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1

Convex Formulations of Aggregate Network Air Traffic Flow Optimization Problems  

E-print Network

Control Center. I. INTRODUCTION Research on the steady increase in air traffic volume has triggeredConvex Formulations of Aggregate Network Air Traffic Flow Optimization Problems Daniel B. Work, Student Member, IEEE, Alexandre M. Bayen, Member, IEEE Abstract--The problem of regulating air traffic

2

Formulating Cyber-Security as Convex Optimization Problems  

E-print Network

Formulating Cyber-Security as Convex Optimization ProblemsÃ? Kyriakos G. Vamvoudakis1 , Jo~ao P,vigna}@cs.ucsb.edu Abstract. Mission-centric cyber-security analysts require a complete overview and understanding a cyber-mission with a limited amount of resources, based on a model that takes into account potential

Vigna, Giovanni

3

Abstract--The optimal power flow (OPF) problem is a critical problem for power generation and is generally non-convex. This  

E-print Network

problem was first discussed in Carpentier's paper [1] in 1962. The objective of an Optimal Power Flow (OPF to convexity the AC OPF problem, various convex relaxation techniques have been developed. Semidefinite

Lavaei, Javad

4

Mapping the Energy Landscape of Non-Convex Optimization Problems  

E-print Network

-convex energy landscapes. In this paper, inspired by the success of visualizing the landscapes of Ising and Spin-glass in the landscape). ELMs can be efficiently constructed by running a MCMC algorithm that fea- tures a dynamic for the spin-glass model. Liang [6, 7] generalizes the Wang-Landau algorithm [13] for random walks in the state

Zhu, Song Chun

5

Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm  

NASA Astrophysics Data System (ADS)

The primal-dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1-26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity x-ray illumination is presented.

Sidky, Emil Y.; Jørgensen, Jakob H.; Pan, Xiaochuan

2012-05-01

6

Convex optimization methods for model reduction  

E-print Network

Model reduction and convex optimization are prevalent in science and engineering applications. In this thesis, convex optimization solution techniques to three different model reduction problems are studied.Parameterized ...

Sou, Kin Cheong, 1979-

2008-01-01

7

Solving large-scale linear circuit problems via convex optimization  

Microsoft Academic Search

A broad class of problems in circuits, electromag- netics, and optics can be expressed as finding some parameters of a linear system with a specific type. This paper is concerned with studying this type of circuit using the available control techniques. It is shown that the underlying problem can be recast as a rank minimization problem that is NP-hard in

Javad Lavaei; Aydin Babakhani; Ali Hajimiri; John C. Doyle

2009-01-01

8

INTRODUCTION PROBLEM FORMULATION METHODOLOGY DUALITY Algorithms CONCLUSION Dense convex optimization for traffic  

E-print Network

INTRODUCTION PROBLEM FORMULATION METHODOLOGY DUALITY Algorithms CONCLUSION Dense convex, 2014 1/30 #12;INTRODUCTION PROBLEM FORMULATION METHODOLOGY DUALITY Algorithms CONCLUSION OUTLINE Methodology Three ways to simplify the problem 2/30 #12;INTRODUCTION PROBLEM FORMULATION METHODOLOGY DUALITY

9

The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications  

PubMed Central

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions. PMID:24747417

Xu, Xudan; Zhu, J. Jim; Zhang, Ping

2014-01-01

10

The optimal solution of a non-convex state-dependent LQR problem and its applications.  

PubMed

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix [Formula: see text] in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting [Formula: see text]. It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting [Formula: see text], in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions. PMID:24747417

Xu, Xudan; Zhu, J Jim; Zhang, Ping

2014-01-01

11

Convex Analysis and Optimization, D. P. Bertsekas! CONVEX OPTIMIZATION  

E-print Network

1! Convex Analysis and Optimization, D. P. Bertsekas! CONVEX OPTIMIZATION: A SELECTIVE OVERVIEW Dimitri Bertsekas! M.I.T.! Taiwan! May 2010! #12;2! Convex Analysis and Optimization, D. P. Bertsekas! · Unifying framework for existence of solutions and duality gap analysis! · Use of duality in algorithms! #12

Bertsekas, Dimitri

12

Optimal risk allocation for convex risk functionals in general domains  

E-print Network

Optimal risk allocation for convex risk functionals in general domains Swen Kiesel and Ludger R¨uschendorf University of Freiburg Abstract In this paper we extend the classical optimal risk allocation problem to the case of general convex risk functionals defined on real Banach spaces. In particular we characterize

Rüschendorf, Ludger

13

Design of PI Controllers based on Non-Convex Optimization  

Microsoft Academic Search

This paper presents an efficient numerical method for designing PI controllers. The design is based on optimization of load disturbance rejection with constraints on sensitivity and weighting of set point response. Thus, the formulation of the design problem captures three essential aspects of industrial control problems, leading to a non-convex optimization problem. Efficient ways to solve the problem are presented.

K. J. ÅSTRÖM; H. PANAGOPOULOS; T. HÄGGLUND

1998-01-01

14

A Survey of Algorithms for Convex Multicommodity Flow Problems  

Microsoft Academic Search

There are many problems related to design a networks. Among them, the message routing problem plays a determinant role in the optimization of network performance. Much of the motivation of this work comes from this problem which is shown to belong to the lass of nonlinear convex multicomodity flow problems.

A. Ouorou; P. Mahey; P. P. H. Vial

1997-01-01

15

A Survey of Algorithms for Convex Multicommodity Flow Problems  

Microsoft Academic Search

Routing problems appear frequently when dealing with the operation of communication or transportation networks. Among them, the message routing problem plays a determinant role in the optimization of network performance. Much of the motivation for this work comes from this problem which is shown to belong to the class of nonlinear convex multicommodity flow problems. This paper emphasizes the message

A. Ouorou; P. Mahey; J.-Ph. Vial

2000-01-01

16

Balancing of high-speed rotating machinery using convex optimization  

Microsoft Academic Search

The vibration caused by rotor mass imbalance is a major source of maintenance problems in high-speed rotating machinery. To minimize the vibration by balancing under practical constraints and data uncertainty is a decision making problem. In this paper, the flexible rotor balancing problem based on the influence coefficient method is formulated as a convex optimization problem. This formulation not only

Guoxin Li; Zongli Lin; C. Untaroiu; P. E. Allaire

2003-01-01

17

A Convex Relaxation Method for a Class of Vector-valued Minimization Problems with  

E-print Network

as problems of this class. We provide several ex- perimental results to demonstrate that our convex algorithm of a number of widely used models. In general, non-convex functionals are much more difficult to minimize than great watershed in optimization isn't between linearity and nonlinear- ity, but convexity and non

