Evaluating the impact of AND/OR search on 0-1 integer linear programming
Dechter, R.
2010-01-01
AND/OR search spaces accommodate advanced algorithmic schemes for graphical models which can exploit the structure of the model. We extend and evaluate the depth-first and best-first AND/OR search algorithms to solving 0-1 Integer Linear Programs (0-1 ILP) within this framework. We also include a class of dynamic variable ordering heuristics while exploring an AND/OR search tree for 0-1 ILPs. We demonstrate the effectiveness of these search algorithms on a variety of benchmarks, including real-world combinatorial auctions, random uncapacitated warehouse location problems and MAX-SAT instances. PMID:21052484
Detection of code spread OFDM based on 0-1 integer quadratic programming
NASA Astrophysics Data System (ADS)
Elghariani, Ali; Zoltowski, Michael D.
2012-05-01
In this paper we introduce Integer Quadratic Programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose combined preprocessing steps that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The first step in this combination is to detect as much as possible symbols using procedures presented in [9], which is basically based on the gradient of quadratic function. The second step detects the undetected symbols from the first step using MMSE estimator. The result of the latter step will be used to predict the initial upper bound of the BB algorithm. Simulation results show that the proposed preprocessing combination when applied prior to BB provides optimal performance with a significantly reduced computational complexity.
A Structural Connection between Linear and 0-1 Integer Linear Formulations
ERIC Educational Resources Information Center
Adlakha, V.; Kowalski, K.
2007-01-01
The connection between linear and 0-1 integer linear formulations has attracted the attention of many researchers. The main reason triggering this interest has been an availability of efficient computer programs for solving pure linear problems including the transportation problem. Also the optimality of linear problems is easily verifiable…
Resupply Scheduler Program Using Integer Optimization
NASA Technical Reports Server (NTRS)
Viterna, L. A.; Reed, D. M.
1994-01-01
Resupply Scheduling Modeler (RSM) fully menu-driven computer program using integer programming techniques to determine optimum schedule for replacing components on or before ends of fixed replacement periods. Written to analyze electrical power system on Space Station Freedom, also used to model resupply of almost any system subject to user-defined constraints on resources. Lifetimes of components, assembly schedules, and other constraints taken into account. Written in APL2(R).
Solving Integer Programming Problems by Using Artificial Bee Colony Algorithm
NASA Astrophysics Data System (ADS)
Akay, Bahriye; Karaboga, Dervis
This paper presents a study that applies the Artificial Bee Colony algorithm to integer programming problems and compares its performance with those of Particle Swarm Optimization algorithm variants and Branch and Bound technique presented to the literature. In order to cope with integer programming problems, in neighbour solution production unit, solutions are truncated to the nearest integer values. The experimental results show that Artificial Bee Colony algorithm can handle integer programming problems efficiently and Artificial Bee Colony algorithm can be considered to be very robust by the statistics calculated such as mean, median, standard deviation.
Optimizing a Library's Loan Policy: An Integer Programming Approach.
ERIC Educational Resources Information Center
Al-Fares, Hesham K.
1998-01-01
Discusses the length of library loan periods and the number of books allowed to be borrowed. An integer programming model is formulated whose solution yields the optimum user satisfaction, and a case study conducted at King Fahd University of Petroleum and Minerals (Saudi Arabia) is presented. (Author/LRW)
Currency Arbitrage Detection Using a Binary Integer Programming Model
ERIC Educational Resources Information Center
Soon, Wanmei; Ye, Heng-Qing
2011-01-01
In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this…
Investigating Integer Restrictions in Linear Programming
ERIC Educational Resources Information Center
Edwards, Thomas G.; Chelst, Kenneth R.; Principato, Angela M.; Wilhelm, Thad L.
2015-01-01
Linear programming (LP) is an application of graphing linear systems that appears in many Algebra 2 textbooks. Although not explicitly mentioned in the Common Core State Standards for Mathematics, linear programming blends seamlessly into modeling with mathematics, the fourth Standard for Mathematical Practice (CCSSI 2010, p. 7). In solving a…
Orbital rendezvous mission planning using mixed integer nonlinear programming
NASA Astrophysics Data System (ADS)
Zhang, Jin; Tang, Guo-jin; Luo, Ya-Zhong; Li, Hai-yang
2011-04-01
The rendezvous and docking mission is usually divided into several phases, and the mission planning is performed phase by phase. A new planning method using mixed integer nonlinear programming, which investigates single phase parameters and phase connecting parameters simultaneously, is proposed to improve the rendezvous mission's overall performance. The design variables are composed of integers and continuous-valued numbers. The integer part consists of the parameters for station-keeping and sensor-switching, the number of maneuvers in each rendezvous phase and the number of repeating periods to start the rendezvous mission. The continuous part consists of the orbital transfer time and the station-keeping duration. The objective function is a combination of the propellant consumed, the sun angle which represents the power available, and the terminal precision of each rendezvous phase. The operational requirements for the spacecraft-ground communication, sun illumination and the sensor transition are considered. The simple genetic algorithm, which is a combination of the integer-coded and real-coded genetic algorithm, is chosen to obtain the optimal solution. A practical rendezvous mission planning problem is solved by the proposed method. The results show that the method proposed can solve the integral rendezvous mission planning problem effectively, and the solution obtained can satisfy the operational constraints and has a good overall performance.
Currency arbitrage detection using a binary integer programming model
NASA Astrophysics Data System (ADS)
Soon, Wanmei; Ye, Heng-Qing
2011-04-01
In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this work, students can learn to link several types of basic optimization models, namely linear programming, integer programming and network models, and apply the well-known sensitivity analysis procedure to accommodate realistic changes in the exchange rates. Beginning with a BIP model, we discuss how it can be reduced to an equivalent but considerably simpler model, where an efficient algorithm can be applied to find the arbitrages and incorporate the sensitivity analysis procedure. A simple comparison is then made with a different arbitrage detection model. This exercise helps students learn to apply basic Operations Research concepts to a practical real-life example, and provides insights into the processes involved in Operations Research model formulations.
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.
Split diversity in constrained conservation prioritization using integer linear programming
Chernomor, Olga; Minh, Bui Quang; Forest, Félix; Klaere, Steffen; Ingram, Travis; Henzinger, Monika; von Haeseler, Arndt
2015-01-01
Phylogenetic diversity (PD) is a measure of biodiversity based on the evolutionary history of species. Here, we discuss several optimization problems related to the use of PD, and the more general measure split diversity (SD), in conservation prioritization. Depending on the conservation goal and the information available about species, one can construct optimization routines that incorporate various conservation constraints. We demonstrate how this information can be used to select sets of species for conservation action. Specifically, we discuss the use of species' geographic distributions, the choice of candidates under economic pressure, and the use of predator–prey interactions between the species in a community to define viability constraints. Despite such optimization problems falling into the area of NP hard problems, it is possible to solve them in a reasonable amount of time using integer programming. We apply integer linear programming to a variety of models for conservation prioritization that incorporate the SD measure. We exemplarily show the results for two data sets: the Cape region of South Africa and a Caribbean coral reef community. Finally, we provide user-friendly software at http://www.cibiv.at/software/pda. PMID:25893087
Ellrott, Kyle; Guo, Jun-tao; Olman, Victor; Xu, Ying
2006-01-01
Integer programming is a combinatorial optimization method that has been successfully applied to the protein threading problem. We seek to expand the model optimized by this technique to allow for a more accurate description of protein threading. We have developed and implemented an expanded model of integer programming that has the capability to model secondary structure element deletion, which was not possible in previous version of integer programming based optimization. PMID:17503397
Validation and assessment of integer programming sensor placement models.
Uber, James G.; Hart, William Eugene; Watson, Jean-Paul; Phillips, Cynthia Ann; Berry, Jonathan W.
2005-02-01
We consider the accuracy of predictions made by integer programming (IP) models of sensor placement for water security applications. We have recently shown that IP models can be used to find optimal sensor placements for a variety of different performance criteria (e.g. minimize health impacts and minimize time to detection). However, these models make a variety of simplifying assumptions that might bias the final solution. We show that our IP modeling assumptions are similar to models developed for other sensor placement methodologies, and thus IP models should give similar predictions. However, this discussion highlights that there are significant differences in how temporal effects are modeled for sensor placement. We describe how these modeling assumptions can impact sensor placements.
Reconstructing cerebrovascular networks under local physiological constraints by integer programming
Rempfler, Markus; Schneider, Matthias; Ielacqua, Giovanna D.; Xiao, Xianghui; Stock, Stuart R.; Klohs, Jan; Szekely, Gabor; Andres, Bjoern; Menze, Bjoern H.
2015-04-23
We introduce a probabilistic approach to vessel network extraction that enforces physiological constraints on the vessel structure. The method accounts for both image evidence and geometric relationships between vessels by solving an integer program, which is shown to yield the maximum a posteriori (MAP) estimate to the probabilistic model. Starting from an over-connected network, it is pruning vessel stumps and spurious connections by evaluating the local geometry and the global connectivity of the graph. We utilize a high-resolution micro computed tomography (µCT) dataset of a cerebrovascular corrosion cast to obtain a reference network and learn the prior distributions of our probabilistic model. As a result, we perform experiments on micro magnetic resonance angiography (µMRA) images of mouse brains and discuss properties of the networks obtained under different tracking and pruning approaches.
Reconstructing cerebrovascular networks under local physiological constraints by integer programming
Rempfler, Markus; Schneider, Matthias; Ielacqua, Giovanna D.; Xiao, Xianghui; Stock, Stuart R.; Klohs, Jan; Szekely, Gabor; Andres, Bjoern; Menze, Bjoern H.
2015-04-23
We introduce a probabilistic approach to vessel network extraction that enforces physiological constraints on the vessel structure. The method accounts for both image evidence and geometric relationships between vessels by solving an integer program, which is shown to yield the maximum a posteriori (MAP) estimate to the probabilistic model. Starting from an over-connected network, it is pruning vessel stumps and spurious connections by evaluating the local geometry and the global connectivity of the graph. We utilize a high-resolution micro computed tomography (µCT) dataset of a cerebrovascular corrosion cast to obtain a reference network and learn the prior distributions of ourmore » probabilistic model. As a result, we perform experiments on micro magnetic resonance angiography (µMRA) images of mouse brains and discuss properties of the networks obtained under different tracking and pruning approaches.« less
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.
ERIC Educational Resources Information Center
Han, Kyung T.; Rudner, Lawrence M.
2014-01-01
This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…
Fish Processed Production Planning Using Integer Stochastic Programming Model
NASA Astrophysics Data System (ADS)
Firmansyah, Mawengkang, Herman
2011-06-01
Fish and its processed products are the most affordable source of animal protein in the diet of most people in Indonesia. The goal in production planning is to meet customer demand over a fixed time horizon divided into planning periods by optimizing the trade-off between economic objectives such as production cost and customer satisfaction level. The major decisions are production and inventory levels for each product and the number of workforce in each planning period. In this paper we consider the management of small scale traditional business at North Sumatera Province which performs processing fish into several local seafood products. The inherent uncertainty of data (e.g. demand, fish availability), together with the sequential evolution of data over time leads the production planning problem to a nonlinear mixed-integer stochastic programming model. We use scenario generation based approach and feasible neighborhood search for solving the model. The results which show the amount of each fish processed product and the number of workforce needed in each horizon planning are presented.
Accurate construction of consensus genetic maps via integer linear programming.
Wu, Yonghui; Close, Timothy J; Lonardi, Stefano
2011-01-01
We study the problem of merging genetic maps, when the individual genetic maps are given as directed acyclic graphs. The computational problem is to build a consensus map, which is a directed graph that includes and is consistent with all (or, the vast majority of) the markers in the input maps. However, when markers in the individual maps have ordering conflicts, the resulting consensus map will contain cycles. Here, we formulate the problem of resolving cycles in the context of a parsimonious paradigm that takes into account two types of errors that may be present in the input maps, namely, local reshuffles and global displacements. The resulting combinatorial optimization problem is, in turn, expressed as an integer linear program. A fast approximation algorithm is proposed, and an additional speedup heuristic is developed. Our algorithms were implemented in a software tool named MERGEMAP which is freely available for academic use. An extensive set of experiments shows that MERGEMAP consistently outperforms JOINMAP, which is the most popular tool currently available for this task, both in terms of accuracy and running time. MERGEMAP is available for download at http://www.cs.ucr.edu/~yonghui/mgmap.html. PMID:20479505
An integer programming approach to DNA sequence assembly.
Chang, Youngjung; Sahinidis, Nikolaos V
2011-08-10
De novo sequence assembly is a ubiquitous combinatorial problem in all DNA sequencing technologies. In the presence of errors in the experimental data, the assembly problem is computationally challenging, and its solution may not lead to a unique reconstruct. The enumeration of all alternative solutions is important in drawing a reliable conclusion on the target sequence, and is often overlooked in the heuristic approaches that are currently available. In this paper, we develop an integer programming formulation and global optimization solution strategy to solve the sequence assembly problem with errors in the data. We also propose an efficient technique to identify all alternative reconstructs. When applied to examples of sequencing-by-hybridization, our approach dramatically increases the length of DNA sequences that can be handled with global optimality certificate to over 10,000, which is more than 10 times longer than previously reported. For some problem instances, alternative solutions exhibited a wide range of different ability in reproducing the target DNA sequence. Therefore, it is important to utilize the methodology proposed in this paper in order to obtain all alternative solutions to reliably infer the true reconstruct. These alternative solutions can be used to refine the obtained results and guide the design of further experiments to correctly reconstruct the target DNA sequence. PMID:21864794
Constrained spacecraft reorientation using mixed integer convex programming
NASA Astrophysics Data System (ADS)
Tam, Margaret; Glenn Lightsey, E.
2016-10-01
A constrained attitude guidance (CAG) system is developed using convex optimization to autonomously achieve spacecraft pointing objectives while meeting the constraints imposed by on-board hardware. These constraints include bounds on the control input and slew rate, as well as pointing constraints imposed by the sensors. The pointing constraints consist of inclusion and exclusion cones that dictate permissible orientations of the spacecraft in order to keep objects in or out of the field of view of the sensors. The optimization scheme drives a body vector towards a target inertial vector along a trajectory that consists solely of permissible orientations in order to achieve the desired attitude for a given mission mode. The non-convex rotational kinematics are handled by discretization, which also ensures that the quaternion stays unity norm. In order to guarantee an admissible path, the pointing constraints are relaxed. Depending on how strict the pointing constraints are, the degree of relaxation is tuneable. The use of binary variables permits the inclusion of logical expressions in the pointing constraints in the case that a set of sensors has redundancies. The resulting mixed integer convex programming (MICP) formulation generates a steering law that can be easily integrated into an attitude determination and control (ADC) system. A sample simulation of the system is performed for the Bevo-2 satellite, including disturbance torques and actuator dynamics which are not modeled by the controller. Simulation results demonstrate the robustness of the system to disturbances while meeting the mission requirements with desirable performance characteristics.
Perlinski, Anthony W.
2004-05-21
The software allows for easy setup and testing of a variety of RF Electronic Sensor Platforms (ESPs). The software interprets RF messages from the ESP and displays the information in a graphical user interface. This program is used primarily for testing of the T-1 Electronic Sensor Platform. The software imports Electronic Tag Data files which are created from the Electronic Sensor Platform Programmer (ESPP). The software will automatically add sensors to its database when a RF message s received that the program recognizes. Any data that is generated can be stored to a file for later analysis.
Energy Science and Technology Software Center (ESTSC)
2004-05-21
The software allows for easy setup and testing of a variety of RF Electronic Sensor Platforms (ESPs). The software interprets RF messages from the ESP and displays the information in a graphical user interface. This program is used primarily for testing of the T-1 Electronic Sensor Platform. The software imports Electronic Tag Data files which are created from the Electronic Sensor Platform Programmer (ESPP). The software will automatically add sensors to its database when amore » RF message s received that the program recognizes. Any data that is generated can be stored to a file for later analysis.« less
The portals 4.0.1 network programming interface.
Barrett, Brian W.; Brightwell, Ronald Brian; Pedretti, Kevin Thomas Tauke; Wheeler, Kyle Bruce; Hemmert, Karl Scott; Riesen, Rolf E.; Underwood, Keith Douglas; Maccabe, Arthur Bernard; Hudson, Trammell B.
2013-04-01
This report presents a specification for the Portals 4.0 network programming interface. Portals 4.0 is intended to allow scalable, high-performance network communication between nodes of a parallel computing system. Portals 4.0 is well suited to massively parallel processing and embedded systems. Portals 4.0 represents an adaption of the data movement layer developed for massively parallel processing platforms, such as the 4500-node Intel TeraFLOPS machine. Sandia's Cplant cluster project motivated the development of Version 3.0, which was later extended to Version 3.3 as part of the Cray Red Storm machine and XT line. Version 4.0 is targeted to the next generation of machines employing advanced network interface architectures that support enhanced offload capabilities. 3
IESIP - AN IMPROVED EXPLORATORY SEARCH TECHNIQUE FOR PURE INTEGER LINEAR PROGRAMMING PROBLEMS
NASA Technical Reports Server (NTRS)
Fogle, F. R.
1994-01-01
IESIP, an Improved Exploratory Search Technique for Pure Integer Linear Programming Problems, addresses the problem of optimizing an objective function of one or more variables subject to a set of confining functions or constraints by a method called discrete optimization or integer programming. Integer programming is based on a specific form of the general linear programming problem in which all variables in the objective function and all variables in the constraints are integers. While more difficult, integer programming is required for accuracy when modeling systems with small numbers of components such as the distribution of goods, machine scheduling, and production scheduling. IESIP establishes a new methodology for solving pure integer programming problems by utilizing a modified version of the univariate exploratory move developed by Robert Hooke and T.A. Jeeves. IESIP also takes some of its technique from the greedy procedure and the idea of unit neighborhoods. A rounding scheme uses the continuous solution found by traditional methods (simplex or other suitable technique) and creates a feasible integer starting point. The Hook and Jeeves exploratory search is modified to accommodate integers and constraints and is then employed to determine an optimal integer solution from the feasible starting solution. The user-friendly IESIP allows for rapid solution of problems up to 10 variables in size (limited by DOS allocation). Sample problems compare IESIP solutions with the traditional branch-and-bound approach. IESIP is written in Borland's TURBO Pascal for IBM PC series computers and compatibles running DOS. Source code and an executable are provided. The main memory requirement for execution is 25K. This program is available on a 5.25 inch 360K MS DOS format diskette. IESIP was developed in 1990. IBM is a trademark of International Business Machines. TURBO Pascal is registered by Borland International.
