methods in both cases. The cooperative metaheuristic presented here can be easily extended to incorporate other global and local search solvers and specific structural information for particular classes of problems.

A cooperative strategy for parameter estimation in large scale systems biology models

PubMed Central

2012-01-01

Background Mathematical models play a key role in systems biology: they summarize the currently available knowledge in a way that allows to make experimentally verifiable predictions. Model calibration consists of finding the parameters that give the best fit to a set of experimental data, which entails minimizing a cost function that measures the goodness of this fit. Most mathematical models in systems biology present three characteristics which make this problem very difficult to solve: they are highly non-linear, they have a large number of parameters to be estimated, and the information content of the available experimental data is frequently scarce. Hence, there is a need for global optimization methods capable of solving this problem efficiently. Results A new approach for parameter estimation of large scale models, called Cooperative Enhanced Scatter Search (CeSS), is presented. Its key feature is the cooperation between different programs (“threads”) that run in parallel in different processors. Each thread implements a state of the art metaheuristic, the enhanced Scatter Search algorithm (eSS). Cooperation, meaning information sharing between threads, modifies the systemic properties of the algorithm and allows to speed up performance. Two parameter estimation problems involving models related with the central carbon metabolism of E. coli which include different regulatory levels (metabolic and transcriptional) are used as case studies. The performance and capabilities of the method are also evaluated using benchmark problems of large-scale global optimization, with excellent results. Conclusions The cooperative CeSS strategy is a general purpose technique that can be applied to any model calibration problem. Its capability has been demonstrated by calibrating two large-scale models of different characteristics, improving the performance of previously existing methods in both cases. The cooperative metaheuristic presented here can be easily extended to incorporate other global and local search solvers and specific structural information for particular classes of problems. PMID:22727112

Mathematical Modelling in the Early School Years

ERIC Educational Resources Information Center

English, Lyn D.; Watters, James J.

2005-01-01

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…

Collective intelligence for control of distributed dynamical systems

NASA Astrophysics Data System (ADS)

Wolpert, D. H.; Wheeler, K. R.; Tumer, K.

2000-03-01

We consider the El Farol bar problem, also known as the minority game (W. B. Arthur, The American Economic Review, 84 (1994) 406; D. Challet and Y. C. Zhang, Physica A, 256 (1998) 514). We view it as an instance of the general problem of how to configure the nodal elements of a distributed dynamical system so that they do not "work at cross purposes", in that their collective dynamics avoids frustration and thereby achieves a provided global goal. We summarize a mathematical theory for such configuration applicable when (as in the bar problem) the global goal can be expressed as minimizing a global energy function and the nodes can be expressed as minimizers of local free energy functions. We show that a system designed with that theory performs nearly optimally for the bar problem.

A Heuristic Placement Selection of Live Virtual Machine Migration for Energy-Saving in Cloud Computing Environment

PubMed Central

Zhao, Jia; Hu, Liang; Ding, Yan; Xu, Gaochao; Hu, Ming

2014-01-01

The field of live VM (virtual machine) migration has been a hotspot problem in green cloud computing. Live VM migration problem is divided into two research aspects: live VM migration mechanism and live VM migration policy. In the meanwhile, with the development of energy-aware computing, we have focused on the VM placement selection of live migration, namely live VM migration policy for energy saving. In this paper, a novel heuristic approach PS-ES is presented. Its main idea includes two parts. One is that it combines the PSO (particle swarm optimization) idea with the SA (simulated annealing) idea to achieve an improved PSO-based approach with the better global search's ability. The other one is that it uses the Probability Theory and Mathematical Statistics and once again utilizes the SA idea to deal with the data obtained from the improved PSO-based process to get the final solution. And thus the whole approach achieves a long-term optimization for energy saving as it has considered not only the optimization of the current problem scenario but also that of the future problem. The experimental results demonstrate that PS-ES evidently reduces the total incremental energy consumption and better protects the performance of VM running and migrating compared with randomly migrating and optimally migrating. As a result, the proposed PS-ES approach has capabilities to make the result of live VM migration events more high-effective and valuable. PMID:25251339

A heuristic placement selection of live virtual machine migration for energy-saving in cloud computing environment.

PubMed

Zhao, Jia; Hu, Liang; Ding, Yan; Xu, Gaochao; Hu, Ming

2014-01-01

The field of live VM (virtual machine) migration has been a hotspot problem in green cloud computing. Live VM migration problem is divided into two research aspects: live VM migration mechanism and live VM migration policy. In the meanwhile, with the development of energy-aware computing, we have focused on the VM placement selection of live migration, namely live VM migration policy for energy saving. In this paper, a novel heuristic approach PS-ES is presented. Its main idea includes two parts. One is that it combines the PSO (particle swarm optimization) idea with the SA (simulated annealing) idea to achieve an improved PSO-based approach with the better global search's ability. The other one is that it uses the Probability Theory and Mathematical Statistics and once again utilizes the SA idea to deal with the data obtained from the improved PSO-based process to get the final solution. And thus the whole approach achieves a long-term optimization for energy saving as it has considered not only the optimization of the current problem scenario but also that of the future problem. The experimental results demonstrate that PS-ES evidently reduces the total incremental energy consumption and better protects the performance of VM running and migrating compared with randomly migrating and optimally migrating. As a result, the proposed PS-ES approach has capabilities to make the result of live VM migration events more high-effective and valuable.

Exploring Primary Student's Problem-Solving Ability by Doing Tasks Like PISA's Question

ERIC Educational Resources Information Center

Novita, Rita; Zulkardi; Hartono, Yusuf

2012-01-01

Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term "problem solving" refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development. In addition, the contextual problem…

On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

ERIC Educational Resources Information Center

Koichu, Boris

2010-01-01

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

ERIC Educational Resources Information Center

Inoue, Noriyuki

2008-01-01

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…