Soatto, Stefano

18

On Equilibrium Pricing as Convex Optimization Jiawei Zhang  

E-print Network

On Equilibrium Pricing as Convex Optimization Lihua Chen Yinyu Ye Jiawei Zhang Abstract We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can be computed as convex

Ye, Yinyu

19

Motion Planning with Sequential Convex Optimization and Convex Collision Checking  

E-print Network

, Pieter Abbeel Abstract--We present a new optimization-based approach for robotic motion planning among OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms for solving high- dimensional motion planning problems. Trajectory optimization is fundamental in optimal

North Carolina at Chapel Hill, University of

20

Efficient Design of Cosine-Modulated Filter Banks via Convex Optimization  

Microsoft Academic Search

Thispaperpresentsefficientapproachesfordesigning cosine-modulated filter banks with linear phase prototype filter. First, we show that the design problem of the prototype filter being a spectral factor of th-band filter is a nonconvex optimization problem with low degree of nonconvexity. As a result, the non- convex optimization problem can be cast into a semi-definite pro- gramming (SDP) problem by a convex relaxation technique.

Ha Hoang Kha; Hoang Duong Tuan; Truong Q. Nguyen

2009-01-01

21

Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization  

E-print Network

. INTRODUCTION Trajectory optimization algorithms have two roles in robotic motion planning. First, they can used our algorithm for motion planning. Top left: planning an arm trajectory for the PR2 in simulation robotic motion planning problems. At the core of our approach are (i) A sequential convex optimization

Abbeel, Pieter

22

ON THE COMPLEXITY OF SOME BASIC PROBLEMS IN COMPUTATIONAL CONVEXITY  

E-print Network

mixed volumes 6. Deterministic approximation of volumes and mixed volumes 6:1 Measures for approximationON THE COMPLEXITY OF SOME BASIC PROBLEMS IN COMPUTATIONAL CONVEXITY: II. Volume and mixed volumes and mixed volumes of convex polytopes and more general convex bodies. In order to keep the paper self

23

1 Automatic Code Generation for Real-Time Convex Optimization  

E-print Network

.3.4 Sliding window estimation 19 1.3.5 Real-time input design 20 1.3.6 Model predictive control 20 11 Automatic Code Generation for Real-Time Convex Optimization Jacob Mattingley and Stephen Boyd Press, 2009. This chapter concerns the use of convex optimization in real-time embedded systems

24

The Convex Geometry of Linear Inverse Problems  

E-print Network

Dec 2, 2010 ... resulting optimization problems can be solved or approximated via semidefinite ... For instance the question of recovering a sparse function over ... generic measurements required for exact recovery of an orthogonal matrix via ...

2010-12-02

25

On the Fermat-Lagrange principle for mixed smooth convex extremal problems  

SciTech Connect

A simple geometric condition that can be attached to an extremal problem of a fairly general form included in a family of problems is indicated. This is used to demonstrate that the task of formulating a uniform condition for smooth convex problems can be satisfactorily accomplished. On the other hand, the necessity of this new condition of optimality is proved under certain technical assumptions.

Brinkhuis, Ya [Erasmus University Rotterdam, Econometric Institute, Rotterdam (Netherlands)

2001-06-30

26

Convex Optimization Methods for Model Reduction Kin Cheong Sou  

E-print Network

procedure based on integral quadratic constraint analysis and a theoretical statement based on L2 gain of the model reduction problem as a quasi-convex program allows the flexi- bility to enforce constraints-Hammerstein system. The identification problem is formulated as a non-convex 3 #12;quadratic prog

Daniel, Luca

27

Convex Optimization Methods for Graphs and Statistical Modeling  

E-print Network

be solved exactly or approximately via semidefinite programming. We provide sharp estimates (based linear measurements required for exact and robust recovery in a variety of settings. · We present convex: · We propose a convex optimization method for decomposing the sum of a sparse matrix and a low

28

Kernel regression for travel time estimation via convex optimization  

E-print Network

Kernel regression for travel time estimation via convex optimization Sébastien Blandin , Laurent El Ghaoui and Alexandre Bayen Abstract--We develop an algorithm aimed at estimating travel time on segments of a road network using a convex optimiza- tion framework. Sampled travel time from probe vehicles

29

Newton-Raphson consensus for distributed convex optimization  

E-print Network

Newton-Raphson consensus for distributed convex optimization Luca Schenato joint work with A of Padova April 28th, 2011 schenato@dei.unipd.it (DEI - UniPD) Distrib. Newton-Raphson optimization April 28PD) Distrib. Newton-Raphson optimization April 28th, 2011 2 / 26 #12;Introduction Distribution optimization

Schenato, Luca

30

A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization  

NASA Astrophysics Data System (ADS)

We combine resolvent-mode decomposition with techniques from convex optimization to optimally approximate velocity spectra in a turbulent channel. The velocity is expressed as a weighted sum of resolvent modes that are dynamically significant, non-empirical, and scalable with Reynolds number. To optimally represent direct numerical simulations (DNS) data at friction Reynolds number 2003, we determine the weights of resolvent modes as the solution of a convex optimization problem. Using only 12 modes per wall-parallel wavenumber pair and temporal frequency, we obtain close agreement with DNS-spectra, reducing the wall-normal and temporal resolutions used in the simulation by three orders of magnitude.

Moarref, R.; Jovanovi?, M. R.; Tropp, J. A.; Sharma, A. S.; McKeon, B. J.

2014-05-01

31

Stable nonlinear identification from noisy repeated experiments via convex optimization  

E-print Network

This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this ...

Tobenkin, Mark M.

32

10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method  

E-print Network

10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method Lecturer: Barnabas Poczos.1 Motivation Newton method is originally developed for finding a root of a function. It is also known as Newton- Raphson method. The problem can be formulated as, given a function f : R R, finding the point x

Tibshirani, Ryan

33

OPTIMAL INEQUALITIES IN PROBABILITY THEORY: A CONVEX OPTIMIZATION APPROACH  

Microsoft Academic Search

We propose a semidefinite optimization approach to the problem of deriving tight moment inequalities for P (X ? S), for a set S defined by polynomial inequalities and a random vector X defined on ? ?R n that has a given collection of up to kth-order moments. In the univariate case, we provide optimal bounds on P (X ? S),

DIMITRIS BERTSIMAS; IOANA POPESCU

2000-01-01

34

Newton-Raphson consensus for distributed convex optimization  

E-print Network

Newton-Raphson consensus for distributed convex optimization Luca Schenato Department;Presentation outline Motivations State-of-the-art Centralized Newton-Raphson: a quick overview Consensus-based Newton-Raphson Convergence properties (theory + simulations) Future directions 6 #12;Presentation outline