A Mixed Integer Linear Program for Airport Departure Scheduling
NASA Technical Reports Server (NTRS)
Gupta, Gautam; Jung, Yoon Chul
2009-01-01
Aircraft departing from an airport are subject to numerous constraints while scheduling departure times. These constraints include wake-separation constraints for successive departures, miles-in-trail separation for aircraft bound for the same departure fixes, and time-window or prioritization constraints for individual flights. Besides these, emissions as well as increased fuel consumption due to inefficient scheduling need to be included. Addressing all the above constraints in a single framework while allowing for resequencing of the aircraft using runway queues is critical to the implementation of the Next Generation Air Transport System (NextGen) concepts. Prior work on airport departure scheduling has addressed some of the above. However, existing methods use pre-determined runway queues, and schedule aircraft from these departure queues. The source of such pre-determined queues is not explicit, and could potentially be a subjective controller input. Determining runway queues and scheduling within the same framework would potentially result in better scheduling. This paper presents a mixed integer linear program (MILP) for the departure-scheduling problem. The program takes as input the incoming sequence of aircraft for departure from a runway, along with their earliest departure times and an optional prioritization scheme based on time-window of departure for each aircraft. The program then assigns these aircraft to the available departure queues and schedules departure times, explicitly considering wake separation and departure fix restrictions to minimize total delay for all aircraft. The approach is generalized and can be used in a variety of situations, and allows for aircraft prioritization based on operational as well as environmental considerations. We present the MILP in the paper, along with benefits over the first-come-first-serve (FCFS) scheme for numerous randomized problems based on real-world settings. The MILP results in substantially reduced
Molecular solutions to the binary integer programming problem based on DNA computation.
Yeh, Chung-Wei; Chu, Chih-Ping; Wu, Kee-Rong
2006-01-01
Binary optimization is a widely investigated topic in integer linear programming. This study proposes a DNA-based computing algorithm for solving the significantly large binary integer programming (BIP) problem. The proposed approach is based upon Adleman and Lipton's DNA operations to solve the BIP problem. The potential of DNA computation for the BIP problem is promising given the operational time complexity of O(nxk). PMID:16229936
McConnel, M B; Galligan, D T
2004-10-01
Optimization programs are currently used to aid in the selection of bulls to be used in herd breeding programs. While these programs offer a systematic approach to the problem of semen selection, they ignore the impact of volume discounts. Volume discounts are discounts that vary depending on the number of straws purchased. The dynamic nature of volume discounts means that, in order to be adequately accounted for, they must be considered in the optimization routine. Failing to do this creates a missed economic opportunity because the potential benefits of optimally selecting and combining breeding company discount opportunities are not captured. To address these issues, an integer program was created which used binary decision variables to incorporate the effects of quantity discounts into the optimization program. A consistent set of trait criteria was used to select a group of bulls from 3 sample breeding companies. Three different selection programs were used to select the bulls, 2 traditional methods and the integer method. After the discounts were applied using each method, the integer program resulted in the lowest cost portfolio of bulls. A sensitivity analysis showed that the integer program also resulted in a low cost portfolio when the genetic trait goals were changed to be more or less stringent. In the sample application, a net benefit of the new approach over the traditional approaches was a 12.3 to 20.0% savings in semen cost. PMID:15377634
Solution of Mixed-Integer Programming Problems on the XT5
Hartman-Baker, Rebecca J; Busch, Ingrid Karin; Hilliard, Michael R; Middleton, Richard S; Schultze, Michael
2009-01-01
In this paper, we describe our experience with solving difficult mixed-integer linear programming problems (MILPs) on the petaflop Cray XT5 system at the National Center for Computational Sciences at Oak Ridge National Laboratory. We describe the algorithmic, software, and hardware needs for solving MILPs and present the results of using PICO, an open-source, parallel, mixed-integer linear programming solver developed at Sandia National Laboratories, to solve canonical MILPs as well as problems of interest arising from the logistics and supply chain management field.
Optimal control of polymer flooding based on mixed-integer iterative dynamic programming
NASA Astrophysics Data System (ADS)
Lei, Yang; Li, Shurong; Zhang, Xiaodong; Zhang, Qiang; Guo, Lanlei
2011-11-01
Polymer flooding is one of the most important technologies for enhanced oil recovery. In this article, a mixed-integer optimal control model of distributed parameter systems (DPS) for the injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding and some inequalities constraints, such as polymer concentration and injection amount limitation. The control variables are the volume size, the injection concentration of each slug and the terminal flooding time. For the constant injection rate, the slug size is determined by the integer time stage length, and thus the integer variables are introduced in the DPS. To cope with the optimal control problem (OCP) of this DPS, a mixed-integer iterative dynamic programming incorporating a special truncation procedure to handle integer restrictions on stage lengths is proposed. First, the OCP with variable time stage lengths is transformed into a fixed time stage problem by introducing a normalised time variable. Then, the optimisation procedure is carried out at each stage and preceded backwards in a systematic way. Finally, the numerical results of an example illustrate the effectiveness of the proposed method.
Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm
NASA Astrophysics Data System (ADS)
Kania, Adhe; Sidarto, Kuntjoro Adji
2016-02-01
Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.
Li, Yongping; Huang, Guohe
2009-03-01
In this study, a dynamic analysis approach based on an inexact multistage integer programming (IMIP) model is developed for supporting municipal solid waste (MSW) management under uncertainty. Techniques of interval-parameter programming and multistage stochastic programming are incorporated within an integer-programming framework. The developed IMIP can deal with uncertainties expressed as probability distributions and interval numbers, and can reflect the dynamics in terms of decisions for waste-flow allocation and facility-capacity expansion over a multistage context. Moreover, the IMIP can be used for analyzing various policy scenarios that are associated with different levels of economic consequences. The developed method is applied to a case study of long-term waste-management planning. The results indicate that reasonable solutions have been generated for binary and continuous variables. They can help generate desired decisions of system-capacity expansion and waste-flow allocation with a minimized system cost and maximized system reliability. PMID:19320267
NASA Astrophysics Data System (ADS)
Khan, Sahubar Ali Bin Mohamed Nadhar; Ahmarofi, Ahmad Afif Bin
2014-12-01
In manufacturing sector, production planning or scheduling is the most important managerial task in order to achieve profit maximization and cost minimization. With limited resources, the management has to satisfy customer demand and at the same time fulfill company's objective, which is to maximize profit or minimize cost. Hence, planning becomes a significant task for production site in order to determine optimal number of units for each product to be produced. In this study, integer programming technique is used to develop an appropriate product-mix planning to obtain the optimal number of audio speaker products that should be produced in order to maximize profit. Branch-and-bound method is applied to obtain exact integer solutions when non-integer solutions occurred. Three major resource constraints are considered in this problem: raw materials constraint, demand constraint and standard production time constraint. It is found that, the developed integer programming model gives significant increase in profit compared to the existing method used by the company. At the end of the study, sensitivity analysis was performed to evaluate the effects of changes in objective function coefficient and available resources on the developed model. This will enable the management to foresee the effects on the results when some changes happen to the profit of its products or available resources.
Scenario Decomposition for 0-1 Stochastic Programs: Improvements and Asynchronous Implementation
Ryan, Kevin; Rajan, Deepak; Ahmed, Shabbir
2016-05-01
We recently proposed scenario decomposition algorithm for stochastic 0-1 programs finds an optimal solution by evaluating and removing individual solutions that are discovered by solving scenario subproblems. In our work, we develop an asynchronous, distributed implementation of the algorithm which has computational advantages over existing synchronous implementations of the algorithm. Improvements to both the synchronous and asynchronous algorithm are proposed. We also test the results on well known stochastic 0-1 programs from the SIPLIB test library and is able to solve one previously unsolved instance from the test set.
Enhanced index tracking modeling in portfolio optimization with mixed-integer programming z approach
NASA Astrophysics Data System (ADS)
Siew, Lam Weng; Jaaman, Saiful Hafizah Hj.; Ismail, Hamizun bin
2014-09-01
Enhanced index tracking is a popular form of portfolio management in stock market investment. Enhanced index tracking aims to construct an optimal portfolio to generate excess return over the return achieved by the stock market index without purchasing all of the stocks that make up the index. The objective of this paper is to construct an optimal portfolio using mixed-integer programming model which adopts regression approach in order to generate higher portfolio mean return than stock market index return. In this study, the data consists of 24 component stocks in Malaysia market index which is FTSE Bursa Malaysia Kuala Lumpur Composite Index from January 2010 until December 2012. The results of this study show that the optimal portfolio of mixed-integer programming model is able to generate higher mean return than FTSE Bursa Malaysia Kuala Lumpur Composite Index return with only selecting 30% out of the total stock market index components.
Smart-Grid Backbone Network Real-Time Delay Reduction via Integer Programming.
Pagadrai, Sasikanth; Yilmaz, Muhittin; Valluri, Pratyush
2016-08-01
This research investigates an optimal delay-based virtual topology design using integer linear programming (ILP), which is applied to the current backbone networks such as smart-grid real-time communication systems. A network traffic matrix is applied and the corresponding virtual topology problem is solved using the ILP formulations that include a network delay-dependent objective function and lightpath routing, wavelength assignment, wavelength continuity, flow routing, and traffic loss constraints. The proposed optimization approach provides an efficient deterministic integration of intelligent sensing and decision making, and network learning features for superior smart grid operations by adaptively responding the time-varying network traffic data as well as operational constraints to maintain optimal virtual topologies. A representative optical backbone network has been utilized to demonstrate the proposed optimization framework whose simulation results indicate that superior smart-grid network performance can be achieved using commercial networks and integer programming. PMID:25935050
PySP : modeling and solving stochastic mixed-integer programs in Python.
Woodruff, David L.; Watson, Jean-Paul
2010-08-01
Although stochastic programming is a powerful tool for modeling decision-making under uncertainty, various impediments have historically prevented its widespread use. One key factor involves the ability of non-specialists to easily express stochastic programming problems as extensions of deterministic models, which are often formulated first. A second key factor relates to the difficulty of solving stochastic programming models, particularly the general mixed-integer, multi-stage case. Intricate, configurable, and parallel decomposition strategies are frequently required to achieve tractable run-times. We simultaneously address both of these factors in our PySP software package, which is part of the COIN-OR Coopr open-source Python project for optimization. To formulate a stochastic program in PySP, the user specifies both the deterministic base model and the scenario tree with associated uncertain parameters in the Pyomo open-source algebraic modeling language. Given these two models, PySP provides two paths for solution of the corresponding stochastic program. The first alternative involves writing the extensive form and invoking a standard deterministic (mixed-integer) solver. For more complex stochastic programs, we provide an implementation of Rockafellar and Wets Progressive Hedging algorithm. Our particular focus is on the use of Progressive Hedging as an effective heuristic for approximating general multi-stage, mixed-integer stochastic programs. By leveraging the combination of a high-level programming language (Python) and the embedding of the base deterministic model in that language (Pyomo), we are able to provide completely generic and highly configurable solver implementations. PySP has been used by a number of research groups, including our own, to rapidly prototype and solve difficult stochastic programming problems.
Stacking-sequence optimization for buckling of laminated plates by integer programming
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.; Walsh, Joanne L.
1991-01-01
Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.
Parametric integer linear programming: a synthesis of branch and bound with cutting planes
Rountree, S.L.K.; Gillett, B.E.
1980-01-01
A branch and bound algorithm is designed to solve the general integer linear programing problem with parametric right-hand sides. The right-hand sides have the form b + THETA d, where b and d are conformable vectors, d consists of nonegative constants, and THETA varies from zero to one. The method consists of first determining all possible right-hand side ineger constants and appending this set of integer constants to the initial tableau to form an expanded problem with a finite number of family members. The implicit enumeration method gives a lower bound on the integer solutions. The branch and bound method is used with fathoming tests that allow one family member possibly to fathom other family members. A cutting plane option applies a finite number of cuts to each node before branching. In addition, the cutting plane method is invoked whenever some members are feasible at a node and others are infeasible. The branching and cutting process is repeated until the entire family of problems has been solved. 3 tables.
NASA Astrophysics Data System (ADS)
Bahri, Susila
2016-04-01
In this research, the minimization of the fire station model is constructed. The maximum time data required by the firefighter is used to construct the minimization model of the fire station in Padang. The model is used to determine the minimum number of the available fire station in Padang town. By using Matlab 2013a, the solution of the model can be found based on the Branch and Bound method. It denotes that the fire station must be built in Lubuk Begalung and Kuranji sub-districts.
Integration of progressive hedging and dual decomposition in stochastic integer programs
Watson, Jean -Paul; Guo, Ge; Hackebeil, Gabriel; Ryan, Sarah M.; Woodruff, David L.
2015-04-07
We present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. As a result, we report computational results on server location and unit commitment instances.
Edit distance for marked point processes revisited: An implementation by binary integer programming
Hirata, Yoshito; Aihara, Kazuyuki
2015-12-15
We implement the edit distance for marked point processes [Suzuki et al., Int. J. Bifurcation Chaos 20, 3699–3708 (2010)] as a binary integer program. Compared with the previous implementation using minimum cost perfect matching, the proposed implementation has two advantages: first, by using the proposed implementation, we can apply a wide variety of software and hardware, even spin glasses and coherent ising machines, to calculate the edit distance for marked point processes; second, the proposed implementation runs faster than the previous implementation when the difference between the numbers of events in two time windows for a marked point process is large.
Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs
Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; Watson, Jean -Paul; Wets, Roger J.-B.; Woodruff, David L.
2016-04-02
We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. In conclusion, we report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.
Edit distance for marked point processes revisited: An implementation by binary integer programming.
Hirata, Yoshito; Aihara, Kazuyuki
2015-12-01
We implement the edit distance for marked point processes [Suzuki et al., Int. J. Bifurcation Chaos 20, 3699-3708 (2010)] as a binary integer program. Compared with the previous implementation using minimum cost perfect matching, the proposed implementation has two advantages: first, by using the proposed implementation, we can apply a wide variety of software and hardware, even spin glasses and coherent ising machines, to calculate the edit distance for marked point processes; second, the proposed implementation runs faster than the previous implementation when the difference between the numbers of events in two time windows for a marked point process is large. PMID:26723156
Nauss, R.
1994-12-31
In this review we describe three integer programming applications involving fixed income securities. A bond trading model is presented that features a number of possible different objectives and collections of constraints including future interest rate scenarios. A mortgage backed security (MBS) financing model that accounts for potential defaults in the MBS is also presented. Finally we describe an approach to allocate collections of bank securities into three categories: hold to maturity, available for sale, or trading. Placement of securities in these categories affects the capital, net income, and liquidity of a bank according to new accounting rules promulgated by the Financial Accounting Standards Board.
Inexact multistage stochastic integer programming for water resources management under uncertainty.
Li, Y P; Huang, G H; Nie, S L; Liu, L
2008-07-01
In this study, an inexact multistage stochastic integer programming (IMSIP) method is developed for water resources management under uncertainty. This method incorporates techniques of inexact optimization and multistage stochastic programming within an integer programming framework. It can deal with uncertainties expressed as both probabilities and discrete intervals, and reflect the dynamics in terms of decisions for water allocation through transactions at discrete points of a complete scenario set over a multistage context. Moreover, the IMSIP can facilitate analyses of the multiple policy scenarios that are associated with economic penalties when the promised targets are violated as well as the economies-of-scale in the costs for surplus water diversion. A case study is provided for demonstrating the applicability of the developed methodology. The results indicate that reasonable solutions have been generated for both binary and continuous variables. For all scenarios under consideration, corrective actions can be undertaken dynamically under various pre-regulated policies and can thus help minimize the penalties and costs. The IMSIP can help water resources managers to identify desired system designs against water shortage and for flood control with maximized economic benefit and minimized system-failure risk. PMID:17532113
NASA Astrophysics Data System (ADS)
Huang, Kai; Huang, Gordon; Dai, Liming; Fan, Yurui
2016-08-01
This article introduces an inexact fuzzy integer chance constraint programming (IFICCP) approach for identifying noise reduction strategy under uncertainty. The IFICCP method integrates the interval programming and fuzzy chance constraint programming approaches into a framework, which is able to deal with uncertainties expressed as intervals and fuzziness. The proposed IFICCP model can be converted into two deterministic submodels corresponding to the optimistic and pessimistic conditions. The modelling approach is applied to a hypothetical control measure selection problem for noise reduction. Results of the case study indicate that useful solutions for noise control practices can be acquired. Three acceptable noise levels for two communities are considered. For each acceptable noise level, several decision alternatives have been obtained and analysed under different fuzzy confidence levels, which reflect the trade-offs between environmental and economic considerations.
Upper Bounds on the Number of Solutions of Binary Integer Programs
NASA Astrophysics Data System (ADS)
Jain, Siddhartha; Kadioglu, Serdar; Sellmann, Meinolf
We present a new method to compute upper bounds of the number of solutions of binary integer programming (BIP) problems. Given a BIP, we create a dynamic programming (DP) table for a redundant knapsack constraint which is obtained by surrogate relaxation. We then consider a Lagrangian relaxation of the original problem to obtain an initial weight bound on the knapsack. This bound is then refined through subgradient optimization. The latter provides a variety of Lagrange multipliers which allow us to filter infeasible edges in the DP table. The number of paths in the final table then provides an upper bound on the number of solutions. Numerical results show the effectiveness of our counting framework on automatic recording and market split problems.
An improved exploratory search technique for pure integer linear programming problems
NASA Technical Reports Server (NTRS)
Fogle, F. R.
1990-01-01
The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed.
Estimating Tree-Structured Covariance Matrices via Mixed-Integer Programming
Bravo, Héctor Corrada; Wright, Stephen; Eng, Kevin H.; Keles, Sündüz; Wahba, Grace
2011-01-01
We present a novel method for estimating tree-structured covariance matrices directly from observed continuous data. Specifically, we estimate a covariance matrix from observations of p continuous random variables encoding a stochastic process over a tree with p leaves. A representation of these classes of matrices as linear combinations of rank-one matrices indicating object partitions is used to formulate estimation as instances of well-studied numerical optimization problems. In particular, our estimates are based on projection, where the covariance estimate is the nearest tree-structured covariance matrix to an observed sample covariance matrix. The problem is posed as a linear or quadratic mixed-integer program (MIP) where a setting of the integer variables in the MIP specifies a set of tree topologies of the structured covariance matrix. We solve these problems to optimality using efficient and robust existing MIP solvers. We present a case study in phylogenetic analysis of gene expression and a simulation study comparing our method to distance-based tree estimating procedures. PMID:22081761
Automatic circuit redesign for delay fault testability using constrained quadratic 0-1 programming
Bushnell, M.; Shaik, I.
1994-12-31
We discuss three methods of automatically redesigning Very Large Scale Integrated circuits so that they can test themselves for excessive delay. A delay fault occurs when a circuit signal arrives too late as it propagates through the circuit. A hazard is the occurrence of multiple circuit signal transitions in a very short time interval. For delay fault testing to be accurate, we must eliminate hazards in the circuit by adding hardware. Our three methods for determining where to place this additional hardware are: (1) Good machine simulation using a higher-order Boolean algebra, (2) A graph algorithm to bound the enumeration of paths and find points where hazards appear, and (3) Quadratic 0-1 Programming to balance all cycles in the circuit graph. We discuss the mathematics of these three methods, present results, and discuss the inadequacies of each method. We conclude by proposing a greedy algorithm that combines two of these methods to make added hardware.
Linderoth, Jeff T.; Luedtke, James R.
2013-05-30
The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Problems involving both discrete and nonlinear components are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems. This research project added to the understanding of this area by making a number of fundamental advances. First, the work demonstrated many novel, strong, tractable relaxations designed to deal with non-convexities arising in mathematical formulation. Second, the research implemented the ideas in software that is available to the public. Finally, the work demonstrated the importance of these ideas on practical applications and disseminated the work through scholarly journals, survey publications, and conference presentations.
NASA Technical Reports Server (NTRS)
Haftka, R. T.; Adelman, H. M.
1984-01-01
Orbiting spacecraft such as large space antennas have to maintain a highly accurate space to operate satisfactorily. Such structures require active and passive controls to mantain an accurate shape under a variety of disturbances. Methods for the optimum placement of control actuators for correcting static deformations are described. In particular, attention is focused on the case were control locations have to be selected from a large set of available sites, so that integer programing methods are called for. The effectiveness of three heuristic techniques for obtaining a near-optimal site selection is compared. In addition, efficient reanalysis techniques for the rapid assessment of control effectiveness are presented. Two examples are used to demonstrate the methods: a simple beam structure and a 55m space-truss-parabolic antenna.
NASA Technical Reports Server (NTRS)
Haftka, R. T.; Adelman, H. M.
1985-01-01
Orbiting spacecraft such as large space antennas have to maintain a highly accurate shape to operate satisfactorily. Such structures require active and passive controls to maintain an accurate shape under a variety of disturbances. Methods for the optimum placement of control actuators for correcting static deformations are described. In particular, attention is focused on the case were control locations have to be selected from a large set of available sites, so that integer programing methods are called for. The effectiveness of three heuristic techniques for obtaining a near-optimal site selection is compared. In addition, efficient reanalysis techniques for the rapid assessment of control effectiveness are presented. Two examples are used to demonstrate the methods: a simple beam structure and a 55m space-truss-parabolic antenna.
Power Minimization for Dual- and Triple-Supply Digital Circuits via Integer Linear Programming
NASA Astrophysics Data System (ADS)
Ahn, Ki-Yong; Kyung, Chong-Min
This paper proposes an Integer Linear Programming (ILP)-based power minimization method by partitioning into regions, first, with three different VDD's(PM3V), and, secondly, with two different VDD's(PM2V). To reduce the solving time of triple-VDD case (PM3V), we also proposed a partitioned ILP method(p-PM3V). The proposed method provides 29% power saving on the average in the case of triple-VDD compared to the case of single VDD. Power reduction of PM3V compared to Clustered Voltage Scaling (CVS) was about 18%. Compared to the unpartitioned ILP formulation(PM3V), the partitioned ILP method(p-PM3V) reduced the total solution time by 46% at the cost of additional power consumption within 1.3%.
Optimization of a wood dryer kiln using the mixed integer programming technique: A case study
Gustafsson, S.I.
1999-07-01
When wood is to be utilized as a raw material for furniture, buildings, etc., it must be dried from approximately 100% to 6% moisture content. This is achieved at least partly in a drying kiln. Heat for this purpose is provided by electrical means, or by steam from boilers fired with wood chips or oil. By making a close examination of monitored values from an actual drying kiln it has been possible to optimize the use of steam and electricity using the so called mixed integer programming technique. Owing to the operating schedule for the drying kiln it has been necessary to divide the drying process in very short time intervals, i.e., a number of minutes. Since a drying cycle takes about two or three weeks, a considerable mathematical problem is presented and this has to be solved.
An integer programming model for gate assignment problem at airline terminals
NASA Astrophysics Data System (ADS)
Chun, Chong Kok; Nordin, Syarifah Zyurina
2015-05-01
In this paper, we concentrate on a gate assignment problem (GAP) at the airlines terminal. Our problem is to assign an arrival plane to a suitable gate. There are two considerations needed to take. One of its is passenger walking distance from arrival gate to departure gate while another consideration is the transport baggage distance from one gate to another. Our objective is to minimize the total distance between the gates that related to assign the arrival plane to the suitable gates. An integer linear programming (ILP) model is proposed to solve this gate assignment problem. We also conduct a computational experiment using CPLEX 12.1 solver in AIMMS 3.10 software to analyze the performance of the model. Results of the computational experiments are presented. The efficiency of flights assignment is depends on the ratio of the weight for both total passenger traveling distances and total baggage transport distances.
An Application of Parametric Mixed-Integer Linear Programming to Hydropower Development
NASA Astrophysics Data System (ADS)
Turgeon, André
1987-03-01
The problem consists in selecting the sites on the river where reservoirs and hydroelectric power plants are to be built and then determining the type and size of the projected installations. The solution obviously depends on the amount of money the utility is willing to invest, which itself is a function of what the new installations will produce. It is therefore necessary to solve the problem for all possible amounts of firm energy produced, since it is not known at the outset which production level the utility will select. This is done in the paper by a parametric mixed-integer linear programming (MILP) method whose efficiency derives from the fact that the branch-and-bound algorithm for selecting the sites to be developed (and consuming most of the computer time) is solved a minimum number of times. Between the points where the MILP problem is solved, LP parametric analysis is applied.
An integer programming framework for inferring disease complexes from network data
Mazza, Arnon; Klockmeier, Konrad; Wanker, Erich; Sharan, Roded
2016-01-01
Motivation: Unraveling the molecular mechanisms that underlie disease calls for methods that go beyond the identification of single causal genes to inferring larger protein assemblies that take part in the disease process. Results: Here, we develop an exact, integer-programming-based method for associating protein complexes with disease. Our approach scores proteins based on their proximity in a protein–protein interaction network to a prior set that is known to be relevant for the studied disease. These scores are combined with interaction information to infer densely interacting protein complexes that are potentially disease-associated. We show that our method outperforms previous ones and leads to predictions that are well supported by current experimental data and literature knowledge. Availability and Implementation: The datasets we used, the executables and the results are available at www.cs.tau.ac.il/roded/disease_complexes.zip Contact: roded@post.tau.ac.il PMID:27307626
Synchronic interval Gaussian mixed-integer programming for air quality management.
Cheng, Guanhui; Huang, Guohe Gordon; Dong, Cong
2015-12-15
To reveal the synchronism of interval uncertainties, the tradeoff between system optimality and security, the discreteness of facility-expansion options, the uncertainty of pollutant dispersion processes, and the seasonality of wind features in air quality management (AQM) systems, a synchronic interval Gaussian mixed-integer programming (SIGMIP) approach is proposed in this study. A robust interval Gaussian dispersion model is developed for approaching the pollutant dispersion process under interval uncertainties and seasonal variations. The reflection of synchronic effects of interval uncertainties in the programming objective is enabled through introducing interval functions. The proposition of constraint violation degrees helps quantify the tradeoff between system optimality and constraint violation under interval uncertainties. The overall optimality of system profits of an SIGMIP model is achieved based on the definition of an integrally optimal solution. Integer variables in the SIGMIP model are resolved by the existing cutting-plane method. Combining these efforts leads to an effective algorithm for the SIGMIP model. An application to an AQM problem in a region in Shandong Province, China, reveals that the proposed SIGMIP model can facilitate identifying the desired scheme for AQM. The enhancement of the robustness of optimization exercises may be helpful for increasing the reliability of suggested schemes for AQM under these complexities. The interrelated tradeoffs among control measures, emission sources, flow processes, receptors, influencing factors, and economic and environmental goals are effectively balanced. Interests of many stakeholders are reasonably coordinated. The harmony between economic development and air quality control is enabled. Results also indicate that the constraint violation degree is effective at reflecting the compromise relationship between constraint-violation risks and system optimality under interval uncertainties. This can
Master plan nurse duty roster using the 0-1 goal programming technique
NASA Astrophysics Data System (ADS)
Ismail, Wan Rosmanira; Jenal, Ruzzakiah
2013-04-01
The scheduling of nurses is particularly challenging because of the nature of the work which is around the clock. In addition, inefficient duty roster can have an effect on the nurses well being as well as their job satisfaction. In nurse scheduling problem (NSP), nurses are generally allocated to periods of work over a specified time horizon. A typical length of the schedule varies from a few weeks to a month. The schedule will be consistently rebuilt after the specified time period and will result in a time-consuming task for the administrative staff involved. Moreover, the task becomes overwhelming when the staff needs to consider the previous duty rosters in order to maintain the quality of schedules. Therefore, this study suggests the development of a master plan for a nurse duty roster for approximately one year. The master plan starts with the development of a blue print for the nurse duty roster using a 0-1 goal programming technique. The appropriate working period for this blue print is formulated based on the number of night shifts and the number of required nurses for night shift per schedule. Subsequently, the blue print is repeated to complete the annual nurse duty roster. These newly developed procedures were then tested on several data sets. The test results found that the master plan has successfully distributed the annual workload evenly among nurses. In addition, the master plan allows nurses to arrange their career and social activities in advance.
A Two-Stage Stochastic Mixed-Integer Programming Approach to the Smart House Scheduling Problem
NASA Astrophysics Data System (ADS)
Ozoe, Shunsuke; Tanaka, Yoichi; Fukushima, Masao
A “Smart House” is a highly energy-optimized house equipped with photovoltaic systems (PV systems), electric battery systems, fuel cell cogeneration systems (FC systems), electric vehicles (EVs) and so on. Smart houses are attracting much attention recently thanks to their enhanced ability to save energy by making full use of renewable energy and by achieving power grid stability despite an increased power draw for installed PV systems. Yet running a smart house's power system, with its multiple power sources and power storages, is no simple task. In this paper, we consider the problem of power scheduling for a smart house with a PV system, an FC system and an EV. We formulate the problem as a mixed integer programming problem, and then extend it to a stochastic programming problem involving recourse costs to cope with uncertain electricity demand, heat demand and PV power generation. Using our method, we seek to achieve the optimal power schedule running at the minimum expected operation cost. We present some results of numerical experiments with data on real-life demands and PV power generation to show the effectiveness of our method.
He, Li; Huang, Guo-He; Zeng, Guang-Ming; Lu, Hong-Wei
2009-01-01
The previous inexact mixed-integer linear programming (IMILP) method can only tackle problems with coefficients of the objective function and constraints being crisp intervals, while the existing inexact mixed-integer semi-infinite programming (IMISIP) method can only deal with single-objective programming problems as it merely allows the number of constraints to be infinite. This study proposes, an inexact mixed-integer bi-infinite programming (IMIBIP) method by incorporating the concept of functional intervals into the programming framework. Different from the existing methods, the IMIBIP can tackle the inexact programming problems that contain both infinite objectives and constraints. The developed method is applied to capacity planning of waste management systems under a variety of uncertainties. Four scenarios are considered for comparing the solutions of IMIBIP with those of IMILP. The results indicate that reasonable solutions can be generated by the IMIBIP method. Compared with IMILP, the system cost from IMIBIP would be relatively high since the fluctuating market factors are considered; however, the IMILP solutions are associated with a raised system reliability level and a reduced constraint violation risk level. PMID:18406594
Caprara, Alberto; Carr, Robert; Istrail, Sorin; Lancia, Giuseppe; Walenz, Brian
2004-01-01
Protein structure comparison is a fundamental problem for structural genomics, with applications to drug design, fold prediction, protein clustering, and evolutionary studies. Despite its importance, there are very few rigorous methods and widely accepted similarity measures known for this problem. In this paper we describe the last few years of developments on the study of an emerging measure, the contact map overlap (CMO), for protein structure comparison. A contact map is a list of pairs of residues which lie in three-dimensional proximity in the protein's native fold. Although this measure is in principle computationally hard to optimize, we show how it can in fact be computed with great accuracy for related proteins by integer linear programming techniques. These methods have the advantage of providing certificates of near-optimality by means of upper bounds to the optimal alignment value. We also illustrate effective heuristics, such as local search and genetic algorithms. We were able to obtain for the first time optimal alignments for large similar proteins (about 1,000 residues and 2,000 contacts) and used the CMO measure to cluster proteins in families. The clusters obtained were compared to SCOP classification in order to validate the measure. Extensive computational experiments showed that alignments which are off by at most 10% from the optimal value can be computed in a short time. Further experiments showed how this measure reacts to the choice of the threshold defining a contact and how to choose this threshold in a sensible way. PMID:15072687
A Mixed Integer Linear Program for Solving a Multiple Route Taxi Scheduling Problem
NASA Technical Reports Server (NTRS)
Montoya, Justin Vincent; Wood, Zachary Paul; Rathinam, Sivakumar; Malik, Waqar Ahmad
2010-01-01
Aircraft movements on taxiways at busy airports often create bottlenecks. This paper introduces a mixed integer linear program to solve a Multiple Route Aircraft Taxi Scheduling Problem. The outputs of the model are in the form of optimal taxi schedules, which include routing decisions for taxiing aircraft. The model extends an existing single route formulation to include routing decisions. An efficient comparison framework compares the multi-route formulation and the single route formulation. The multi-route model is exercised for east side airport surface traffic at Dallas/Fort Worth International Airport to determine if any arrival taxi time savings can be achieved by allowing arrivals to have two taxi routes: a route that crosses an active departure runway and a perimeter route that avoids the crossing. Results indicate that the multi-route formulation yields reduced arrival taxi times over the single route formulation only when a perimeter taxiway is used. In conditions where the departure aircraft are given an optimal and fixed takeoff sequence, accumulative arrival taxi time savings in the multi-route formulation can be as high as 3.6 hours more than the single route formulation. If the departure sequence is not optimal, the multi-route formulation results in less taxi time savings made over the single route formulation, but the average arrival taxi time is significantly decreased.
Poos, Alexandra M; Maicher, André; Dieckmann, Anna K; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer
2016-06-01
Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments. PMID:26908654
Uncluttered Single-Image Visualization of Vascular Structures using GPU and Integer Programming
Won, Joong-Ho; Jeon, Yongkweon; Rosenberg, Jarrett; Yoon, Sungroh; Rubin, Geoffrey D.; Napel, Sandy
2013-01-01
Direct projection of three-dimensional branching structures, such as networks of cables, blood vessels, or neurons onto a 2D image creates the illusion of intersecting structural parts and creates challenges for understanding and communication. We present a method for visualizing such structures, and demonstrate its utility in visualizing the abdominal aorta and its branches, whose tomographic images might be obtained by computed tomography or magnetic resonance angiography, in a single two-dimensional stylistic image, without overlaps among branches. The visualization method, termed uncluttered single-image visualization (USIV), involves optimization of geometry. This paper proposes a novel optimization technique that utilizes an interesting connection of the optimization problem regarding USIV to the protein structure prediction problem. Adopting the integer linear programming-based formulation for the protein structure prediction problem, we tested the proposed technique using 30 visualizations produced from five patient scans with representative anatomical variants in the abdominal aortic vessel tree. The novel technique can exploit commodity-level parallelism, enabling use of general-purpose graphics processing unit (GPGPU) technology that yields a significant speedup. Comparison of the results with the other optimization technique previously reported elsewhere suggests that, in most aspects, the quality of the visualization is comparable to that of the previous one, with a significant gain in the computation time of the algorithm. PMID:22291148
Poos, Alexandra M.; Maicher, André; Dieckmann, Anna K.; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer
2016-01-01
Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments. PMID:26908654
An integer programming approach to the phase problem for centrosymmetric structures.
Vaia, Anastasia; Sahinidis, Nikolaos V
2003-09-01
The problem addressed in this paper is the determination of three-dimensional structures of centrosymmetric crystals from X-ray diffraction measurements. The 'minimal principle' that a certain quantity is minimized only by the crystal structure is employed to solve the phase problem. The mathematical formulation of the minimal principle is a nonconvex nonlinear optimization problem. To date, local optimization techniques and advanced computer architectures have been used to solve this problem, which may have a very large number of local optima. In this paper, the minimal principle model is reformulated for the case of centrosymmetric structures into an integer programming problem in terms of the missing phases. This formulation is solvable by well established combinatorial optimization techniques that are guaranteed to provide the global optimum in a finite number of steps without explicit enumeration of all possible combinations of phases. Computational experience with the proposed method on a number of structures of moderate complexity is provided and demonstrates that the approach yields a fast and reliable method that resolves the crystallographic phase problem for the case of centrosymmetric structures. PMID:12944609
Automatic design of synthetic gene circuits through mixed integer non-linear programming.
Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias
2012-01-01
Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits. PMID:22536398
Integer Linear Programming for Constrained Multi-Aspect Committee Review Assignment
Karimzadehgan, Maryam; Zhai, ChengXiang
2011-01-01
Automatic review assignment can significantly improve the productivity of many people such as conference organizers, journal editors and grant administrators. A general setup of the review assignment problem involves assigning a set of reviewers on a committee to a set of documents to be reviewed under the constraint of review quota so that the reviewers assigned to a document can collectively cover multiple topic aspects of the document. No previous work has addressed such a setup of committee review assignments while also considering matching multiple aspects of topics and expertise. In this paper, we tackle the problem of committee review assignment with multi-aspect expertise matching by casting it as an integer linear programming problem. The proposed algorithm can naturally accommodate any probabilistic or deterministic method for modeling multiple aspects to automate committee review assignments. Evaluation using a multi-aspect review assignment test set constructed using ACM SIGIR publications shows that the proposed algorithm is effective and efficient for committee review assignments based on multi-aspect expertise matching. PMID:22711970
An integer programming formulation of the parsimonious loss of heterozygosity problem.