Schenato, Luca

35

GLOBAL OPTIMIZATION IN COMPUTER VISION: CONVEXITY, CUTS AND  

E-print Network

GLOBAL OPTIMIZATION IN COMPUTER VISION: CONVEXITY, CUTS AND APPROXIMATION ALGORITHMS CARL OLSSON in computer vision. Numerous prob- lems in this field as well as in image analysis and other branches. International Conference on Computer Vision (ICCV), Rio de Janeiro, Brazil, 2007. · C. Olsson, F. Kahl, R

Lunds Universitet

36

Convex Analysis and Optimization, D. P. Bertsekas A NEW LOOK AT  

E-print Network

1 Convex Analysis and Optimization, D. P. Bertsekas A NEW LOOK AT CONVEX ANALYSIS AND OPTIMIZATION Dimitri Bertsekas M.I.T. May 2007 #12;2 Convex Analysis and Optimization, D. P. Bertsekas OUTLINE by visualization ­ Unification and intuition enhanced by geometry · Three unifying lines of analysis ­ Common

Bertsekas, Dimitri

37

On An Evolution Problem For Convex Curves Lishang Jiang  

E-print Network

On An Evolution Problem For Convex Curves Lishang Jiang and more circular during the evolution process, and the final shape of the evolving curve will be a circle. What happens to a curve X0(u) as it flows in this way? Some facts * *of the flow are rather straight

38

Robust quantum error correction via convex optimization.  

PubMed

We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the encoding, recovery, or both, and is amenable to approximations that significantly improve computational cost while retaining fidelity. We illustrate our theory numerically for optimized 5-qubit codes, using the standard [5,1,3] code as a benchmark. Our optimized encoding and recovery yields fidelities that are uniformly higher by 1-2 orders of magnitude against random unitary weight-2 errors compared to the [5,1,3] code with standard recovery. PMID:18232841

Kosut, Robert L; Shabani, Alireza; Lidar, Daniel A

2008-01-18

39

Efficient Market Making via Convex Optimization, and a Connection to Online Learning  

E-print Network

]: Social and Behavioral Sciences General Terms: Algorithms, Economics, Theory Additional Key Words and Phrases: Market design, securities market, prediction market, automated market maker, convex analysis12 Efficient Market Making via Convex Optimization, and a Connection to Online Learning JACOB

Chen, Yiling

40

Convex Optimization for Big Data: Scalable, randomized, and parallel algorithms for big data analytics  

NASA Astrophysics Data System (ADS)

This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary approximation techniques like first-order methods and randomization for scalability, and survey the important role of parallel and distributed computation. The new Big Data algorithms are based on surprisingly simple principles and attain staggering accelerations even on classical problems.

Cevher, Volkan; Becker, Stephen; Schmidt, Mark

2014-09-01

41

Target position localization in a passive radar system through convex optimization  

NASA Astrophysics Data System (ADS)

This paper proposes efficient target localization methods for a passive radar system using bistatic time-of-arrival (TOA) information measured at multiple synthetic array locations, where the position of these synthetic array locations is subject to random errors. Since maximum likelihood (ML) formulation of this target localization problem is a non-convex optimization problem, semi-definite relaxation (SDR)-based optimization methods in general do not provide satisfactory performance. As a result, approximated ML optimization problems are proposed and solved with SDR plus bisection methods. For the case without position errors, it is shown that the relaxation guarantees a rank-one solution. The optimization problem for the case with position errors involves only a relaxation of a scalar quadratic term. Simulation results show that the proposed algorithms outperform existing methods and provide mean square position error performance very close to the Cramer-Rao lower bound even for larger values of noise and position estimation errors.

Chalise, Batu K.; Zhang, Yimin D.; Amin, Moeness G.; Himed, Braham

2013-05-01

42

Optimal Stochastic Approximation Algorithms for Strongly Convex ...  

E-print Network

Jul 1, 2010 ... The analysis of these SA methods (goes back to the works [8] .... We would like to find a linear form V(u) = ?x, u? to describe the ... support vector machine [5]: f(x) = E[max{0,v?x, u?] + ?x2 ... For example, in the ridge regression problem, the l2 norm regularization term can be stated as a .... the conditional.

2012-06-18

43

Controlling the dose distribution with gEUD-type constraints within the convex radiotherapy optimization framework.  

PubMed

Radiation therapy is an important modality in treating various cancers. Various treatment planning and delivery technologies have emerged to support intensity modulated radiation therapy (IMRT), creating significant opportunities to advance this type of treatment. However, one of the fundamental questions in treatment planning and optimization, 'can we produce better treatment plans relying on the existing delivery technology?' still remains unanswered, in large part due to the underlying computational complexity of the problem, which, in turn, often stems from the optimization model being non-convex. We investigate the possibility of including the dose prescription, specified by the dose-volume histogram (DVH), within the convex optimization framework for inverse radiotherapy treatment planning. Specifically, we study the quality of approximating a given DVH with a superset of generalized equivalent uniform dose (gEUD)-based constraints, the so-called generalized moment constraints (GMCs). As a bi-product, we establish an analytic relationship between a DVH and a sequence of gEUD values. The newly proposed approach is promising as demonstrated by the computational study where the rectum DVH is considered. Unlike the precise partial-volume constraints formulation, which is commonly based on the mixed-integer model and necessitates the use of expensive computing resources to be solved to global optimality, our convex optimization approach is expected to be feasible for implementation on a conventional treatment planning station. PMID:18506069

Zinchenko, Y; Craig, T; Keller, H; Terlaky, T; Sharpe, M

2008-06-21

44

COMMIT: Convex Optimization Modeling for Microstructure Informed Tractography.  

PubMed

Tractography is a class of algorithms aiming at in vivo mapping the major neuronal pathways in the white matter from diffusion magnetic resonance imaging (MRI) data. These techniques offer a powerful tool to noninvasively investigate at the macroscopic scale the architecture of the neuronal connections of the brain. However, unfortunately, the reconstructions recovered with existing tractography algorithms are not really quantitative even though diffusion MRI is a quantitative modality by nature. As a matter of fact, several techniques have been proposed in recent years to estimate, at the voxel level, intrinsic microstructural features of the tissue, such as axonal density and diameter, by using multicompartment models. In this paper, we present a novel framework to reestablish the link between tractography and tissue microstructure. Starting from an input set of candidate fiber-tracts, which are estimated from the data using standard fiber-tracking techniques, we model the diffusion MRI signal in each voxel of the image as a linear combination of the restricted and hindered contributions generated in every location of the brain by these candidate tracts. Then, we seek for the global weight of each of them, i.e., the effective contribution or volume, such that they globally fit the measured signal at best. We demonstrate that these weights can be easily recovered by solving a global convex optimization problem and using efficient algorithms. The effectiveness of our approach has been evaluated both on a realistic phantom with known ground-truth and in vivo brain data. Results clearly demonstrate the benefits of the proposed formulation, opening new perspectives for a more quantitative and biologically plausible assessment of the structural connectivity of the brain. PMID:25167548