Catanzaro, Daniele; Labbé, Martine; Halldórsson, Bjarni V
2013-01-01
A loss of heterozygosity (LOH) event occurs when, by the laws of Mendelian inheritance, an individual should be heterozygote at a given site but, due to a deletion polymorphism, is not. Deletions play an important role in human disease and their detection could provide fundamental insights for the development of new diagnostics and treatments. In this paper, we investigate the parsimonious loss of heterozygosity problem (PLOHP), i.e., the problem of partitioning suspected polymorphisms from a set of individuals into a minimum number of deletion areas. Specifically, we generalize Halldórsson et al.'s work by providing a more general formulation of the PLOHP and by showing how one can incorporate different recombination rates and prior knowledge about the locations of deletions. Moreover, we show that the PLOHP can be formulated as a specific version of the clique partition problem in a particular class of graphs called undirected catch-point interval graphs and we prove its general $({\\cal NP})$-hardness. Finally, we provide a state-of-the-art integer programming (IP) formulation and strengthening valid inequalities to exactly solve real instances of the PLOHP containing up to 9,000 individuals and 3,000 SNPs. Our results give perspectives on the mathematics of the PLOHP and suggest new directions on the development of future efficient exact solution approaches. PMID:24407298
Gorissen, Bram L; den Hertog, Dick; Hoffmann, Aswin L
2013-02-21
Current inverse treatment planning methods that optimize both catheter positions and dwell times in prostate HDR brachytherapy use surrogate linear or quadratic objective functions that have no direct interpretation in terms of dose-volume histogram (DVH) criteria, do not result in an optimum or have long solution times. We decrease the solution time of the existing linear and quadratic dose-based programming models (LP and QP, respectively) to allow optimizing over potential catheter positions using mixed integer programming. An additional average speed-up of 75% can be obtained by stopping the solver at an early stage, without deterioration of the plan quality. For a fixed catheter configuration, the dwell time optimization model LP solves to optimality in less than 15 s, which confirms earlier results. We propose an iterative procedure for QP that allows us to prescribe the target dose as an interval, while retaining independence between the solution time and the number of dose calculation points. This iterative procedure is comparable in speed to the LP model and produces better plans than the non-iterative QP. We formulate a new dose-volume-based model that maximizes V(100%) while satisfying pre-set DVH criteria. This model optimizes both catheter positions and dwell times within a few minutes depending on prostate volume and number of catheters, optimizes dwell times within 35 s and gives better DVH statistics than dose-based models. The solutions suggest that the correlation between the objective value and the clinical plan quality is weak in the existing dose-based models. PMID:23363622
Doolittle, R.
1994-11-15
The title integer anatomy is intended to convey the idea of a systematic method for displaying the prime decomposition of the integers. Just as the biological study of anatomy does not teach us all things about behavior of species neither would we expect to learn everything about the number theory from a study of its anatomy. But, some number-theoretic theorems are illustrated by inspection of integer anatomy, which tend to validate the underlying structure and the form as developed and displayed in this treatise. The first statement to be made in this development is: the way structure of the natural numbers is displayed depends upon the allowed operations.
Munguia, Lluis-Miquel; Oxberry, Geoffrey; Rajan, Deepak
2016-05-01
Stochastic mixed-integer programs (SMIPs) deal with optimization under uncertainty at many levels of the decision-making process. When solved as extensive formulation mixed- integer programs, problem instances can exceed available memory on a single workstation. In order to overcome this limitation, we present PIPS-SBB: a distributed-memory parallel stochastic MIP solver that takes advantage of parallelism at multiple levels of the optimization process. We also show promising results on the SIPLIB benchmark by combining methods known for accelerating Branch and Bound (B&B) methods with new ideas that leverage the structure of SMIPs. Finally, we expect the performance of PIPS-SBB to improve furthermore » as more functionality is added in the future.« less
Hasuike, Takashi; Ishii, Hiroaki; Katagiri, Hideki
2009-10-08
This paper considers a bi-criteria general 0-1 random fuzzy programming problem based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not well-defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goals for objectives, and considering the maximization of the aspiration level for total profit and the degree of necessity that the objective function's value satisfies the fuzzy goal, the main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed according to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed.
Mixed-integer programming methods for transportation and power generation problems
NASA Astrophysics Data System (ADS)
Damci Kurt, Pelin
This dissertation conducts theoretical and computational research to solve challenging problems in application areas such as supply chain and power systems. The first part of the dissertation studies a transportation problem with market choice (TPMC) which is a variant of the classical transportation problem in which suppliers with limited capacities have a choice of which demands (markets) to satisfy. We show that TPMC is strongly NP-complete. We consider a version of the problem with a service level constraint on the maximum number of markets that can be rejected and show that if the original problem is polynomial, its cardinality-constrained version is also polynomial. We propose valid inequalities for mixed-integer cover and knapsack sets with variable upper bound constraints, which appear as substructures of TPMC and use them in a branch-and-cut algorithm to solve this problem. The second part of this dissertation studies a unit commitment (UC) problem in which the goal is to minimize the operational cost of power generators over a time period subject to physical constraints while satisfying demand. We provide several exponential classes of multi-period ramping and multi-period variable upper bound inequalities. We prove the strength of these inequalities and describe polynomial-time separation algorithms. Computational results show the effectiveness of the proposed inequalities when used as cuts in a branch-and-cut algorithm to solve the UC problem. The last part of this dissertation investigates the effects of uncertain wind power on the UC problem. A two-stage robust model and a three-stage stochastic program are compared.
NASA Astrophysics Data System (ADS)
Tang, Jiafu; Liu, Yang; Fung, Richard; Luo, Xinggang
2008-12-01
Manufacturers have a legal accountability to deal with industrial waste generated from their production processes in order to avoid pollution. Along with advances in waste recovery techniques, manufacturers may adopt various recycling strategies in dealing with industrial waste. With reuse strategies and technologies, byproducts or wastes will be returned to production processes in the iron and steel industry, and some waste can be recycled back to base material for reuse in other industries. This article focuses on a recovery strategies optimization problem for a typical class of industrial waste recycling process in order to maximize profit. There are multiple strategies for waste recycling available to generate multiple byproducts; these byproducts are then further transformed into several types of chemical products via different production patterns. A mixed integer programming model is developed to determine which recycling strategy and which production pattern should be selected with what quantity of chemical products corresponding to this strategy and pattern in order to yield maximum marginal profits. The sales profits of chemical products and the set-up costs of these strategies, patterns and operation costs of production are considered. A simulated annealing (SA) based heuristic algorithm is developed to solve the problem. Finally, an experiment is designed to verify the effectiveness and feasibility of the proposed method. By comparing a single strategy to multiple strategies in an example, it is shown that the total sales profit of chemical products can be increased by around 25% through the simultaneous use of multiple strategies. This illustrates the superiority of combinatorial multiple strategies. Furthermore, the effects of the model parameters on profit are discussed to help manufacturers organize their waste recycling network.
Mixed integer programming model for optimizing the layout of an ICU vehicle
2009-01-01
Background This paper presents a Mixed Integer Programming (MIP) model for designing the layout of the Intensive Care Units' (ICUs) patient care space. In particular, this MIP model was developed for optimizing the layout for materials to be used in interventions. This work was developed within the framework of a joint project between the Madrid Technical Unverstity and the Medical Emergency Services of the Madrid Regional Government (SUMMA 112). Methods The first task was to identify the relevant information to define the characteristics of the new vehicles and, in particular, to obtain a satisfactory interior layout to locate all the necessary materials. This information was gathered from health workers related to ICUs. With that information an optimization model was developed in order to obtain a solution. From the MIP model, a first solution was obtained, consisting of a grid to locate the different materials needed for the ICUs. The outcome from the MIP model was discussed with health workers to tune the solution, and after slightly altering that solution to meet some requirements that had not been included in the mathematical model, the eventual solution was approved by the persons responsible for specifying the characteristics of the new vehicles. According to the opinion stated by the SUMMA 112's medical group responsible for improving the ambulances (the so-called "coaching group"), the outcome was highly satisfactory. Indeed, the final design served as a basis to draw up the requirements of a public tender. Results As a result from solving the Optimization model, a grid was obtained to locate the different necessary materials for the ICUs. This grid had to be slightly altered to meet some requirements that had not been included in the mathematical model. The results were discussed with the persons responsible for specifying the characteristics of the new vehicles. Conclusion The outcome was highly satisfactory. Indeed, the final design served as a basis
NASA Astrophysics Data System (ADS)
Li, Hong; Zhang, Li; Jiao, Yong-Chang
2016-07-01
This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.
Li, Y P; Huang, G H
2006-11-01
In this study, an interval-parameter two-stage mixed integer linear programming (ITMILP) model is developed for supporting long-term planning of waste management activities in the City of Regina. In the ITMILP, both two-stage stochastic programming and interval linear programming are introduced into a general mixed integer linear programming framework. Uncertainties expressed as not only probability density functions but also discrete intervals can be reflected. The model can help tackle the dynamic, interactive and uncertain characteristics of the solid waste management system in the City, and can address issues concerning plans for cost-effective waste diversion and landfill prolongation. Three scenarios are considered based on different waste management policies. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment or justification of the existing waste flow allocation patterns, the long-term capacity planning of the City's waste management system, and the formulation of local policies and regulations regarding waste generation and management. PMID:16678336
Davila, Eric; Chang, Ni-Bin; Diwakaruni, Syamala
2005-06-01
The Lower Rio Grande Valley (LRGV) region in South Texas emerges as a warehouse and transportation center between Central America and the US with positive growth impacts due to the North American Free Trade Agreement (NAFTA). In 10 years time, a 39.8% population increase has resulted in a 25% boost in solid waste per capita disposal rate in the region. A landfill space shortage drives a need for landfill operators to understand their optimal management strategies in this highly-competitive market. Initially, a strategic plan for optimal solid waste pattern distribution minimizes net costs for cities. This is accomplished through a grey integer programming algorithm that encapsulates all uncertainty present in the solid waste system. Secondly, a series of grey integer submodels construct payoff matrices for a zero-sum two-person game. The ensuing game theoretic analysis is critical for evaluating optimal pricing strategies for tipping fees available to the most significant regional landfills (e.g. Browning-Ferris Industries (BFI) and City of Edinburg) as they compete over disposal contracts. The BFI landfill intrinsically benefits from its competitive pricing policy and central location to solid waste generators. The City of Edinburg landfill, on the other hand, wishes to secure its lucrative solid waste management revenue. It desires a gaming strategy backed by optimality that integrates ambiguity in solid waste generation, design capacity boundaries, and unitary shipping costs. Results show that a two-tiered analysis via grey integer programming-based games may pave the way for 'grey Nash equilibria' pricing tactics that will help the Edinburg landfill maintain its waste contracts. PMID:15854728
NASA Astrophysics Data System (ADS)
Skulovich, Olya; Bent, Russell; Judi, David; Perelman, Lina Sela; Ostfeld, Avi
2015-06-01
Despite their potential catastrophic impact, transients are often ignored or presented ad hoc when designing water distribution systems. To address this problem, we introduce a new piece-wise function fitting model that is integrated with mixed integer programming to optimally place and size surge tanks for transient control. The key features of the algorithm are a model-driven discretization of the search space, a linear approximation nonsmooth system response surface to transients, and a mixed integer linear programming optimization. Results indicate that high quality solutions can be obtained within a reasonable number of function evaluations and demonstrate the computational effectiveness of the approach through two case studies. The work investigates one type of surge control devices (closed surge tank) for a specified set of transient events. The performance of the algorithm relies on the assumption that there exists a smooth relationship between the objective function and tank size. Results indicate the potential of the approach for the optimal surge control design in water systems.
NASA Astrophysics Data System (ADS)
Sawyer, Charles S.; Ahlfeld, David P.; King, Alan J.
1995-05-01
A three-dimensional groundwater flow management model for making decisions on the design of hydrodynamic control of a groundwater flow system using a combination of extraction and/or injection wells is developed. The model takes into account constraints imposed on the system to stop the horizontal spread of contaminants and to ensure a net upward flow in areas where downward vertical gradients exist. The mathematical formulation of the groundwater remediation problem as a mixed-integer model and the strategy for solving the model are presented. Numerical results are presented for the Toms River Plant site, which is modeled as a five-layer aquifer system with interconnecting aquitards. A sensitivity analysis on the relative magnitude of the continuous operating costs and the fixed-charge costs is also presented.
NASA Astrophysics Data System (ADS)
Yin, Sisi; Nishi, Tatsushi
2014-11-01
Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.
NASA Astrophysics Data System (ADS)
Noor-E-Alam, Md.; Doucette, John
2015-08-01
Grid-based location problems (GBLPs) can be used to solve location problems in business, engineering, resource exploitation, and even in the field of medical sciences. To solve these decision problems, an integer linear programming (ILP) model is designed and developed to provide the optimal solution for GBLPs considering fixed cost criteria. Preliminary results show that the ILP model is efficient in solving small to moderate-sized problems. However, this ILP model becomes intractable in solving large-scale instances. Therefore, a decomposition heuristic is proposed to solve these large-scale GBLPs, which demonstrates significant reduction of solution runtimes. To benchmark the proposed heuristic, results are compared with the exact solution via ILP. The experimental results show that the proposed method significantly outperforms the exact method in runtime with minimal (and in most cases, no) loss of optimality.
Mixed interval-fuzzy two-stage integer programming and its application to flood-diversion planning
NASA Astrophysics Data System (ADS)
Li, Y. P.; Huang, G. H.; Nie, S. L.
2007-03-01
Innovative prevention, adaptation, and mitigation approaches as well as policies for sustainable flood management continue to be challenges faced by decision-makers. In this study, a mixed interval-fuzzy two-stage integer programming (IFTIP) method is developed for flood-diversion planning under uncertainty. This method improves upon the existing interval, fuzzy, and two-stage programming approaches by allowing uncertainties expressed as probability distributions, fuzzy sets, and discrete intervals to be directly incorporated within the optimization framework. In its modelling formulation, economic penalties as corrective measures against any infeasibilities arising because of a particular realization of the uncertainties are taken into account. The method can also be used for analysing a variety of policy scenarios that are associated with different levels of economic penalties. A management problem in terms of flood control is studied to illustrate the applicability of the proposed approach. The results indicate that reasonable solutions have been generated. They can provide desired flood-diversion alternatives and capacity-expansion schemes with a minimized system cost and a maximized safety level. The developed IFTIP is also applicable to other management problems that involve uncertainties presented in multiple formats as well as complexities in policy dynamics.
DRIESSEN,BRIAN; SADEGH,NADER
2000-04-25
This work presents a method of finding near global optima to minimum-time trajectory generation problem for systems that would be linear if it were not for the presence of Coloumb friction. The required final state of the system is assumed to be maintainable by the system, and the input bounds are assumed to be large enough so that they can overcome the maximum static Coloumb friction force. Other than the previous work for generating minimum-time trajectories for non redundant robotic manipulators for which the path in joint space is already specified, this work represents, to the best of the authors' knowledge, the first approach for generating near global optima for minimum-time problems involving a nonlinear class of dynamic systems. The reason the optima generated are near global optima instead of exactly global optima is due to a discrete-time approximation of the system (which is usually used anyway to simulate such a system numerically). The method closely resembles previous methods for generating minimum-time trajectories for linear systems, where the core operation is the solution of a Phase I linear programming problem. For the nonlinear systems considered herein, the core operation is instead the solution of a mixed integer linear programming problem.
Lee, Dongyul; Lee, Chaewoo
2014-01-01
The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC) with adaptive modulation and coding (AMC) provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs) to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP) and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm. PMID:25276862
Lee, Chaewoo
2014-01-01
The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC) with adaptive modulation and coding (AMC) provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs) to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP) and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm. PMID:25276862
Ryan, Jason C; Banerjee, Ashis Gopal; Cummings, Mary L; Roy, Nicholas
2014-06-01
Planning operations across a number of domains can be considered as resource allocation problems with timing constraints. An unexplored instance of such a problem domain is the aircraft carrier flight deck, where, in current operations, replanning is done without the aid of any computerized decision support. Rather, veteran operators employ a set of experience-based heuristics to quickly generate new operating schedules. These expert user heuristics are neither codified nor evaluated by the United States Navy; they have grown solely from the convergent experiences of supervisory staff. As unmanned aerial vehicles (UAVs) are introduced in the aircraft carrier domain, these heuristics may require alterations due to differing capabilities. The inclusion of UAVs also allows for new opportunities for on-line planning and control, providing an alternative to the current heuristic-based replanning methodology. To investigate these issues formally, we have developed a decision support system for flight deck operations that utilizes a conventional integer linear program-based planning algorithm. In this system, a human operator sets both the goals and constraints for the algorithm, which then returns a proposed schedule for operator approval. As a part of validating this system, the performance of this collaborative human-automation planner was compared with that of the expert user heuristics over a set of test scenarios. The resulting analysis shows that human heuristics often outperform the plans produced by an optimization algorithm, but are also often more conservative. PMID:23934675
Li, Jing; Jiang, Tao
2005-01-01
We study the problem of reconstructing haplotype configurations from genotypes on pedigree data with missing alleles under the Mendelian law of inheritance and the minimum-recombination principle, which is important for the construction of haplotype maps and genetic linkage/association analyses. Our previous results show that the problem of finding a minimum-recombinant haplotype configuration (MRHC) is in general NP-hard. This paper presents an effective integer linear programming (ILP) formulation of the MRHC problem with missing data and a branch-and-bound strategy that utilizes a partial order relationship and some other special relationships among variables to decide the branching order. Nontrivial lower and upper bounds on the optimal number of recombinants are introduced at each branching node to effectively prune the search tree. When multiple solutions exist, a best haplotype configuration is selected based on a maximum likelihood approach. The paper also shows for the first time how to incorporate marker interval distance into a rule-based haplotyping algorithm. Our results on simulated data show that the algorithm could recover haplotypes with 50 loci from a pedigree of size 29 in seconds on a Pentium IV computer. Its accuracy is more than 99.8% for data with no missing alleles and 98.3% for data with 20% missing alleles in terms of correctly recovered phase information at each marker locus. A comparison with a statistical approach SimWalk2 on simulated data shows that the ILP algorithm runs much faster than SimWalk2 and reports better or comparable haplotypes on average than the first and second runs of SimWalk2. As an application of the algorithm to real data, we present some test results on reconstructing haplotypes from a genome-scale SNP dataset consisting of 12 pedigrees that have 0.8% to 14.5% missing alleles. PMID:16108713
Zhang, Huiling; Huang, Qingsheng; Bei, Zhendong; Wei, Yanjie; Floudas, Christodoulos A
2016-03-01
In this article, we present COMSAT, a hybrid framework for residue contact prediction of transmembrane (TM) proteins, integrating a support vector machine (SVM) method and a mixed integer linear programming (MILP) method. COMSAT consists of two modules: COMSAT_SVM which is trained mainly on position-specific scoring matrix features, and COMSAT_MILP which is an ab initio method based on optimization models. Contacts predicted by the SVM model are ranked by SVM confidence scores, and a threshold is trained to improve the reliability of the predicted contacts. For TM proteins with no contacts above the threshold, COMSAT_MILP is used. The proposed hybrid contact prediction scheme was tested on two independent TM protein sets based on the contact definition of 14 Å between Cα-Cα atoms. First, using a rigorous leave-one-protein-out cross validation on the training set of 90 TM proteins, an accuracy of 66.8%, a coverage of 12.3%, a specificity of 99.3% and a Matthews' correlation coefficient (MCC) of 0.184 were obtained for residue pairs that are at least six amino acids apart. Second, when tested on a test set of 87 TM proteins, the proposed method showed a prediction accuracy of 64.5%, a coverage of 5.3%, a specificity of 99.4% and a MCC of 0.106. COMSAT shows satisfactory results when compared with 12 other state-of-the-art predictors, and is more robust in terms of prediction accuracy as the length and complexity of TM protein increase. COMSAT is freely accessible at http://hpcc.siat.ac.cn/COMSAT/. PMID:26756402
Armutlu, Pelin; Ozdemir, Muhittin E; Uney-Yuksektepe, Fadime; Kavakli, I Halil; Turkay, Metin
2008-01-01
Background A priori analysis of the activity of drugs on the target protein by computational approaches can be useful in narrowing down drug candidates for further experimental tests. Currently, there are a large number of computational methods that predict the activity of drugs on proteins. In this study, we approach the activity prediction problem as a classification problem and, we aim to improve the classification accuracy by introducing an algorithm that combines partial least squares regression with mixed-integer programming based hyper-boxes classification method, where drug molecules are classified as low active or high active regarding their binding activity (IC50 values) on target proteins. We also aim to determine the most significant molecular descriptors for the drug molecules. Results We first apply our approach by analyzing the activities of widely known inhibitor datasets including Acetylcholinesterase (ACHE), Benzodiazepine Receptor (BZR), Dihydrofolate Reductase (DHFR), Cyclooxygenase-2 (COX-2) with known IC50 values. The results at this stage proved that our approach consistently gives better classification accuracies compared to 63 other reported classification methods such as SVM, Naïve Bayes, where we were able to predict the experimentally determined IC50 values with a worst case accuracy of 96%. To further test applicability of this approach we first created dataset for Cytochrome P450 C17 inhibitors and then predicted their activities with 100% accuracy. Conclusion Our results indicate that this approach can be utilized to predict the inhibitory effects of inhibitors based on their molecular descriptors. This approach will not only enhance drug discovery process, but also save time and resources committed. PMID:18834515
Alexopoulos, Leonidas G.; Klamt, Steffen
2013-01-01
Cross-referencing experimental data with our current knowledge of signaling network topologies is one central goal of mathematical modeling of cellular signal transduction networks. We present a new methodology for data-driven interrogation and training of signaling networks. While most published methods for signaling network inference operate on Bayesian, Boolean, or ODE models, our approach uses integer linear programming (ILP) on interaction graphs to encode constraints on the qualitative behavior of the nodes. These constraints are posed by the network topology and their formulation as ILP allows us to predict the possible qualitative changes (up, down, no effect) of the activation levels of the nodes for a given stimulus. We provide four basic operations to detect and remove inconsistencies between measurements and predicted behavior: (i) find a topology-consistent explanation for responses of signaling nodes measured in a stimulus-response experiment (if none exists, find the closest explanation); (ii) determine a minimal set of nodes that need to be corrected to make an inconsistent scenario consistent; (iii) determine the optimal subgraph of the given network topology which can best reflect measurements from a set of experimental scenarios; (iv) find possibly missing edges that would improve the consistency of the graph with respect to a set of experimental scenarios the most. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGFR/ErbB signaling against a library of high-throughput phosphoproteomic data measured in primary hepatocytes. Our methods detect interactions that are likely to be inactive in hepatocytes and provide suggestions for new interactions that, if included, would significantly improve the goodness of fit. Our framework is highly flexible and the underlying model requires only easily accessible biological knowledge. All related algorithms were implemented in a freely
Guo, P.; Huang, G.H.
2010-03-15
In this study, an interval-parameter semi-infinite fuzzy-chance-constrained mixed-integer linear programming (ISIFCIP) approach is developed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing interval-parameter semi-infinite programming (ISIP) and fuzzy-chance-constrained programming (FCCP) by incorporating uncertainties expressed as dual uncertainties of functional intervals and multiple uncertainties of distributions with fuzzy-interval admissible probability of violating constraint within a general optimization framework. The binary-variable solutions represent the decisions of waste-management-facility expansion, and the continuous ones are related to decisions of waste-flow allocation. The interval solutions can help decision-makers to obtain multiple decision alternatives, as well as provide bases for further analyses of tradeoffs between waste-management cost and system-failure risk. In the application to the City of Regina, Canada, two scenarios are considered. In Scenario 1, the City's waste-management practices would be based on the existing policy over the next 25 years. The total diversion rate for the residential waste would be approximately 14%. Scenario 2 is associated with a policy for waste minimization and diversion, where 35% diversion of residential waste should be achieved within 15 years, and 50% diversion over 25 years. In this scenario, not only landfill would be expanded, but also CF and MRF would be expanded. Through the scenario analyses, useful decision support for the City's solid-waste managers and decision-makers has been generated. Three special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it is useful for tackling multiple uncertainties expressed as intervals, functional intervals, probability distributions, fuzzy sets, and their
ERIC Educational Resources Information Center
Dirks, Michael K.
1984-01-01
The abacus method for instruction on addition, subtraction, and multiplication with integers is explained. How to represent the integers for each operation is detailed with words and illustrations. (MNS)
ERIC Educational Resources Information Center
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
ERIC Educational Resources Information Center
Siegel, Jonathan W.; Siegel, P. B.
2011-01-01
Integers are sometimes used in physics problems to simplify the mathematics so the arithmetic does not distract students from the physics concepts. This is particularly important in exams where students should not have to spend a lot of time using their calculators. Common uses of integers in physics problems include integer solutions to…
NASA Astrophysics Data System (ADS)
Guo, P.; Huang, G. H.; Li, Y. P.
2010-01-01
In this study, an inexact fuzzy-chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is developed for flood diversion planning under multiple uncertainties. A concept of the distribution with fuzzy boundary interval probability is defined to address multiple uncertainties expressed as integration of intervals, fuzzy sets and probability distributions. IFCTIP integrates the inexact programming, two-stage stochastic programming, integer programming and fuzzy-stochastic programming within a general optimization framework. IFCTIP incorporates the pre-regulated water-diversion policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised targets are violated. More importantly, it can facilitate dynamic programming for decisions of capacity-expansion planning under fuzzy-stochastic conditions. IFCTIP is applied to a flood management system. Solutions from IFCTIP provide desired flood diversion plans with a minimized system cost and a maximized safety level. The results indicate that reasonable solutions are generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of flood flows.
Zou, Meng; Zhang, Peng-Jun; Wen, Xin-Yu; Chen, Luonan; Tian, Ya-Ping; Wang, Yong
2015-07-15
Multi-biomarker panels can capture the nonlinear synergy among biomarkers and they are important to aid in the early diagnosis and ultimately battle complex diseases. However, identification of these multi-biomarker panels from case and control data is challenging. For example, the exhaustive search method is computationally infeasible when the data dimension is high. Here, we propose a novel method, MILP_k, to identify serum-based multi-biomarker panel to distinguish colorectal cancers (CRC) from benign colorectal tumors. Specifically, the multi-biomarker panel detection problem is modeled by a mixed integer programming to maximize the classification accuracy. Then we measured the serum profiling data for 101 CRC patients and 95 benign patients. The 61 biomarkers were analyzed individually and further their combinations by our method. We discovered 4 biomarkers as the optimal small multi-biomarker panel, including known CRC biomarkers CEA and IL-10 as well as novel biomarkers IMA and NSE. This multi-biomarker panel obtains leave-one-out cross-validation (LOOCV) accuracy to 0.7857 by nearest centroid classifier. An independent test of this panel by support vector machine (SVM) with threefold cross validation gets an AUC 0.8438. This greatly improves the predictive accuracy by 20% over the single best biomarker. Further extension of this 4-biomarker panel to a larger 13-biomarker panel improves the LOOCV to 0.8673 with independent AUC 0.8437. Comparison with the exhaustive search method shows that our method dramatically reduces the searching time by 1000-fold. Experiments on the early cancer stage samples reveal two panel of biomarkers and show promising accuracy. The proposed method allows us to select the subset of biomarkers with best accuracy to distinguish case and control samples given the number of selected biomarkers. Both receiver operating characteristic curve and precision-recall curve show our method's consistent performance gain in accuracy. Our method
Guo, P; Huang, G H
2009-01-01
In this study, an inexact fuzzy chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is proposed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing inexact two-stage programming and mixed-integer linear programming techniques by incorporating uncertainties expressed as multiple uncertainties of intervals and dual probability distributions within a general optimization framework. The developed method can provide an effective linkage between the predefined environmental policies and the associated economic implications. Four special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it provides a linkage to predefined policies that have to be respected when a modeling effort is undertaken; secondly, it is useful for tackling uncertainties presented as intervals, probabilities, fuzzy sets and their incorporation; thirdly, it facilitates dynamic analysis for decisions of facility-expansion planning and waste-flow allocation within a multi-facility, multi-period, multi-level, and multi-option context; fourthly, the penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised solid waste-generation rates are violated. In a companion paper, the developed method is applied to a real case for the long-term planning of waste management in the City of Regina, Canada. PMID:19800164
Albuquerque, Fabio; Beier, Paul
2015-01-01
Here we report that prioritizing sites in order of rarity-weighted richness (RWR) is a simple, reliable way to identify sites that represent all species in the fewest number of sites (minimum set problem) or to identify sites that represent the largest number of species within a given number of sites (maximum coverage problem). We compared the number of species represented in sites prioritized by RWR to numbers of species represented in sites prioritized by the Zonation software package for 11 datasets in which the size of individual planning units (sites) ranged from <1 ha to 2,500 km2. On average, RWR solutions were more efficient than Zonation solutions. Integer programming remains the only guaranteed way find an optimal solution, and heuristic algorithms remain superior for conservation prioritizations that consider compactness and multiple near-optimal solutions in addition to species representation. But because RWR can be implemented easily and quickly in R or a spreadsheet, it is an attractive alternative to integer programming or heuristic algorithms in some conservation prioritization contexts. PMID:25780930
NASA Astrophysics Data System (ADS)
Irmeilyana, Puspita, Fitri Maya; Indrawati
2016-02-01
The pricing for wireless networks is developed by considering linearity factors, elasticity price and price factors. Mixed Integer Nonlinear Programming of wireless pricing model is proposed as the nonlinear programming problem that can be solved optimally using LINGO 13.0. The solutions are expected to give some information about the connections between the acceptance factor and the price. Previous model worked on the model that focuses on bandwidth as the QoS attribute. The models attempt to maximize the total price for a connection based on QoS parameter. The QoS attributes used will be the bandwidth and the end to end delay that affect the traffic. The maximum goal to maximum price is achieved when the provider determine the requirement for the increment or decrement of price change due to QoS change and amount of QoS value.
Winebrake, James J; Corbett, James J; Wang, Chengfeng; Farrell, Alexander E; Woods, Pippa
2005-04-01
Emissions from passenger ferries operating in urban harbors may contribute significantly to emissions inventories and commuter exposure to air pollution. In particular, ferries are problematic because of high emissions of oxides of nitrogen (NOx) and particulate matter (PM) from primarily unregulated diesel engines. This paper explores technical solutions to reduce pollution from passenger ferries operating in the New York-New Jersey Harbor. The paper discusses and demonstrates a mixed-integer, non-linear programming model used to identify optimal control strategies for meeting NOx and PM reduction targets for 45 privately owned commuter ferries in the harbor. Results from the model can be used by policy-makers to craft programs aimed at achieving least-cost reduction targets. PMID:15887889
El-Qulity, Said Ali; Mohamed, Ali Wagdy
2016-01-01
This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness. PMID:26819583
El-Qulity, Said Ali; Mohamed, Ali Wagdy
2016-01-01
This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness. PMID:26819583
Gusfield, Dan
2010-03-01
The Multi-State Perfect Phylogeny Problem is an extension of the Binary Perfect Phylogeny Problem, allowing characters to take on more than two states. In this article, we consider three problems that extend the utility of the multi-state perfect phylogeny model: (1) the Missing Data (MD) Problem, where some entries in the input are missing and the question is whether (bounded) values for the missing data can be imputed so that the resulting data has a multi-state perfect phylogeny; (2) the Character-Removal (CR) Problem, where we want to minimize the number of characters to remove from the data so that the resulting data has a multi-state perfect phylogeny; and (3) the Missing-Data Character-Removal (MDCR) Problem, where the input has missing data and we want to impute values for the missing data to minimize the solution to the resulting Character-Removal Problem. We discuss Integer Linear Programming (ILP) solutions to these problems for the special case of three, four, and five permitted states per character, and we report on extensive empirical testing of these solutions. Then we develop a general theory to solve the MD problem for an arbitrary number of permitted states, using chordal graph theory and results on minimal triangulation of non-chordal graphs. This establishes new necessary and sufficient conditions for the existence of a perfect phylogeny with (or without) missing data. We implement the general theory using integer linear programming, although other optimization methods are possible. We extensively explore the empirical behavior of the general solution, showing that the methods are very practical for data of size and complexity that is characteristic of many current applications in phylogenetics. Some of the empirical results for the MD problem with an arbitrary number of permitted states are very surprising, suggesting the existence of additional combinatorial structure in multi-state perfect phylogenies. Finally, we note some relationships
ERIC Educational Resources Information Center
Griffiths, Martin
2011-01-01
One of the author's undergraduate students recently asked him whether it was possible to generate a random positive integer. After some thought, the author realised that there were plenty of interesting mathematical ideas inherent in her question. So much so in fact, that the author decided to organise a workshop, open both to undergraduates and…
Meyers, C A; Schulz, A S
2009-01-07
The integer equal flow problem is an NP-hard network flow problem, in which all arcs in given sets R{sub 1}, ..., R{sub {ell}} must carry equal flow. We show this problem is effectively inapproximable, even if the cardinality of each set R{sub k} is two. When {ell} is fixed, it is solvable in polynomial time.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8224.0-1 Section 8224.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES Fossil Forest Research Natural Area § 8224.0-1...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8224.0-1 Section 8224.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES Fossil Forest Research Natural Area § 8224.0-1...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8365.0-1 Section 8365.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS VISITOR SERVICES Rules of Conduct § 8365.0-1 Purpose. The...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8200.0-1 Section 8200.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES General § 8200.0-1 Purpose. This part 8200...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8351.0-1 Section 8351.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS MANAGEMENT AREAS Designated National Area § 8351.0-1 Purpose....
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8340.0-1 Section 8340.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS OFF-ROAD VEHICLES General § 8340.0-1 Purpose. The purpose of...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 1601.0-1 Section 1601.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR GENERAL MANAGEMENT (1000) PLANNING, PROGRAMMING, BUDGETING Planning § 1601.0-1 Purpose. The purpose of this subpart is to...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8351.0-1 Section 8351.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS MANAGEMENT AREAS Designated National Area § 8351.0-1 Purpose....
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8365.0-1 Section 8365.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS VISITOR SERVICES Rules of Conduct § 8365.0-1 Purpose. The...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8223.0-1 Section 8223.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES Research Natural Areas § 8223.0-1 Purpose. The...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8223.0-1 Section 8223.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES Research Natural Areas § 8223.0-1 Purpose. The...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8340.0-1 Section 8340.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS OFF-ROAD VEHICLES General § 8340.0-1 Purpose. The purpose of...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8200.0-1 Section 8200.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES General § 8200.0-1 Purpose. This part 8200...
NASA Astrophysics Data System (ADS)
Purnomo, Muhammad Ridwan Andi; Satrio Wiwoho, Yoga
2016-01-01
Facility layout becomes one of production system factor that should be managed well, as it is designated for the location of production. In managing the layout, designing the layout by considering the optimal layout condition that supports the work condition is essential. One of the method for facility layout optimization is Mixed Integer Programming (MIP). In this study, the MIP is solved using Lingo 9.0 software and considering quantitative and qualitative objectives to be achieved simultaneously: minimizing material handling cost, maximizing closeness rating, and minimizing re-layout cost. The research took place in Rekayasa Wangdi as a make to order company, focusing on the making of concrete brick dough stirring machine with 10 departments involved. The result shows an improvement in the new layout for 333,72 points of objective value compared with the initial layout. As the conclusion, the proposed MIP is proven to be used to model facility layout problem under multi objective consideration for a more realistic look.
Ko, Andi Setiady; Chang, Ni-Bin
2008-07-01
Energy supply and use is of fundamental importance to society. Although the interactions between energy and environment were originally local in character, they have now widened to cover regional and global issues, such as acid rain and the greenhouse effect. It is for this reason that there is a need for covering the direct and indirect economic and environmental impacts of energy acquisition, transport, production and use. In this paper, particular attention is directed to ways of resolving conflict between economic and environmental goals by encouraging a power plant to consider co-firing biomass and refuse-derived fuel (RDF) with coal simultaneously. It aims at reducing the emission level of sulfur dioxide (SO(2)) in an uncertain environment, using the power plant in Michigan City, Indiana as an example. To assess the uncertainty by a comparative way both deterministic and grey nonlinear mixed integer programming (MIP) models were developed to minimize the net operating cost with respect to possible fuel combinations. It aims at generating the optimal portfolio of alternative fuels while maintaining the same electricity generation simultaneously. To ease the solution procedure stepwise relaxation algorithm was developed for solving the grey nonlinear MIP model. Breakeven alternative fuel value can be identified in the post-optimization stage for decision-making. Research findings show that the inclusion of RDF does not exhibit comparative advantage in terms of the net cost, albeit relatively lower air pollution impact. Yet it can be sustained by a charge system, subsidy program, or emission credit as the price of coal increases over time. PMID:17395362
2013-01-01
that these constraints can often lead to significant reductions in the gap between the optimal solution and its non-integral linear programming bound relative to the prior art as well as often substantially faster processing of moderately hard problem instances. Conclusion We provide an indication of the conditions under which such an optimal enumeration approach is likely to be feasible, suggesting that these strategies are usable for relatively large numbers of taxa, although with stricter limits on numbers of variable sites. The work thus provides methodology suitable for provably optimal solution of some harder instances that resist all prior approaches. PMID:23343437
Aerospace Applications of Integer and Combinatorial Optimization
NASA Technical Reports Server (NTRS)
Padula, S. L.; Kincaid, R. K.