Daducci, Alessandro; Dal Palu, Alessandro; Lemkaddem, Alia; Thiran, Jean-Philippe

2015-01-01

45

An Inner Convex Approximation Algorithm for BMI Optimization and Applications in Control  

E-print Network

In this work, we propose a new local optimization method to solve a class of nonconvex semidefinite programming (SDP) problems. The basic idea is to approximate the feasible set of the nonconvex SDP problem by inner positive semidefinite convex approximations via a parameterization technique. This leads to an iterative procedure to search a local optimum of the nonconvex problem. The convergence of the algorithm is analyzed under mild assumptions. Applications in static output feedback control are benchmarked and numerical tests are implemented based on the data from the COMPLeib library.

Dinh, Quoc Tran; Diehl, Moritz

2012-01-01

46

Online optimization problems  

E-print Network

In this thesis, we study online optimization problems in routing and allocation applications. Online problems are problems where information is revealed incrementally, and decisions must be made before all information is ...

Lu, Xin, Ph. D. Massachusetts Institute of Technology. Operations Research Center

2013-01-01

47

From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM.  

PubMed

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

48

From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM  

PubMed Central

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

49

Applications of Fitzpatrick functions for solving optimization problems  

NASA Astrophysics Data System (ADS)

This paper presents applications of Fitzparick functions to optimization problems. The main purpose of the present work is to introduce applications of the Fitzpatrick functions, involving their specific properties as the maximal monotonicity, or the proper, convex and lower semi-continuity, for solving optimization problems.

Nashed, Z.; Raykov, I.

2012-10-01

50

Pooling problems - Optimization Online  

E-print Network

in the petroleum industry, is a type of minimum cost network flow problem with only two sets of nodes: ... appear in many different and important petrochemical optimization problems such as front-end scheduling ..... NP-hardness of the pooling problem. ...... Global optimization for the synthesis of integrated water systems in ...

2013-09-02

51

Piercing convex sets and the Hadwiger Debrunner (p, q)-problem Department of Mathematics  

E-print Network

Piercing convex sets and the Hadwiger Debrunner (p, q)-problem Noga Alon Department of Mathematics. The piercing number of H, denoted by P(H), is the minimum value of k such that H is k-pierceable. (If considered the more general problem of studying the piercing numbers of families F of compact, convex sets

Shamir, Ron

52

Smoothers for Optimization Problems  

NASA Technical Reports Server (NTRS)

We present a multigrid one-shot algorithm, and a smoothing analysis, for the numerical solution of optimal control problems which are governed by an elliptic PDE. The analysis provides a simple tool to determine a smoothing minimization process which is essential for multigrid application. Numerical results include optimal control of boundary data using different discretization schemes and an optimal shape design problem in 2D with Dirichlet boundary conditions.

Arian, Eyal; Ta'asan, Shlomo

1996-01-01

53

BROADBAND SENSOR LOCATION SELECTION USING CONVEX OPTIMIZATION IN VERY LARGE SCALE ARRAYS  

E-print Network

BROADBAND SENSOR LOCATION SELECTION USING CONVEX OPTIMIZATION IN VERY LARGE SCALE ARRAYS Yenming M pattern design, sensor location selection, very large scale arrays, convex op- timization, simulated annealing 1. INTRODUCTION Consider a large scale sensor array having N sensors that monitors a surveillance

Balan, Radu V.

54

An iterated 1 Algorithm for Non-smooth Non-convex Optimization in Computer Vision  

E-print Network

An iterated 1 Algorithm for Non-smooth Non-convex Optimization in Computer Vision Peter Ochs1-convexity is particularly interesting in combination with total general- ized variation and learned image priors. Efficient algorithms. About two decades ago, people started to replace quadratic regularization terms by non-smooth 1

Teschner, Matthias

55

Efficient Market Making via Convex Optimization, and a Connection to Online Learning  

E-print Network

and Behavioral Sciences General Terms: Algorithms, Economics, Theory Additional Key Words and Phrases: Market design, securities market, prediction market, automated market maker, convex analysis, online linearX Efficient Market Making via Convex Optimization, and a Connection to Online Learning Jacob

Abernethy, Jake

56

DC optimization approach to robust controls: the optimal scaling value problem  

Microsoft Academic Search

The optimal scaling problem (OSP) for constant scaling in output feedback control is an inherently difficult nonconvex problem for which in general existing local search algorithms can at best locate a local solution. However, it can be restated as a problem of globally minimizing a convex function under DC constraints, i.e., constraints that can be expressed in terms of differences

H. D. Tuan; S. Hosoe; H. Tuy

2000-01-01

57

A Parallel Inertial Proximal Optimization Method - Optimization Online  

E-print Network

Hilbert space the sum of a finite number of proper, lower semicontinuous convex functions ... convex programming problems and for block-separable convex optimization problems ... Hm will denote the components of a generic element x of H.

2011-07-01

58

Implementation of a Point Algorithm for Real-Time Convex Optimization  

NASA Technical Reports Server (NTRS)

The primal-dual interior-point algorithm implemented in G-OPT is a relatively new and efficient way of solving convex optimization problems. Given a prescribed level of accuracy, the convergence to the optimal solution is guaranteed in a predetermined, finite number of iterations. G-OPT Version 1.0 is a flight software implementation written in C. Onboard application of the software enables autonomous, real-time guidance and control that explicitly incorporates mission constraints such as control authority (e.g. maximum thrust limits), hazard avoidance, and fuel limitations. This software can be used in planetary landing missions (Mars pinpoint landing and lunar landing), as well as in proximity operations around small celestial bodies (moons, asteroids, and comets). It also can be used in any spacecraft mission for thrust allocation in six-degrees-of-freedom control.