1995-01-01
Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.
Aerospace applications on integer and combinatorial optimization
NASA Technical Reports Server (NTRS)
Padula, S. L.; Kincaid, R. K.
1995-01-01
Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 1601.0-1 Section 1601.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR GENERAL MANAGEMENT (1000) PLANNING, PROGRAMMING, BUDGETING Planning §...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 1601.0-1 Section 1601.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR GENERAL MANAGEMENT (1000) PLANNING, PROGRAMMING, BUDGETING Planning §...
Computer Corner: Spreadsheets, Power Series, Generating Functions, and Integers.
ERIC Educational Resources Information Center
Snow, Donald R.
1989-01-01
Implements a table algorithm on a spreadsheet program and obtains functions for several number sequences such as the Fibonacci and Catalan numbers. Considers other applications of the table algorithm to integers represented in various number bases. (YP)
Mixed integer evolution strategies for parameter optimization.
Li, Rui; Emmerich, Michael T M; Eggermont, Jeroen; Bäck, Thomas; Schütz, M; Dijkstra, J; Reiber, J H C
2013-01-01
Evolution strategies (ESs) are powerful probabilistic search and optimization algorithms gleaned from biological evolution theory. They have been successfully applied to a wide range of real world applications. The modern ESs are mainly designed for solving continuous parameter optimization problems. Their ability to adapt the parameters of the multivariate normal distribution used for mutation during the optimization run makes them well suited for this domain. In this article we describe and study mixed integer evolution strategies (MIES), which are natural extensions of ES for mixed integer optimization problems. MIES can deal with parameter vectors consisting not only of continuous variables but also with nominal discrete and integer variables. Following the design principles of the canonical evolution strategies, they use specialized mutation operators tailored for the aforementioned mixed parameter classes. For each type of variable, the choice of mutation operators is governed by a natural metric for this variable type, maximal entropy, and symmetry considerations. All distributions used for mutation can be controlled in their shape by means of scaling parameters, allowing self-adaptation to be implemented. After introducing and motivating the conceptual design of the MIES, we study the optimality of the self-adaptation of step sizes and mutation rates on a generalized (weighted) sphere model. Moreover, we prove global convergence of the MIES on a very general class of problems. The remainder of the article is devoted to performance studies on artificial landscapes (barrier functions and mixed integer NK landscapes), and a case study in the optimization of medical image analysis systems. In addition, we show that with proper constraint handling techniques, MIES can also be applied to classical mixed integer nonlinear programming problems. PMID:22122384
Code of Federal Regulations, 2014 CFR
2014-10-01
... and Mining, Wilderness Review Program § 3802.0-1 Purpose. The purpose of this subpart is to establish procedures to prevent impairment of the suitability of lands under wilderness review for inclusion in the wilderness system and to prevent unnecessary or undue degradation by activities authorized by the U.S....
Code of Federal Regulations, 2012 CFR
2012-10-01
... and Mining, Wilderness Review Program § 3802.0-1 Purpose. The purpose of this subpart is to establish procedures to prevent impairment of the suitability of lands under wilderness review for inclusion in the wilderness system and to prevent unnecessary or undue degradation by activities authorized by the U.S....
Code of Federal Regulations, 2013 CFR
2013-10-01
... and Mining, Wilderness Review Program § 3802.0-1 Purpose. The purpose of this subpart is to establish procedures to prevent impairment of the suitability of lands under wilderness review for inclusion in the wilderness system and to prevent unnecessary or undue degradation by activities authorized by the U.S....
Code of Federal Regulations, 2011 CFR
2011-10-01
... and Mining, Wilderness Review Program § 3802.0-1 Purpose. The purpose of this subpart is to establish procedures to prevent impairment of the suitability of lands under wilderness review for inclusion in the wilderness system and to prevent unnecessary or undue degradation by activities authorized by the U.S....
Aerospace applications of integer and combinatorial optimization
NASA Technical Reports Server (NTRS)
Padula, S. L.; Kincaid, R. K.
1995-01-01
Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in solving combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on a large space structure and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.
Integer Operations Using a Whiteboard
ERIC Educational Resources Information Center
Andrews, Delise R.
2011-01-01
Interactive whiteboards are somewhat unimpressive at first and look like the whiteboards that already hang on the walls of many classrooms. However, integrating interactive whiteboard technology in a unit on adding and subtracting integers enhances student engagement and understanding. In this article, the author describes how she used an…
Integers Made Easy: Just Walk It Off
ERIC Educational Resources Information Center
Nurnberger-Haag, Julie
2007-01-01
This article describes a multisensory method for teaching students how to multiply and divide as well as add and subtract integers. The author uses sidewalk chalk and the underlying concept of integers to physically and mentally engage students in understanding the concepts of integers, making connections, and developing computational fluency.…
Investigating data envelopment analysis model with potential improvement for integer output values
NASA Astrophysics Data System (ADS)
Hussain, Mushtaq Taleb; Ramli, Razamin; Khalid, Ruzelan
2015-12-01
The decrement of input proportions in DEA model is associated with its input reduction. This reduction is apparently good for economy since it could reduce unnecessary cost resources. However, in some situations the reduction of relevant inputs such as labour could create social problems. Such inputs should thus be maintained or increased. This paper develops an advanced radial DEA model dealing with mixed integer linear programming to improve integer output values through the combination of inputs. The model can deal with real input values and integer output values. This model is valuable for situations dealing with input combination to improve integer output values as faced by most organizations.
Solving the Water Jugs Problem by an Integer Sequence Approach
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2012-01-01
In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…
Order and Value: Transitioning to Integers
ERIC Educational Resources Information Center
Bofferding, Laura
2014-01-01
As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…
Prospective Elementary Teachers' Conceptual Understanding of Integers
ERIC Educational Resources Information Center
Reeder, Stacy; Bateiha, Summer
2016-01-01
This investigation examined the degree to which prospective elementary teachers had developed a meaningful and conceptual understanding of what integers are and explored their development of models for multiplication with integers that are related to everyday activities. Additionally, this study explored how these understandings informed…
Code of Federal Regulations, 2012 CFR
2012-01-01
... 16 Commercial Practices 1 2012-01-01 2012-01-01 false The Commission. 0.1 Section 0.1 Commercial Practices FEDERAL TRADE COMMISSION ORGANIZATION, PROCEDURES AND RULES OF PRACTICE ORGANIZATION § 0.1 The Commission. The Federal Trade Commission is an independent administrative agency which was organized in...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 3150.0-1 Section 3150.0-1 Public... Interest Lands Conservation Act (See 50 CFR part 37). ... and Gas Geophysical Exploration; General § 3150.0-1 Purpose. The purpose of this part is to...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 3150.0-1 Section 3150.0-1 Public... Interest Lands Conservation Act (See 50 CFR part 37). ... and Gas Geophysical Exploration; General § 3150.0-1 Purpose. The purpose of this part is to...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 3150.0-1 Section 3150.0-1 Public... Interest Lands Conservation Act (See 50 CFR part 37). ... and Gas Geophysical Exploration; General § 3150.0-1 Purpose. The purpose of this part is to...
Code of Federal Regulations, 2012 CFR
2012-04-01
... 26 Internal Revenue 14 2012-04-01 2012-04-01 false Introduction. 25.0-1 Section 25.0-1 Internal...; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations... Revenue Code of 1954 by Treasury Decision 6091, signed August 16, 1954 (19 FR 5167, Aug. 17, 1954)....
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Purpose. 3150.0-1 Section 3150.0-1 Public... Interest Lands Conservation Act (See 50 CFR part 37). ... and Gas Geophysical Exploration; General § 3150.0-1 Purpose. The purpose of this part is to...
Code of Federal Regulations, 2014 CFR
2014-04-01
... 26 Internal Revenue 14 2014-04-01 2013-04-01 true Introduction. 20.0-1 Section 20.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES ESTATE TAX; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1) The regulations in this part (part...
Code of Federal Regulations, 2013 CFR
2013-04-01
... 26 Internal Revenue 14 2013-04-01 2013-04-01 false Introduction. 20.0-1 Section 20.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES ESTATE TAX; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1) The regulations in this part (part...
28 CFR 0.1 - Organizational units.
Code of Federal Regulations, 2012 CFR
2012-07-01
... Structure of the Department of Justice § 0.1 Organizational units. The Department of Justice shall consist... Register citations affecting § 0.1, see the List of CFR Sections Affected, which appears in the Finding... 28 Judicial Administration 1 2012-07-01 2012-07-01 false Organizational units. 0.1 Section...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 16 Commercial Practices 1 2011-01-01 2011-01-01 false The Commission. 0.1 Section 0.1 Commercial Practices FEDERAL TRADE COMMISSION ORGANIZATION, PROCEDURES AND RULES OF PRACTICE ORGANIZATION § 0.1 The Commission. The Federal Trade Commission is an independent administrative agency which was organized in...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 1 2014-10-01 2014-10-01 false The Commission. 0.1 Section 0.1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization General § 0.1 The Commission. The Federal Communications Commission is composed of five (5) members who are appointed by...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 16 Commercial Practices 1 2010-01-01 2010-01-01 false The Commission. 0.1 Section 0.1 Commercial Practices FEDERAL TRADE COMMISSION ORGANIZATION, PROCEDURES AND RULES OF PRACTICE ORGANIZATION § 0.1 The Commission. The Federal Trade Commission is an independent administrative agency which was organized in...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 1 2013-10-01 2013-10-01 false The Commission. 0.1 Section 0.1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization General § 0.1 The Commission. The Federal Communications Commission is composed of five (5) members who are appointed by...
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false The Commission. 0.1 Section 0.1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization General § 0.1 The Commission. The Federal Communications Commission is composed of five (5) members who are appointed by...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 1 2011-10-01 2011-10-01 false The Commission. 0.1 Section 0.1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization General § 0.1 The Commission. The Federal Communications Commission is composed of five (5) members who are appointed by...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 2300.0-1 Section 2300.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LAND WITHDRAWALS Withdrawals, General § 2300.0-1 Purpose. (a) These regulations set...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 1784.0-1 Section 1784.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR GENERAL MANAGEMENT (1000) COOPERATIVE RELATIONS Advisory Committees § 1784.0-1 Purpose. This subpart contains standards...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 2911.0-1 Section 2911.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LEASES Airport § 2911.0-1 Purpose. This subpart sets forth procedures for issuance of...
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Purpose. 2911.0-1 Section 2911.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LEASES Airport § 2911.0-1 Purpose. This subpart...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 26 Internal Revenue 15 2010-04-01 2010-04-01 false Introduction. 31.0-1 Section 31.0-1 Internal... OF INCOME TAX AT SOURCE EMPLOYMENT TAXES AND COLLECTION OF INCOME TAX AT SOURCE Introduction § 31.0-1 Introduction. (a) In general. The regulations in this part relate to the employment taxes imposed by subtitle...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 44.0-1 Section 44.0-1 Internal... ON WAGERING; EFFECTIVE JANUARY 1, 1955 Introduction § 44.0-1 Introduction. (a) In general. The... provisions of subtitle F of the Code (Procedure and Administration) which have special application to...
Factorization of large integers on a massively parallel computer
Davis, J.A.; Holdridge, D.B.
1988-01-01
Our interest in integer factorization at Sandia National Laboratories is motivated by cryptographic applications and in particular the security of the RSA encryption-decryption algorithm. We have implemented our version of the quadratic sieve procedure on the NCUBE computer with 1024 processors (nodes). The new code is significantly different in all important aspects from the program used to factor number of order 10/sup 70/ on a single processor CRAY computer. Capabilities of parallel processing and limitation of small local memory necessitated this entirely new implementation. This effort involved several restarts as realizations of program structures that seemed appealing bogged down due to inter-processor communications. We are presently working with integers of magnitude about 10/sup 70/ in tuning this code to the novel hardware. 6 refs., 3 figs.
Solving the water jugs problem by an integer sequence approach
NASA Astrophysics Data System (ADS)
Man, Yiu-Kwong
2012-01-01
In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and lecturers involved in teaching mathematical problem solving, recreational mathematics, or elementary number theory.
Integer cosine transform for image compression
NASA Technical Reports Server (NTRS)
Cheung, K.-M.; Pollara, F.; Shahshahani, M.
1991-01-01
This article describes a recently introduced transform algorithm called the integer cosine transform (ICT), which is used in transform-based data compression schemes. The ICT algorithm requires only integer operations on small integers and at the same time gives a rate-distortion performance comparable to that offered by the floating-point discrete cosine transform (DCT). The article addresses the issue of implementation complexity, which is of prime concern for source coding applications of interest in deep-space communications. Complexity reduction in the transform stage of the compression scheme is particularly relevant, since this stage accounts for most (typically over 80 percent) of the computational load.
RSM 1.0 - A RESUPPLY SCHEDULER USING INTEGER OPTIMIZATION
NASA Technical Reports Server (NTRS)
Viterna, L. A.
1994-01-01
RSM, Resupply Scheduling Modeler, is a fully menu-driven program that uses integer programming techniques to determine an optimum schedule for replacing components on or before the end of a fixed replacement period. Although written to analyze the electrical power system on the Space Station Freedom, RSM is quite general and can be used to model the resupply of almost any system subject to user-defined resource constraints. RSM is based on a specific form of the general linear programming problem in which all variables in the objective function and all variables in the constraints are integers. While more computationally intensive, integer programming was required for accuracy when modeling systems with small quantities of components. Input values for component life cane be real numbers, RSM converts them to integers by dividing the lifetime by the period duration, then reducing the result to the next lowest integer. For each component, there is a set of constraints that insure that it is replaced before its lifetime expires. RSM includes user-defined constraints such as transportation mass and volume limits, as well as component life, available repair crew time and assembly sequences. A weighting factor allows the program to minimize factors such as cost. The program then performs an iterative analysis, which is displayed during the processing. A message gives the first period in which resources are being exceeded on each iteration. If the scheduling problem is unfeasible, the final message will also indicate the first period in which resources were exceeded. RSM is written in APL2 for IBM PC series computers and compatibles. A stand-alone executable version of RSM is provided; however, this is a "packed" version of RSM which can only utilize the memory within the 640K DOS limit. This executable requires at least 640K of memory and DOS 3.1 or higher. Source code for an APL2/PC workspace version is also provided. This version of RSM can make full use of any
Code of Federal Regulations, 2011 CFR
2011-04-01
... 26 Internal Revenue 14 2011-04-01 2010-04-01 true Introduction. 25.0-1 Section 25.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES GIFT TAX; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations in this part are designated “Gift...
Code of Federal Regulations, 2013 CFR
2013-04-01
... 26 Internal Revenue 14 2013-04-01 2013-04-01 false Introduction. 25.0-1 Section 25.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES GIFT TAX; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations in this part are designated “Gift...
Code of Federal Regulations, 2014 CFR
2014-04-01
... 26 Internal Revenue 14 2014-04-01 2013-04-01 true Introduction. 25.0-1 Section 25.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES GIFT TAX; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations in this part are designated “Gift...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 26 Internal Revenue 14 2010-04-01 2010-04-01 false Introduction. 25.0-1 Section 25.0-1 Internal...; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations... pursuant to Subchapter C are set forth in §§ 25.2521-1 through 25.2524-1. (4) Procedure and...
Code of Federal Regulations, 2011 CFR
2011-10-01
... transfer of certain public lands under the Recreation and Public Purposes Act as amended (43 U.S.C. 869 et... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 2740.0-1 Section 2740.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT,...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 2300.0-1 Section 2300.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LAND WITHDRAWALS Withdrawals, General §...
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Purpose. 2300.0-1 Section 2300.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LAND WITHDRAWALS Withdrawals, General §...
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Purpose. 1601.0-1 Section 1601.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT... for public lands administered by the Bureau of Land Management....
Mixed-Integer Formulations for Constellation Scheduling
NASA Astrophysics Data System (ADS)
Valicka, C.; Hart, W.; Rintoul, M.
Remote sensing systems have expanded the set of capabilities available for and critical to national security. Cooperating, high-fidelity sensing systems and growing mission applications have exponentially increased the set of potential schedules. A definitive lack of advanced tools places an increased burden on operators, as planning and scheduling remain largely manual tasks. This is particularly true in time-critical planning activities where operators aim to accomplish a large number of missions through optimal utilization of single or multiple sensor systems. Automated scheduling through identification and comparison of alternative schedules remains a challenging problem applicable across all remote sensing systems. Previous approaches focused on a subset of sensor missions and do not consider ad-hoc tasking. We have begun development of a robust framework that leverages the Pyomo optimization modeling language for the design of a tool to assist sensor operators planning under the constraints of multiple concurrent missions and uncertainty. Our scheduling models have been formulated to address the stochastic nature of ad-hoc tasks inserted under a variety of scenarios. Operator experience is being leveraged to select appropriate model objectives. Successful development of the framework will include iterative development of high-fidelity mission models that consider and expose various schedule performance metrics. Creating this tool will aid time-critical scheduling by increasing planning efficiency, clarifying the value of alternative modalities uniquely provided by multi-sensor systems, and by presenting both sets of organized information to operators. Such a tool will help operators more quickly and fully utilize sensing systems, a high interest objective within the current remote sensing operations community. Preliminary results for mixed-integer programming formulations of a sensor scheduling problem will be presented. Assumptions regarding sensor geometry
Code of Federal Regulations, 2012 CFR
2012-10-01
... OF THE INTERIOR TECHNICAL SERVICES (9000) FIRE MANAGEMENT Wildfire Prevention § 9212.0-1 Purpose. The purpose of this subpart is to set forth procedures to prevent wildfires on the public lands....
Code of Federal Regulations, 2011 CFR
2011-10-01
... OF THE INTERIOR TECHNICAL SERVICES (9000) FIRE MANAGEMENT Wildfire Prevention § 9212.0-1 Purpose. The purpose of this subpart is to set forth procedures to prevent wildfires on the public lands....
Code of Federal Regulations, 2014 CFR
2014-10-01
... OF THE INTERIOR TECHNICAL SERVICES (9000) FIRE MANAGEMENT Wildfire Prevention § 9212.0-1 Purpose. The purpose of this subpart is to set forth procedures to prevent wildfires on the public lands....
Code of Federal Regulations, 2013 CFR
2013-10-01
... OF THE INTERIOR TECHNICAL SERVICES (9000) FIRE MANAGEMENT Wildfire Prevention § 9212.0-1 Purpose. The purpose of this subpart is to set forth procedures to prevent wildfires on the public lands....
Code of Federal Regulations, 2011 CFR
2011-10-01
... HORSES AND BURROS General § 4700.0-1 Purpose. The purpose of these regulations is to implement the laws relating to the protection, management, and control of wild horses and burros under the administration...
Code of Federal Regulations, 2013 CFR
2013-10-01
... OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) DESERT-LAND ENTRIES Desert-Land Entries: General § 2520.0-1 Purpose. (a) It is the purpose of the statutes governing desert-land entries to encourage...
Code of Federal Regulations, 2011 CFR
2011-10-01
... OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) DESERT-LAND ENTRIES Desert-Land Entries: General § 2520.0-1 Purpose. (a) It is the purpose of the statutes governing desert-land entries to encourage...
Code of Federal Regulations, 2014 CFR
2014-10-01
... OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) DESERT-LAND ENTRIES Desert-Land Entries: General § 2520.0-1 Purpose. (a) It is the purpose of the statutes governing desert-land entries to encourage...
Code of Federal Regulations, 2012 CFR
2012-10-01
... OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) DESERT-LAND ENTRIES Desert-Land Entries: General § 2520.0-1 Purpose. (a) It is the purpose of the statutes governing desert-land entries to encourage...
Code of Federal Regulations, 2014 CFR
2014-10-01
... HORSES AND BURROS General § 4700.0-1 Purpose. The purpose of these regulations is to implement the laws relating to the protection, management, and control of wild horses and burros under the administration...
Slip and Slide Method of Factoring Trinomials with Integer Coefficients over the Integers
ERIC Educational Resources Information Center
Donnell, William A.
2012-01-01
In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss…
Integer Solutions of a Special Diophantine Equation
NASA Astrophysics Data System (ADS)
Özkoç, Arzu; Tekcan, Ahmet
2011-09-01
Let t≠1 be an integer. In this work, we determine the integer solutions of Diophantine equation D:x2+(2-t2)y2+(-2t2-2t+2)x+(2t5-6t3+4t)y-t8+4t6-4t4+2t3+t2-2t = 0 over Z and also over finite fields Fp for primes p≥2. Also we derive some recurrence relations on the integer solutions (xn,yn) of D and formulate the the n—th solution (xn,yn) by using the simple continued fraction expansion of xn/yn.
PSLQ: An Algorithm to Discover Integer Relations
Bailey, David H.; Borwein, J. M.
2009-04-03
Let x = (x{sub 1}, x{sub 2} {hor_ellipsis}, x{sub n}) be a vector of real or complex numbers. x is said to possess an integer relation if there exist integers a{sub i}, not all zero, such that a{sub 1}x{sub 1} + a{sub 2}x{sub 2} + {hor_ellipsis} + a{sub n}x{sub n} = 0. By an integer relation algorithm, we mean a practical computational scheme that can recover the vector of integers ai, if it exists, or can produce bounds within which no integer relation exists. As we will see in the examples below, an integer relation algorithm can be used to recognize a computed constant in terms of a formula involving known constants, or to discover an underlying relation between quantities that can be computed to high precision. At the present time, the most effective algorithm for integer relation detection is the 'PSLQ' algorithm of mathematician-sculptor Helaman Ferguson [10, 4]. Some efficient 'multi-level' implementations of PSLQ, as well as a variant of PSLQ that is well-suited for highly parallel computer systems, are given in [4]. PSLQ constructs a sequence of integer-valued matrices B{sub n} that reduces the vector y = xB{sub n}, until either the relation is found (as one of the columns of B{sub n}), or else precision is exhausted. At the same time, PSLQ generates a steadily growing bound on the size of any possible relation. When a relation is found, the size of smallest entry of the vector y abruptly drops to roughly 'epsilon' (i.e. 10{sup -p}, where p is the number of digits of precision). The size of this drop can be viewed as a 'confidence level' that the relation is real and not merely a numerical artifact - a drop of 20 or more orders of magnitude almost always indicates a real relation. Very high precision arithmetic must be used in PSLQ. If one wishes to recover a relation of length n, with coefficients of maximum size d digits, then the input vector x must be specified to at least nd digits, and one must employ nd-digit floating-point arithmetic. Maple and
Reducing Truncation Error In Integer Processing
NASA Technical Reports Server (NTRS)
Thomas, J. Brooks; Berner, Jeffrey B.; Graham, J. Scott
1995-01-01
Improved method of rounding off (truncation of least-significant bits) in integer processing of data devised. Provides for reduction, to extremely low value, of numerical bias otherwise generated by accumulation of truncation errors from many arithmetic operations. Devised for use in integer signal processing, in which rescaling and truncation usually performed to reduce number of bits, which typically builds up in sequence of operations. Essence of method to alternate direction of roundoff (plus, then minus) on alternate occurrences of truncated values contributing to bias.
Code of Federal Regulations, 2011 CFR
2011-10-01
... OF THE INTERIOR MINERALS MANAGEMENT (3000) LEASING IN SPECIAL TAR SAND AREAS Leasing in Special Tar Sand Areas § 3141.0-1 Purpose. The purpose of this subpart is to provide for the competitive leasing of lands and issuance of Combined Hydrocarbon Leases, Oil and Gas Leases, or Tar Sand Leases within...
Code of Federal Regulations, 2012 CFR
2012-10-01
... OF THE INTERIOR MINERALS MANAGEMENT (3000) LEASING IN SPECIAL TAR SAND AREAS Leasing in Special Tar Sand Areas § 3141.0-1 Purpose. The purpose of this subpart is to provide for the competitive leasing of lands and issuance of Combined Hydrocarbon Leases, Oil and Gas Leases, or Tar Sand Leases within...
Code of Federal Regulations, 2014 CFR
2014-10-01
... OF THE INTERIOR MINERALS MANAGEMENT (3000) LEASING IN SPECIAL TAR SAND AREAS Leasing in Special Tar Sand Areas § 3141.0-1 Purpose. The purpose of this subpart is to provide for the competitive leasing of lands and issuance of Combined Hydrocarbon Leases, Oil and Gas Leases, or Tar Sand Leases within...
Code of Federal Regulations, 2013 CFR
2013-10-01
... OF THE INTERIOR MINERALS MANAGEMENT (3000) LEASING IN SPECIAL TAR SAND AREAS Leasing in Special Tar Sand Areas § 3141.0-1 Purpose. The purpose of this subpart is to provide for the competitive leasing of lands and issuance of Combined Hydrocarbon Leases, Oil and Gas Leases, or Tar Sand Leases within...
Code of Federal Regulations, 2010 CFR
2010-04-01
...; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1... dying after August 16, 1954, and (ii) certain related administrative provisions of subtitle F of the... provided, the Estate Tax Regulations are applicable to the estates of decedents dying after August 16,...
Code of Federal Regulations, 2011 CFR
2011-04-01
...; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1... dying after August 16, 1954, and (ii) certain related administrative provisions of subtitle F of the... provided, the Estate Tax Regulations are applicable to the estates of decedents dying after August 16,...
Code of Federal Regulations, 2012 CFR
2012-04-01
...; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1... dying after August 16, 1954, and (ii) certain related administrative provisions of subtitle F of the... provided, the Estate Tax Regulations are applicable to the estates of decedents dying after August 16,...
Semiperfect and Integer-Perfect Numbers.
ERIC Educational Resources Information Center
Costello, Patrick
1991-01-01
The number theory concepts of perfect, deficient, and abundant numbers are subdivided and then utilized to discuss propositions concerning semiperfect, weird, and integer-perfect numbers. Conjectures about relationships among these latter numbers are suggested as avenues for further investigation. (JJK)
Dollars & Sense: Students' Integer Perspectives
ERIC Educational Resources Information Center
Whitacre, Ian; Bishop, Jessica Pierson; Philipp, Randolph A.; Lamb, Lisa L.; Schappelle, Bonnie P.
2014-01-01
A story problem about borrowing money, presented in this article, may be represented with positive or negative numbers and thought about in different ways. The authors describe ideas related to integers (both positive and negative) and how students used them in relation to a story problem, and how they related these ideas to equations.
How to Differentiate an Integer Modulo n
ERIC Educational Resources Information Center
Emmons, Caleb; Krebs, Mike; Shaheen, Anthony
2009-01-01
A number derivative is a numerical mapping that satisfies the product rule. In this paper, we determine all number derivatives on the set of integers modulo n. We also give a list of undergraduate research projects to pursue using these maps as a starting point.
ERIC Educational Resources Information Center
Richardson, William H., Jr.
2006-01-01
Computational precision is sometimes given short shrift in a first programming course. Treating this topic requires discussing integer and floating-point number representations and inaccuracies that may result from their use. An example of a moderately simple programming problem from elementary statistics was examined. It forced students to…
Slip and slide method of factoring trinomials with integer coefficients over the integers
NASA Astrophysics Data System (ADS)
Donnell, William A.
2012-06-01
In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss the Slip and Slide Method and present a theoretical justification of why it works.
On the computation of the best integer equivariant estimator
NASA Astrophysics Data System (ADS)
Teunissen, P. J. G.
Carrier phase integer ambiguity resolution is the key to high precision Global Navigation Satellite System (GNSS) positioning and navigation. In this contribution we study some of the computational aspects of best integer equivariant estimation. The best integer equivariant (BIE) estimator is the optimal estimator of the class of integer equivariant estimators, which is one of the three classes of estimators for carrier phase ambiguity resolution. The two other classes are the class of integer estimators and the class of integer aperture estimators. Since the BIE-estimator can not be computed exactly, it is shown how to approximate this estimator while retaining the property of integer equivariance. It is also shown how the decorrelating Z-transformation and the integer search of the LAMBDA method can be used to speed up the computation of the BIE-estimator.
Unlimited Capacity Parallel Quantity Comparison of Multiple Integers
ERIC Educational Resources Information Center
Blanc-Goldhammer, Daryn R.; Cohen, Dale J.
2014-01-01
Research has shown that integer comparison is quick and efficient. This efficiency may be a function of the structure of the integer comparison system. The present study tests whether integers are compared with an unlimited capacity system or a limited capacity system. We tested these models using a visual search task with time delimitation. The…
Integer sparse distributed memory: analysis and results.
Snaider, Javier; Franklin, Stan; Strain, Steve; George, E Olusegun
2013-10-01
Sparse distributed memory is an auto-associative memory system that stores high dimensional Boolean vectors. Here we present an extension of the original SDM, the Integer SDM that uses modular arithmetic integer vectors rather than binary vectors. This extension preserves many of the desirable properties of the original SDM: auto-associativity, content addressability, distributed storage, and robustness over noisy inputs. In addition, it improves the representation capabilities of the memory and is more robust over normalization. It can also be extended to support forgetting and reliable sequence storage. We performed several simulations that test the noise robustness property and capacity of the memory. Theoretical analyses of the memory's fidelity and capacity are also presented. PMID:23747569
CRAY-1S integer vector utility library
Rogers, J.N.; Tooman, T.P.
1982-06-01
This report describes thirty-five integer or packed vector utility routines, and documents their testing. These routines perform various vector searches, linear algebra functions, memory resets, and vector boolean operations. They are written in CAL, the assembly language on the CRAY-1S computer. By utilizing the vector processing features of that machine, they are optimized in terms of run time. Each routine has been extensively tested.
HypExp 2, expanding hypergeometric functions about half-integer parameters
NASA Astrophysics Data System (ADS)
Huber, Tobias; Maître, Daniel
2012-04-01
HypExp is a Mathematica package for expanding hypergeometric functions about integer and half-integer parameters. New version program summaryProgram title: HypExp 2 Catalogue identifier: ADXF_v2_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXF_v2_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 107 274 No. of bytes in distributed program, including test data, etc.: 2 690 337 Distribution format: tar.gz Programming language: Mathematica 7 and 8 Computer: Computers running Mathematica Operating system: Linux, Windows, Mac RAM: Depending on the complexity of the problem Supplementary material: Library files which contain the expansion of certain hypergeometric functions around their parameters are available Classification: 4.7, 5 Catalogue identifier of previous version: ADXF_v2_0 Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 755 Does the new version supersede the previous version?: Yes Nature of problem: Expansion of hypergeometric functions about parameters that are integer and/or half-integer valued. Solution method: New algorithm implemented in Mathematica. Reasons for new version: Compatibility with new versions of Mathematica. Summary of revisions: Support for versions 7 and 8 of Mathematica added. No changes in the features of the package. Restrictions: The classes of hypergeometric functions with half-integer parameters that can be expanded are listed in the long write-up. Additional comments: The package uses the package HPL included in the distribution. Running time: Depending on the expansion.
NASA Astrophysics Data System (ADS)
Jazaeri, S.; Amiri-Simkooei, A. R.; Sharifi, M. A.
2012-02-01
GNSS ambiguity resolution is the key issue in the high-precision relative geodetic positioning and navigation applications. It is a problem of integer programming plus integer quality evaluation. Different integer search estimation methods have been proposed for the integer solution of ambiguity resolution. Slow rate of convergence is the main obstacle to the existing methods where tens of ambiguities are involved. Herein, integer search estimation for the GNSS ambiguity resolution based on the lattice theory is proposed. It is mathematically shown that the closest lattice point problem is the same as the integer least-squares (ILS) estimation problem and that the lattice reduction speeds up searching process. We have implemented three integer search strategies: Agrell, Eriksson, Vardy, Zeger (AEVZ), modification of Schnorr-Euchner enumeration (M-SE) and modification of Viterbo-Boutros enumeration (M-VB). The methods have been numerically implemented in several simulated examples under different scenarios and over 100 independent runs. The decorrelation process (or unimodular transformations) has been first used to transform the original ILS problem to a new one in all simulations. We have then applied different search algorithms to the transformed ILS problem. The numerical simulations have shown that AEVZ, M-SE, and M-VB are about 320, 120 and 50 times faster than LAMBDA, respectively, for a search space of dimension 40. This number could change to about 350, 160 and 60 for dimension 45. The AEVZ is shown to be faster than MLAMBDA by a factor of 5. Similar conclusions could be made using the application of the proposed algorithms to the real GPS data.
28 CFR 0.1 - Organizational units.
Code of Federal Regulations, 2010 CFR
2010-07-01
... Division. Justice Management Division. Bureaus Federal Bureau of Investigation. Bureau of Prisons. Drug.... INTERPOL—United States National Central Bureau. Office of International Programs. Office of Community Oriented Policing Services. Office on Violence Against Women. Office of the Federal Detention......
28 CFR 0.1 - Organizational units.
Code of Federal Regulations, 2014 CFR
2014-07-01
... Security Division. Tax Division. Justice Management Division. Bureaus Federal Bureau of Investigation.... INTERPOL—United States National Central Bureau. Office of International Programs. Office of Community Oriented Policing Services. Office on Violence Against Women. Office of the Federal Detention...
28 CFR 0.1 - Organizational units.
Code of Federal Regulations, 2013 CFR
2013-07-01
... Security Division. Tax Division. Justice Management Division. Bureaus Federal Bureau of Investigation.... INTERPOL—United States National Central Bureau. Office of International Programs. Office of Community Oriented Policing Services. Office on Violence Against Women. Office of the Federal Detention...
28 CFR 0.1 - Organizational units.
Code of Federal Regulations, 2011 CFR
2011-07-01
... Security Division. Tax Division. Justice Management Division. Bureaus Federal Bureau of Investigation.... INTERPOL—United States National Central Bureau. Office of International Programs. Office of Community Oriented Policing Services. Office on Violence Against Women. Office of the Federal Detention...
Multi-objective mixed integer strategy for the optimisation of biological networks.
Sendín, J O H; Exler, O; Banga, J R
2010-05-01
In this contribution, the authors consider multi-criteria optimisation problems arising from the field of systems biology when both continuous and integer decision variables are involved. Mathematically, they are formulated as mixed-integer non-linear programming problems. The authors present a novel solution strategy based on a global optimisation approach for dealing with this class of problems. Its usefulness and capabilities are illustrated with two metabolic engineering case studies. For these problems, the authors show how the set of optimal solutions (the so-called Pareto front) is successfully and efficiently obtained, providing further insight into the systems under consideration regarding their optimal manipulation. PMID:20500003
Horizontal visibility graphs from integer sequences
NASA Astrophysics Data System (ADS)
Lacasa, Lucas
2016-09-01
The horizontal visibility graph (HVG) is a graph-theoretical representation of a time series and builds a bridge between dynamical systems and graph theory. In recent years this representation has been used to describe and theoretically compare different types of dynamics and has been applied to characterize empirical signals, by extracting topological features from the associated HVGs which have shown to be informative on the class of dynamics. Among some other measures, it has been shown that the degree distribution of these graphs is a very informative feature that encapsulates nontrivial information of the series's generative dynamics. In particular, the HVG associated to a bi-infinite real-valued series of independent and identically distributed random variables is a universal exponential law P(k)=(1/3){(2/3)}k-2, independent of the series marginal distribution. Most of the current applications have however only addressed real-valued time series, as no exact results are known for the topological properties of HVGs associated to integer-valued series. In this paper we explore this latter situation and address univariate time series where each variable can only take a finite number n of consecutive integer values. We are able to construct an explicit formula for the parametric degree distribution {P}n(k), which we prove to converge to the continuous case for large n and deviates otherwise. A few applications are then considered.
Camera placement in integer lattices (extended abstract)
NASA Astrophysics Data System (ADS)
Pocchiola, Michel; Kranakis, Evangelos
1990-09-01
Techniques for studying an art gallery problem (the camera placement problem) in the infinite lattice (L sup d) of d tuples of integers are considered. A lattice point A is visible from a camera C positioned at a vertex of (L sup d) if A does not equal C and if the line segment joining A and C crosses no other lattice vertex. By using a combination of probabilistic, combinatorial optimization and algorithmic techniques the position they must occupy in the lattice (L sup d) in the order to maximize their visibility can be determined in polynomial time, for any given number s less than or equal to (5 sup d) of cameras. This improves previous results for s less than or equal to (3 sup d).
NASA Astrophysics Data System (ADS)
Pratheep Kumar, Sathasivam; Gopal, Buvaneswari
2015-03-01
In this work, incorporation of hexavalent molybdenum and selected trivalent lanthanides using divalent calcium as charge compensator into the monazite structure were studied. Rare earth substituted phosphomolybdates of the formula REE0.9Ca0.1P0.9Mo0.1O4 (REE = Ce, Nd, Sm, Gd) and the wasteform La0.4Nd0.1Y0.1Gd0.1Sm0.1Ce0.1Ca0.1P0.9Mo0.1O4 were synthesized by simple solution route. The prepared compounds were characterized by powder X-ray diffraction, Fourier transformed infrared spectra, thermogravimetric analysis, energy dispersive X-ray analysis and scanning electron microscopic techniques. Chemical durability of the wasteform was studied by dynamic MCC-5 test for a period of one month. Normalized elemental mass loss and leach rate of molybdenum was found to be in the order of 103 g/m2 and 103-101 g/m2/d respectively. Polymer-monazite composite wasteform was prepared to control the leaching of molybdenum. The composite approach reduced molybdenum leach rate order from 101 to 10-4 g/m2/d.