Acikmese, Behcet; Motaghedi, Shui; Carson, John

2007-01-01

59

Tractable problems in optimal decentralized control  

NASA Astrophysics Data System (ADS)

This thesis considers the problem of constructing optimal decentralized controllers. The problem is formulated as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. The notion of quadratic invariance of a constraint set with respect to a system is defined. It is shown that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. It is further shown that if the constraint set has this property, this allows the constrained minimum-norm problem to be solved via convex programming. These results are developed in a very general framework, and are shown to hold for continuous-time systems, discrete-time systems, or operators on Banach spaces, for stable or unstable plants, and for the minimization of any norm. The utility of these results is then demonstrated on some specific constraint classes. An explicit test is derived for sparsity constraints on a controller to be quadratically invariant, and thus amenable to convex synthesis. Symmetric synthesis is also shown to be quadratically invariant. The problem of control over networks with delays is then addressed as another constraint class. Multiple subsystems are considered, each with its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. It is shown that if the communication delays are less than the propagation delays, then the associated constraints are quadratically invariant, and thus optimal controllers can be synthesized. We further show that this result still holds in the presence of computational delays. This thesis unifies the few previous results on specific tractable decentralized control problems, identifies broad and useful classes of new solvable problems, and delineates the largest known class of convex problems in decentralized control.

Rotkowitz, Michael Charles

2005-07-01

60

Worst-Case Violation of Sampled Convex Programs for Optimization ...  

E-print Network

rameter is u ? U, the constraint for optimization problem is expressed as f(x,u) ? 0 ...... the truncated normal distribution on A, the integration in q1 is reduced to one ...... Lipschitz constant L: We consider a quadratic constraint function f(x,u) in x ...

2008-12-23

61

Feature selection for linear SVMs under uncertain data: robust optimization based on difference of convex functions algorithms.  

PubMed

In this paper, we consider the problem of feature selection for linear SVMs on uncertain data that is inherently prevalent in almost all datasets. Using principles of Robust Optimization, we propose robust schemes to handle data with ellipsoidal model and box model of uncertainty. The difficulty in treating ?0-norm in feature selection problem is overcome by using appropriate approximations and Difference of Convex functions (DC) programming and DC Algorithms (DCA). The computational results show that the proposed robust optimization approaches are superior than a traditional approach in immunizing perturbation of the data. PMID:25064040

Le Thi, Hoai An; Vo, Xuan Thanh; Pham Dinh, Tao

2014-11-01

62

Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions  

E-print Network

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation [bar through "X" symbol] of the sum ...

Agarwal, Alekh

63

Introduction Optimal Control Problem  

E-print Network

problem of minimizing concentration of the polluted water at the terminal time T is stated and solved water cleaning plant Ellina Grigorieva and Evgenii Khailov Denton, TX, USA and Moscow, Russia May 7 -9 and Computational Simulations Ellina Grigorieva and Evgenii Khailov Optimal control of a waste water cleaning plant

Grigorieva, Ellina V.

64

Output-Sensitive Results on Convex Hulls, Extreme Points, and Related Problems  

Microsoft Academic Search

We use known data structures for ray-shooting and linear-programming queries to derive new output-sensitive results on convex\\u000a hulls, extreme points, and related problems. We show that thef-face convex hull of ann-point setP in a fixed dimensiond?2 can be constructed in\\u000a $$0\\\\left( {n log f + \\\\left( {nf} \\\\right)^{1 - 1\\/\\\\left( {\\\\left[ {d\\/2} \\\\right] + 1} \\\\right)} \\\\log ^{0\\\\left( 1 \\\\right)}

Timothy M. Chan

1996-01-01

65

Simultaneous Optimization via Approximate Majorization for Concave Profits or Convex Costs  

Microsoft Academic Search

For multi-criteria problems and problems with poorly characterized objective, it is often desirable to simultaneously approximate the optimum solution for a large class of objective functions. We consider two such classes: 1. Maximizing all symmetric concave functions, and 2. Minimizing all symmetric convex functions. The first class corresponds to maximizing profit for a resource allocation problem (such as allocation of

Ashish Goel; Adam Meyerson

2006-01-01

66

Filterbank optimization with convex objectives and the optimality of principal component forms  

Microsoft Academic Search

This paper proposes a general framework for the optimization of orthonormal filterbanks (FBs) for given input statistics. This includes as special cases, many previous results on FB optimization for compression. It also solves problems that have not been considered thus far. FB optimization for coding gain maximization (for compression applications) has been well studied before. The optimum FB has been

Sony Akkarakaran; P. P. Vaidyanathan

2001-01-01

67

libCreme: An optimization library for evaluating convex-roof entanglement measures  

NASA Astrophysics Data System (ADS)

We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the MATLAB programming language, but is fully compatible to the free and open-source OCTAVE platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focusing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems. Program summaryProgram title:libCreme Catalogue identifier: AEKD_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKD_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL version 3 No. of lines in distributed program, including test data, etc.: 4323 No. of bytes in distributed program, including test data, etc.: 70 542 Distribution format: tar.gz Programming language: Matlab/Octave and C/C++ Computer: All systems running Matlab or Octave Operating system: All systems running Matlab or Octave Classification: 4.9, 4.15 Nature of problem: Evaluate convex-roof entanglement measures. This involves solving a non-linear (unitary) optimization problem. Solution method: Two algorithms are provided: A conjugate-gradient method using a differential-geometric approach and a quasi-Newton method together with a mapping to Euclidean space. Running time: Typically seconds to minutes for a density matrix of a few low-dimensional systems and a decent implementation of the pure-state entanglement measure.

Röthlisberger, Beat; Lehmann, Jörg; Loss, Daniel

2012-01-01

68

PATTERN SYNTHESIS OF PLANAR ANTENNA ARRAY VIA CONVEX OPTIMIZATION FOR AIRBORNE FORWARD LOOKING RADAR  

Microsoft Academic Search

When airborne forward looking planar antenna is used to detect ground moving target, targets may be masked by strong clutter due to high sidelobes of the antenna pattern. In this paper, transmitting pattern is synthesized via convex optimization in order to suppress clutter from ground. Transmitting pattern has a low sidelobe illuminating short ranges and a high sidelobe focused into

Yi Qu; Guisheng Liao; Sheng-Qi Zhu; Xiang-Yang Liu

2008-01-01

69

Automated bone segmentation from dental CBCT images using patch-based sparse representation and convex optimization  

SciTech Connect

Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segment CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT segmentation based on 15 patients.