A Proposed Instructional Theory for Integer Addition and Subtraction
ERIC Educational Resources Information Center
Stephan, Michelle; Akyuz, Didem
2012-01-01
This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…
Certain integers related to Ankeny-Artin-Chowla conjecture
NASA Astrophysics Data System (ADS)
Hashimoto, RyÅ«ta
2008-01-01
Let d be a non-square integer which is congruent to 1 modulo 4. Let t and u be the fundamental solution of the diophantine equation X2-dY2 = -4. A family of integers d satisfying d
Harmonic oscillator states with integer and non-integer orbital angular momentum
NASA Astrophysics Data System (ADS)
Land, Martin
2011-12-01
We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as basis states for representing their respective symmetry groups — O(2), O(1,1), O(3), and O(2,1). The goal of this study is to establish a correspondence between Hilbert space descriptions found by solving the Schrodinger equation in polar coordinates, and Fock space descriptions constructed by expressing the symmetry operators in terms of creation/annihilation operators. We obtain wavefunctions characterized by a principal quantum number, the group Casimir eigenvalue, and one group generator whose eigenvalue is m + s, for integer m and real constant parameter s. For the three groups that contain O(2), the solutions split into two inequivalent representations, one associated with s = 0, from which we recover the familiar description of the oscillator as a product of one-dimensional solutions, and the other with s > 0 (in three dimensions, solutions are found for s = 0 and s = 1/2) whose solutions are non-separable in Cartesian coordinates, and are hence overlooked by the standard Fock space approach. The O(1,1) solutions are singlet states, restricted to zero eigenvalue of the symmetry operator, which represents the boost, not angular momentum. For O(2), a single set of creation and annihilation operators forms a ladder representation for the allowed oscillator states for any s, and the degeneracy of energy states is always finite. However, in three dimensions, the integer and half-integer eigenstates are qualitatively different: the former can be expressed as finite dimensional irreducible tensors under O(3) or O(2,1) while the latter exhibit infinite degeneracy. Creation operators that produce the allowed integer states by acting on the non-degenerate ground state are constructed as irreducible tensor products of the fundamental vector representation. However, the half-integer eigenstates are infinite-dimensional, as expected for the non
The integer quantum hall effect revisited
Michalakis, Spyridon; Hastings, Matthew
2009-01-01
For T - L x L a finite subset of Z{sup 2}, let H{sub o} denote a Hamiltonian on T with periodic boundary conditions and finite range, finite strength intetactions and a unique ground state with a nonvanishing spectral gap. For S {element_of} T, let q{sub s} denote the charge at site s and assume that the total charge Q = {Sigma}{sub s {element_of} T} q{sub s} is conserved. Using the local charge operators q{sub s}, we introduce a boundary magnetic flux in the horizontal and vertical direction and allow the ground state to evolve quasiadiabatically around a square of size one magnetic flux, in flux space. At the end of the evolution we obtain a trivial Berry phase, which we compare, via a method reminiscent of Stokes Theorem. to the Berry phase obtained from an evolution around an exponentially small loop near the origin. As a result, we show, without any averaging assumption, that the Hall conductance is quantized in integer multiples of e{sup 2}/h up to exponentially small corrections of order e{sup -L/{zeta}}, where {zeta}, is a correlation length that depends only on the gap and the range and strength of the interactions.
A review of «integer PPP» applications
NASA Astrophysics Data System (ADS)
Perosanz, Felix; Mercier, Flavien; Loyer, Sylvain; Petit, Gérard; Marty, Jean-Charles
2016-04-01
The possibility of fixing GNSS phase observations to integer values in PPP mode has been demonstrated by several authors. Various scientific and commercial services have started offering this option. In this presentation we first summarize the mathematical formalism needed to recover integer ambiguities while processing un-differenced GNSS phase observations. The improvements but also the limitations of "integer PPP" (IPPP) solutions are discussed. Then we make a review of several scientific results based on this method to illustrate its wide field of applications like oceanic buoy tracking, glacier deformation, atomic oscillator frequency transfer, LEO satellite orbit determination. Several ideas for future improvement are also discussed including the recommendation to IGS Analysis Centers to adopt a compatible approach to deliver "integer" clock products for a combined solution that would allow for IPPP solutions.
Integer aperture ambiguity resolution based on difference test
NASA Astrophysics Data System (ADS)
Zhang, Jingyu; Wu, Meiping; Li, Tao; Zhang, Kaidong
2015-07-01
Carrier-phase integer ambiguity resolution (IAR) is the key to highly precise, fast positioning and attitude determination with Global Navigation Satellite System (GNSS). It can be seen as the process of estimating the unknown cycle ambiguities of the carrier-phase observations as integers. Once the ambiguities are fixed, carrier phase data will act as the very precise range data. Integer aperture (IA) ambiguity resolution is the combination of acceptance testing and integer ambiguity resolution, which can realize better quality control of IAR. Difference test (DT) is one of the most popular acceptance tests. This contribution will give a detailed analysis about the following properties of IA ambiguity resolution based on DT: 1.
Fractal electrodynamics via non-integer dimensional space approach
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2015-09-01
Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.
Adaptive Source Coding Schemes for Geometrically Distributed Integer Alphabets
NASA Technical Reports Server (NTRS)
Cheung, K-M.; Smyth, P.
1993-01-01
Revisit the Gallager and van Voorhis optimal source coding scheme for geometrically distributed non-negative integer alphabets and show that the various subcodes in the popular Rice algorithm can be derived from the Gallager and van Voorhis code.
NASA Astrophysics Data System (ADS)
Wang, Bin; Chiang, Hsiao-Dong
Many applications of smart grid can be formulated as constrained optimization problems. Because of the discrete controls involved in power systems, these problems are essentially mixed-integer nonlinear programs. In this paper, we review the Trust-Tech-based methodology for solving mixed-integer nonlinear optimization. Specifically, we have developed a two-stage Trust-Tech-based methodology to systematically compute all the local optimal solutions for constrained mixed-integer nonlinear programming (MINLP) problems. In the first stage, for a given MINLP problem this methodology starts with the construction of a new, continuous, unconstrained problem through relaxation and the penalty function method. A corresponding dynamical system is then constructed to search for a set of local optimal solutions for the unconstrained problem. In the second stage, a reduced constrained NLP is defined for each local optimal solution by determining and fixing the values of integral variables of the MINLP problem. The Trust-Tech-based method is used to compute a set of local optimal solutions for these reduced NLP problems, from which the optimal solution of the original MINLP problem is determined. A numerical simulation of several testing problems is provided to illustrate the effectiveness of our proposed method.
Design and multiparticle simulation of the half integer slow extraction system for the Main Injector
Trbojevic, D.; Harrison, M.
1991-05-01
One of the roles of the new Main Injector ring, in the second phase of the Fermilab upgrade, is to deliver all year around the slow extracted 120 GeV test beams. The half-integer slow extraction system design and results from a Monte-Carlo simulation of fast spill are presented. The simulation was performed with a computer tracking program based on the TEVLAT program with a large number of particles (up to 1000). Particle tracking included the systematic errors produced by the magnetic multipoles within the dipoles and quadrupoles as well as random multipole errors.
Polynomial-time algorithms for the integer minimal principle for centrosymmetric structures.
Vaia, Anastasia; Sahinidis, Nikolaos V
2005-07-01
The minimal principle for structure determination from single-crystal X-ray diffraction measurements has recently been formulated as an integer linear optimization model for the case of centrosymmetric structures. Solution of this model via established combinatorial branch-and-bound algorithms provides the true global minimum of the minimal principle while operating exclusively in reciprocal space. However, integer programming techniques may require an exponential number of iterations to exhaust the search space. In this paper, a new approach is developed to solve the integer minimal principle to global optimality without requiring the solution of an optimization problem. Instead, properties of the solution of the optimization problem, as observed in a large number of computational experiments, are exploited in order to reduce the optimization formulation to a system of linear equations in the number field of two elements (F(2)). Two specialized Gaussian elimination algorithms are then developed to solve this system of equations in polynomial time in the number of atoms. Computational results on a collection of 38 structures demonstrate that the proposed approach provides very fast and accurate solutions to the phase problem for centrosymmetric structures. This approach also provided much better crystallographic R values than SHELXS for all 38 structures tested. PMID:15972998
Finite pure integer programming algorithms employing only hyperspherically deduced cuts
NASA Technical Reports Server (NTRS)
Young, R. D.
1971-01-01
Three algorithms are developed that may be based exclusively on hyperspherically deduced cuts. The algorithms only apply, therefore, to problems structured so that these cuts are valid. The algorithms are shown to be finite.
Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks
NASA Technical Reports Server (NTRS)
Lee, Charles H.; Cheung, Kar-Ming
2012-01-01
In this paper, we propose to solve the constrained optimization problem in two phases. The first phase uses heuristic methods such as the ant colony method, particle swarming optimization, and genetic algorithm to seek a near optimal solution among a list of feasible initial populations. The final optimal solution can be found by using the solution of the first phase as the initial condition to the SQP algorithm. We demonstrate the above problem formulation and optimization schemes with a large-scale network that includes the DSN ground stations and a number of spacecraft of deep space missions.
Non-integer expansion embedding techniques for reversible image watermarking
NASA Astrophysics Data System (ADS)
Xiang, Shijun; Wang, Yi
2015-12-01
This work aims at reducing the embedding distortion of prediction-error expansion (PE)-based reversible watermarking. In the classical PE embedding method proposed by Thodi and Rodriguez, the predicted value is rounded to integer number for integer prediction-error expansion (IPE) embedding. The rounding operation makes a constraint on a predictor's performance. In this paper, we propose a non-integer PE (NIPE) embedding approach, which can proceed non-integer prediction errors for embedding data into an audio or image file by only expanding integer element of a prediction error while keeping its fractional element unchanged. The advantage of the NIPE embedding technique is that the NIPE technique can really bring a predictor into full play by estimating a sample/pixel in a noncausal way in a single pass since there is no rounding operation. A new noncausal image prediction method to estimate a pixel with four immediate pixels in a single pass is included in the proposed scheme. The proposed noncausal image predictor can provide better performance than Sachnev et al.'s noncausal double-set prediction method (where data prediction in two passes brings a distortion problem due to the fact that half of the pixels were predicted with the watermarked pixels). In comparison with existing several state-of-the-art works, experimental results have shown that the NIPE technique with the new noncausal prediction strategy can reduce the embedding distortion for the same embedding payload.
A Polynomial Time, Numerically Stable Integer Relation Algorithm
NASA Technical Reports Server (NTRS)
Ferguson, Helaman R. P.; Bailey, Daivd H.; Kutler, Paul (Technical Monitor)
1998-01-01
Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.
Bosonic Integer Quantum Hall Effect in Optical Flux Lattices
NASA Astrophysics Data System (ADS)
Sterdyniak, A.; Cooper, Nigel R.; Regnault, N.
2015-09-01
In two dimensions strongly interacting bosons in a magnetic field can realize a bosonic integer quantum Hall state, the simplest two-dimensional example of a symmetry-protected topological phase. We propose a realistic implementation of this phase using an optical flux lattice. Through exact diagonalization calculations, we show that the system exhibits a clear bulk gap and the topological signature of the bosonic integer quantum Hall state. In particular, the calculation of the many-body Chern number leads to a quantized Hall conductance in agreement with the analytical predictions. We also study the stability of the phase with respect to some of the experimentally relevant parameters.
FPGA Implementation of Optimal 3D-Integer DCT Structure for Video Compression
Jacob, J. Augustin; Kumar, N. Senthil
2015-01-01
A novel optimal structure for implementing 3D-integer discrete cosine transform (DCT) is presented by analyzing various integer approximation methods. The integer set with reduced mean squared error (MSE) and high coding efficiency are considered for implementation in FPGA. The proposed method proves that the least resources are utilized for the integer set that has shorter bit values. Optimal 3D-integer DCT structure is determined by analyzing the MSE, power dissipation, coding efficiency, and hardware complexity of different integer sets. The experimental results reveal that direct method of computing the 3D-integer DCT using the integer set [10, 9, 6, 2, 3, 1, 1] performs better when compared to other integer sets in terms of resource utilization and power dissipation. PMID:26601120
FPGA Implementation of Optimal 3D-Integer DCT Structure for Video Compression.
Jacob, J Augustin; Kumar, N Senthil
2015-01-01
A novel optimal structure for implementing 3D-integer discrete cosine transform (DCT) is presented by analyzing various integer approximation methods. The integer set with reduced mean squared error (MSE) and high coding efficiency are considered for implementation in FPGA. The proposed method proves that the least resources are utilized for the integer set that has shorter bit values. Optimal 3D-integer DCT structure is determined by analyzing the MSE, power dissipation, coding efficiency, and hardware complexity of different integer sets. The experimental results reveal that direct method of computing the 3D-integer DCT using the integer set [10, 9, 6, 2, 3, 1, 1] performs better when compared to other integer sets in terms of resource utilization and power dissipation. PMID:26601120
Partial integer decorrelation: optimum trade-off between variance reduction and bias amplification
NASA Astrophysics Data System (ADS)
Henkel, Patrick; Günther, Christoph
2010-01-01
Different techniques have been developed for determining carrier phase ambiguities, ranging from float approximations to the efficient solution of the integer least square problem by the LAMBDA method. The focus so far was on double-differenced measurements. Practical implementations of the LAMBDA method lead to a residual probability of wrong fixing of the order one percent. For safety critical applications, this probability had to be reduced by eight orders of magnitude, which could be achieved by linear multi-frequency code-carrier combinations. Scenarios with single or no differences include biases due to orbit errors, satellite clock offsets, as well as residual code and phase biases. For this case, a linear combination of Galileo E1 and E5 code and carrier phase measurements with a wavelength of 3.285 m and a noise level of a few centimeters is derived. This ionosphere-free combination preserves the orbit and clock errors, and suppresses the E1 code multipath by 12.6 dB. Since integer decorrelation transformations, as used in the LAMBDA method, inflate biases, the number of such transformations must be limited, and applied in a judicious order. With a Galileo type constellation, this leads to a vertical standard deviation of ca. 20 cm, while keeping the probability of wrong fixing extremely low for code biases of 10 cm, and phase biases of 0.1 cycle, combined in a worst case.
Comparison of penalty functions on a penalty approach to mixed-integer optimization
NASA Astrophysics Data System (ADS)
Francisco, Rogério B.; Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.
2016-06-01
In this paper, we present a comparative study involving several penalty functions that can be used in a penalty approach for globally solving bound mixed-integer nonlinear programming (bMIMLP) problems. The penalty approach relies on a continuous reformulation of the bMINLP problem by adding a particular penalty term to the objective function. A penalty function based on the `erf' function is proposed. The continuous nonlinear optimization problems are sequentially solved by the population-based firefly algorithm. Preliminary numerical experiments are carried out in order to analyze the quality of the produced solutions, when compared with other penalty functions available in the literature.
A fast DFT algorithm using complex integer transforms
NASA Technical Reports Server (NTRS)
Reed, I. S.; Truong, T. K.
1978-01-01
Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.
INTEGER ELEVATION MODEL GRIDS FOR US EPA REGION 9
Integer Digital Elevation Models in GRID format for the mainland US administrative boundary of the US EPA Region 9 developed from the United States Geological Survey (USGS) National Elevation Dataset (NED). The administrative boundary is represented by the state boundaries of Ca...
Using Set Model for Learning Addition of Integers
ERIC Educational Resources Information Center
Lestari, Umi Puji; Putri, Ratu Ilma Indra; Hartono, Yusuf
2015-01-01
This study aims to investigate how set model can help students' understanding of addition of integers in fourth grade. The study has been carried out to 23 students and a teacher of IVC SD Iba Palembang in January 2015. This study is a design research that also promotes PMRI as the underlying design context and activity. Results showed that the…
Negative Integer Understanding: Characterizing First Graders' Mental Models
ERIC Educational Resources Information Center
Bofferding, Laura
2014-01-01
This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…
Unique Factorization in Cyclotomic Integers of Degree Seven
ERIC Educational Resources Information Center
Duckworth, W. Ethan
2008-01-01
This article provides a survey of some basic results in algebraic number theory and applies this material to prove that the cyclotomic integers generated by a seventh root of unity are a unique factorization domain. Part of the proof uses the computer algebra system Maple to find and verify factorizations. The proofs use a combination of historic…
Informing Practice: Making Sense of Integers through Storytelling
ERIC Educational Resources Information Center
Wessman-Enzinger, Nicole M.; Mooney, Edward S.
2014-01-01
The authors asked fifth-grade and eighth-grade students to pose stories for number sentences involving the addition and subtraction of integers. In this article, the authors look at eight stories from students. Which of these stories works for the given number sentence? What do they reveal about student thinking? When the authors examined these…
Using the Finite Difference Calculus to Sum Powers of Integers.
ERIC Educational Resources Information Center
Zia, Lee
1991-01-01
Summing powers of integers is presented as an example of finite differences and antidifferences in discrete mathematics. The interrelation between these concepts and their analogues in differential calculus, the derivative and integral, is illustrated and can form the groundwork for students' understanding of differential and integral calculus.…
Happy and Sad Thoughts: An Exploration of Children's Integer Reasoning
ERIC Educational Resources Information Center
Whitacre, Ian; Bishop, Jessica Pierson; Lamb, Lisa L. C.; Philipp, Randolph A.; Schappelle, Bonnie P.; Lewis, Melinda L.
2012-01-01
The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…
Triangular Numbers, Gaussian Integers, and KenKen
ERIC Educational Resources Information Center
Watkins, John J.
2012-01-01
Latin squares form the basis for the recreational puzzles sudoku and KenKen. In this article we show how useful several ideas from number theory are in solving a KenKen puzzle. For example, the simple notion of triangular number is surprisingly effective. We also introduce a variation of KenKen that uses the Gaussian integers in order to…
Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic
ERIC Educational Resources Information Center
Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
2016-01-01
Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…
Exploring the Sums of Powers of Consecutive q-Integers
ERIC Educational Resources Information Center
Kim, T.; Ryoo, C. S.; Jang, L. C.; Rim, S. H.
2005-01-01
The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…