Wang, Li; Gao, Yaozong; Shi, Feng; Liao, Shu; Li, Gang [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 (United States)] [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 (United States); Chen, Ken Chung [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Stomatology, National Cheng Kung University Medical College and Hospital, Tainan, Taiwan 70403 (China)] [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Stomatology, National Cheng Kung University Medical College and Hospital, Tainan, Taiwan 70403 (China); Shen, Steve G. F.; Yan, Jin [Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China)] [Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Lee, Philip K. M.; Chow, Ben [Hong Kong Dental Implant and Maxillofacial Centre, Hong Kong, China 999077 (China)] [Hong Kong Dental Implant and Maxillofacial Centre, Hong Kong, China 999077 (China); Liu, Nancy X. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing, China 100050 (China)] [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing, China 100050 (China); Xia, James J. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 (United States) [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 (United States); Department of Surgery (Oral and Maxillofacial Surgery), Weill Medical College, Cornell University, New York, New York 10065 (United States); Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Shen, Dinggang, E-mail: dgshen@med.unc.edu [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 and Department of Brain and Cognitive Engineering, Korea University, Seoul, 136701 (Korea, Republic of)] [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 and Department of Brain and Cognitive Engineering, Korea University, Seoul, 136701 (Korea, Republic of)

2014-04-15

70

Local Cuts and Two-Period Convex Hull Closures for Big Bucket lot-sizing Problems  

E-print Network

Local Cuts and Two-Period Convex Hull Closures for Big Bucket lot-sizing Problems Kerem Akartunali Hull Closure, Integer Programming, Quadratic Pro- gramming, Column Generation 1 Introduction Despite that has generated promising results on the "closures" of general cutting planes and some particular

Paris-Sud XI, Université de

71

The Convex Hull of Two Core Capacitated Network Design Problems  

E-print Network

The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated ...

Magnanti, Thomas L.

72

Compensation of modal dispersion in multimode fiber systems using adaptive optics via convex optimization  

NASA Astrophysics Data System (ADS)

Multimode fibers (MMF) are widely deployed in local-, campus-, and storage-area-networks. Achievable data rates and transmission distances are, however, limited by the phenomenon of modal dispersion. We propose a system to compensate for modal dispersion using adaptive optics. This leads to a 10- to 100-fold improvement in performance over current standards. We propose a provably optimal technique for minimizing inter-symbol interference (ISI) in MMF systems using adaptive optics via convex optimization. We use a spatial light modulator (SLM) to shape the spatial profile of light launched into an MMF. We derive an expression for the system impulse response in terms of the SLM reflectance and the field patterns of the MMF principal modes. Finding optimal SLM settings to minimize ISI, subject to physical constraints, is posed as an optimization problem. We observe that our problem can be cast as a second-order cone program, which is a convex optimization problem. Its global solution can, therefore, be found with minimal computational complexity. Simulations show that this technique opens up an eye pattern originally closed due to ISI. We then propose fast, low-complexity adaptive algorithms for optimizing the SLM settings. We show that some of these converge to the global optimum in the absence of noise. We also propose modified versions of these algorithms to improve resilience to noise and speed of convergence. Next, we experimentally compare the proposed adaptive algorithms in 50-mum graded-index (GRIN) MMFs using a liquid-crystal SLM. We show that continuous-phase sequential coordinate ascent (CPSCA) gives better bit-error-ratio performance than 2- or 4-phase sequential coordinate ascent, in concordance with simulations. We evaluate the bandwidth characteristics of CPSCA, and show that a single SLM is able to simultaneously compensate over up to 9 wavelength-division-multiplexed (WDM) 10-Gb/s channels, spaced by 50 GHz, over a total bandwidth of 450 GHz. We also show that CPSCA is able to compensate for modal dispersion over up to 2.2 km, even in the presence of mid-span connector offsets up to 4 mum (simulated in experiment by offset splices). A known non-adaptive launching technique using a fusion-spliced single-mode-to-multimode patchcord is shown to fail under these conditions. Finally, we demonstrate 10 x 10 Gb/s dense WDM transmission over 2.2 km of 50-mum GRIN MMF. We combine transmitter-based adaptive optics and receiver-based single-mode filtering, and control the launched field pattern for ten 10-Gb/s non-return-to-zero channels, wavelength-division multiplexed on a 200-GHz grid in the C band. We achieve error-free transmission through 2.2 km of 50-mum GRIN MMF for launch offsets up to 10 mum and for worst-case launched polarization. We employ a ten-channel transceiver based on parallel integration of electronics and photonics.

Panicker, Rahul Alex

73

Easy distributions for combinatorial optimization problems with ...  

E-print Network

Feb 22, 2010 ... We show how we can linearize probabilistic linear constraints with binary variables ... linear probabilistic constraints are in general non convex non linear ... problems such as unsplittable multicommodity flow and generalized ...

2010-02-22

74

Tensor completion and low-n-rank tensor recovery via convex optimization  

NASA Astrophysics Data System (ADS)

In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas-Rachford splitting technique and its dual variant, the alternating direction method of multipliers.

Gandy, Silvia; Recht, Benjamin; Yamada, Isao

2011-02-01

75

On optimality and duality for multiobjective programming problems involving generalized d-type-I and related n-set functions  

Microsoft Academic Search

In this paper we establish some optimality and duality results under generalized convexity assumptions for a multiobjective programming problem involving generalized d-type-I and related n-set functions.

Vasile Preda; I. M. Stancu-Minasian; Eduard Koller

2003-01-01

76

Templates for Convex Cone Problems with Applications to Sparse ...  

E-print Network

exact number depends upon the desired level of accuracy. ... ing problems can be easily cast into standard conic form, our software .... Furthermore, [35] proves that the gradient of g is Lipschitz continuous, obeying ..... model was constructed for a data set built from a DCT measurement matrix of ...... SIAM Journal on Control.

2010-09-22

77

PARTIALLY AFFINE CONTROL PROBLEMS - Optimization Online  

E-print Network

Consider a locally convex topological space X, a finite-faced cone C ? X, .... yields a new quadratic operator called ?P2 on the transformed space. Consider hence the linear ...... [18] B.S. Goh. Optimal singular rocket and aircraft trajectories.

2011-10-17

78

Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems  

NASA Technical Reports Server (NTRS)

In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.

Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III

2012-01-01

79

Construction of Convex Relaxations Using Automated Code Generation Techniques  

Microsoft Academic Search

This paper describes how the automated code generation tool DAEPACK can be used to construct convex relaxations of codes implementing nonconvex functions. Modern deterministic global optimization algorithms involving continuous and\\/or integer variables often require such convex relaxations. Within the described framework, the user supplies a code implementing the objective and constraints of a nonconvex optimization problem. DAEPACK then analyzes this

Edward P. Gatzke; John E. Tolsma; Paul I. Barton

2002-01-01

80

From Convex Optimization to Randomized Mechanisms: Toward Optimal Combinatorial Auctions for Submodular Bidders  

E-print Network

We design a polynomial-time, truthful-in-expectation, (1-1/e)-approximation mechanism for welfare maximization for a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are matroid rank sums (MRS), which encompass most concrete examples of submodular functions studied in this context, including coverage functions and matroid weighted-rank functions. Our approximation factor is the best possible, even for known and explicitly given coverage valuations, assuming P != NP. Our mechanism is the first truthful-in-expectation and polynomial-time mechanism to achieve a constant-factor approximation for an NP-hard welfare maximization problem in combinatorial auctions with heterogeneous goods and restricted valuations. Our mechanism is an instantiation of a new framework for designing approximation mechanisms based on randomized rounding algorithms. A typical such algorithm first optimizes over a fractional relaxation of the original problem, and then randomly rounds the frac...

Dughmi, Shaddin; Yan, Qiqi

2011-01-01

81

Optimization and geophysical inverse problems  

SciTech Connect

A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness or distance from a prior model. Various other constraints may also be imposed upon the process. Inverse problems are not restricted to geophysics, but can be found in a wide variety of disciplines where inferences must be made on the basis of indirect measurements. For instance, most imaging problems, whether in the field of medicine or non-destructive evaluation, require the solution of an inverse problem. In this report, however, the examples used for illustration are taken exclusively from the field of geophysics. The generalization of these examples to other disciplines should be straightforward, as all are based on standard second-order partial differential equations of physics. In fact, sometimes the non-geophysical inverse problems are significantly easier to treat (as in medical imaging) because the limitations on data collection, and in particular on multiple views, are not so severe as they generally are in geophysics. This report begins with an introduction to geophysical inverse problems by briefly describing four canonical problems that are typical of those commonly encountered in geophysics. Next the connection with optimization methods is made by presenting a general formulation of geophysical inverse problems. This leads into the main subject of this report, a discussion of methods for solving such problems with an emphasis upon newer approaches that have not yet become prominent in geophysics. A separate section is devoted to a subject that is not encountered in all optimization problems but is particularly important in geophysics, the need for a careful appraisal of the results in terms of their resolution and uncertainty. The impact on geophysical inverse problems of continuously improving computational resources is then discussed. The main results are then brought together in a final summary and conclusions section.

Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F.; Gill, P.; Heinkenschloss, M.; Johnson, L.; McEvilly, T.; More, J.; Newman, G.; Oldenburg, D.; Parker, P.; Porto, B.; Sen, M.; Torczon, V.; Vasco, D.; Woodward, N.B.

2000-10-01

82

Formulating Cyber-Security as Convex Optimization Problems  

E-print Network

to a conference through an online submission system, or printing a bank statement at an ATM machine. Cyber at accomplishing a specific purpose or task, such as placing an online shopping order, submitting a paper-missions typically require a large num- ber of computer services, including encryption services, authentication

Hespanha, João Pedro

83

Solving nonconvex problems of multibody dynamics with contact and small friction by successive convex relaxation.  

SciTech Connect

Time-stepping methods using impulse-velocity approaches are guaranteed to have a solution for any friction coefficient, but they may have nonconvex solution sets. We present an example of a configuration with a nonconvex solution set for any nonzero value of the friction coefficient. We construct an iterative algorithm that solves convex subproblems and that is guaranteed, for sufficiently small friction coefficients, to retrieve, at a linear convergence rate, the velocity solution of the nonconvex linear complementarity problem whenever the frictionless configuration can be disassembled. In addition, we show that one step of the iterative algorithm provides an excellent approximation to the velocity solution of the original, possibly nonconvex, problem if the product between the friction coefficient and the slip velocity is small.

Anitescu, M.; Hart, G. D.; Mathematics and Computer Science; Univ. Pittsburg

2003-01-01

84

PID Design by Convex-Concave Optimization M. Hast1, K.J. Astrom1, B. Bernhardsson1, S. Boyd2  

E-print Network

PID Design by Convex-Concave Optimization M. Hast1, K.J. °Astr¨om1, B. Bernhardsson1, S. Boyd2 Abstract-- This paper describes how PID controllers can be designed by optimizing performance subject convex-concave program- ming for design of PID controllers. Following the ideas in [2], [15] we consider

85

Interval-valued optimization problems involving (?, ?)-right upper-Dini-derivative functions.  

PubMed

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals. PMID:24982989

Preda, Vasile

2014-01-01

86

Interval-Valued Optimization Problems Involving (?, ?)-Right Upper-Dini-Derivative Functions  

PubMed Central

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals. PMID:24982989

2014-01-01

87

D.C. Optimization Approach to Robust Control: Feasibility Problems  

Microsoft Academic Search

. The feasibility problem for constant scaling in output feedback control isconsidered. This is an inherently difficult problem [20, 21] since the set of feasible solutionsis nonconvex and may be disconnected. Nevertheless, we show that this problemcan be reduced to the global maximization of a concave function over a convex set, oralternatively, to the global minimization of a convex program

H. d. Tuan; P. Apkarian; S. Hosoe; H. Tuy

1997-01-01

88

Approximating random quantum optimization problems  

NASA Astrophysics Data System (ADS)

We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem k-body quantum satisfiability (k-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random k-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random k-QSAT in a two-dimensional energy-density-clause-density space.

Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L.

2013-06-01

89

A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces  

NASA Astrophysics Data System (ADS)

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the Hilbert space structure of the underlying problems, we propose a fast iterative regularization method which reduces to the classical nonstationary iterated Tikhonov regularization when the penalty term is chosen to be the square of norm. Each iteration of the method consists of two steps: the first step involves only the operator from the problem while the second step involves only the penalty term. This splitting character has the advantage of making the computation efficient. In case the data is corrupted by noise, a stopping rule is proposed to terminate the method and the corresponding regularization property is established. Finally, we test the performance of the method by reporting various numerical simulations, including the image deblurring, the determination of source term in Poisson equation, and the de-autoconvolution problem.

Jin, Qinian; Lu, Xiliang

2014-04-01

90

Applying optimization software libraries to engineering problems  

NASA Technical Reports Server (NTRS)

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.

1984-01-01

91

Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems  

NASA Astrophysics Data System (ADS)

Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.

Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao

92

Quadratic based primal-dual algorithms for multicommodity convex and linear cost transportation problems with serial and parallel implementations  

SciTech Connect

In this paper we present a new class of sequential and parallel algorithms for multicommodity transportation problems with linear and convex costs. First, we consider a capacitated multicommodity transportation problem with an orthogonal quadratic objective function. We develop two new solution methods. Both exploit the fact that a projection on the conservation of flow constraints has an explicit form which was proved in an early paper by I. Chabini and M. Florian. The two algorithms deal differently with the remaining constraints namely the non negativity and capacity constraints. We prove the convergence of both algorithms using a basic general theory (developed by the author) which generalizes Bregman`s theory. The above algorithms can be extended for differentiable convex cost multicommodity transportation problems as follows. For strictly convex costs we use a variant of the projected gradient method. The quadratic proximal minimization algorithm is applied to the linear cost multicommodity transportation problems. For both cases we solve an orthogonal projection multicommodity transportation problem at each iteration. The algorithms developed are well-suited for a coarse grained parallelization. The different steps may be decomposed by nodes, by arcs and/or by commodities. We investigate different strategies depending on the structure of the problem, the number of commodities and the architecture of the parallel machine. We present computational results for these different approaches on parallel and serial platforms such as a network of Transputers or Sun workstations. Very large problems are solved. The parallel implementations are analyzed using especially a new measure of performance developed previously by I. Chabini and M. Florian.

Chabini, I.

1994-12-31

93

Constrained Graph Optimization: Interdiction and Preservation Problems  

SciTech Connect

The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.

Schild, Aaron V [Los Alamos National Laboratory

2012-07-30

94

An optimal control problem arising in flexible manufacturing systems  

Microsoft Academic Search

A controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems. The existence of a homogeneous Markov nonrandomized optimal policy is established by a convex analytic method. Using the existence of such a policy, the existence of a unique solution in a certain class to the associated Hamilton-Jacobi-Bellman equations is established, and the optimal policy

MRINAL K. GHOSH; ARISTOTLE ARAPOSTATHIS; STEVEN I. MARCUS

1991-01-01

95

Representations in Problem Solving: A Case Study with Optimization Problems  

ERIC Educational Resources Information Center

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

96

Problem Solving through an Optimization Problem in Geometry  

ERIC Educational Resources Information Center

This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

Poon, Kin Keung; Wong, Hang-Chi

2011-01-01

97

Genetic symbiosis algorithm for multiobjective optimization problem  

Microsoft Academic Search

Evolutionary algorithms are often well-suited for optimization problems. Since the mid-1980's, interest in multiobjective problems has been expanding rapidly. Various evolutionary algorithms have been developed which are capable of searching for multiple solutions concurrently in a single run. In this paper, we proposed a genetic symbiosis algorithm (GSA) for multi-object optimization problems (MOP) based on the symbiotic concept found widely

Jiangming Mao; K. Hirasawa; Jinlu Hu; J. Murata

2000-01-01

98

On the Multiple-Query Optimization Problem  

Microsoft Academic Search

The complexity of the multiple-query optimization problem in database management systems is examined. It is shown that the problem is NP-hard. Then the authors examine the performance of a heuristic algorithm to solve the multiple-query optimization problem and suggest some heuristics for query ordering which improve the efficiency of the algorithm considerably. Some experimental results on the performance of various

Timos K. Sellis; Subrata Ghosh

1990-01-01

99

The [unk]-Neumann Problem on (Weakly) Pseudo-Convex Two-Dimensional Manifolds.  

PubMed

When the Levi-form vanishes at boundary points of a pseudo-convex manifold, more delicate invariants are required to describe the function theoretic properties of the manifold. These are introduced here; the proof of the main theorem and other results, which will be described in more detail elsewhere, are described. PMID:16591982

Kohn, J J

1972-05-01

100

The [unk]-Neumann Problem on (Weakly) Pseudo-Convex Two-Dimensional Manifolds  

PubMed Central

When the Levi-form vanishes at boundary points of a pseudo-convex manifold, more delicate invariants are required to describe the function theoretic properties of the manifold. These are introduced here; the proof of the main theorem and other results, which will be described in more detail elsewhere, are described. PMID:16591982

Kohn, J. J.

1972-01-01

101

Optimization problems in network connectivity  

E-print Network

Besides being one of the principal driving forces behind research in algorithmic theory for more than five decades, network optimization has assumed increased significance in recent times with the advent and widespread use ...

Panigrahi, Debmalya

2012-01-01

102

Large Scale Computational Problems in Numerical Optimization  

SciTech Connect

Our work under this support broadly falls into five categories: automatic differentiation, sparsity, constraints, parallel computation, and applications. Automatic Differentiation (AD): We developed strong practical methods for computing sparse Jacobian and Hessian matrices which arise frequently in large scale optimization problems [10,35]. In addition, we developed a novel view of "structure" in applied problems along with AD techniques that allowed for the efficient application of sparse AD techniques to dense, but structured, problems. Our AD work included development of freely available MATLAB AD software. Sparsity: We developed new effective and practical techniques for exploiting sparsity when solving a variety of optimization problems. These problems include: bound constrained problems, robust regression problems, the null space problem, and sparse orthogonal factorization. Our sparsity work included development of freely available and published software [38,39]. Constraints: Effectively handling constraints in large scale optimization remains a challenge. We developed a number of new approaches to constrained problems with emphasis on trust region methodologies. Parallel Computation: Our work included the development of specifically parallel techniques for the linear algebra tasks underpinning optimization algorithms. Our work contributed to the nonlinear least-squares problem, nonlinear equations, triangular systems, orthogonalization, and linear programming. Applications: Our optimization work is broadly applicable across numerous application domains. Nevertheless we have specifically worked in several application areas including molecular conformation, molecular energy minimization, computational finance, and bone remodeling.

coleman, thomas f. [cornell university] [cornell university

2000-07-01

103

Stochastic optimization problems under incomplete information  

SciTech Connect

Many problems related with reliability and inventory control and its applications lead to optimization of functionals depending on some probability function F(x), which is not completely known. The information about F(x) is restricted to the knowledge of some of its initial moments only. In the present work a short survey of some known results on optimal problems for technical maintenance is given as well as a brief review of the author`s and other results on optimal control of unreliable process. Some problems of the Warranty analysis and stochastic inventory models with incomplete demand information are given.

Dimitrov, B.; Green, D. Jr.

1994-12-31

104

Analog Processor To Solve Optimization Problems  

NASA Technical Reports Server (NTRS)

Proposed analog processor solves "traveling-salesman" problem, considered paradigm of global-optimization problems involving routing or allocation of resources. Includes electronic neural network and auxiliary circuitry based partly on concepts described in "Neural-Network Processor Would Allocate Resources" (NPO-17781) and "Neural Network Solves 'Traveling-Salesman' Problem" (NPO-17807). Processor based on highly parallel computing solves problem in significantly less time.

Duong, Tuan A.; Eberhardt, Silvio P.; Thakoor, Anil P.

1993-01-01

105

An optimal replacement problem in aluminum production  

E-print Network

AN OPTIMAL REPLACEMENT PROBLEM IN ALUMINUM PRODUCTION Thesis by LISA MARIE SPANKS Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE May 1992... Major Subject: Industrial Engineering AN OPTIMAL REPLACEMENT PROBLEM IN ALUMINUM PRODUCTION Thesis by LISA MARIE SPANKS Approved as to style and content by: Richard M. Feldman (Chair of Committee) James H. Matis (Member) ryan L. Deuermey r...

Spanks, Lisa Marie

2012-06-07

106

MODEL PROBLEMS FOR THE MULTIGRID OPTIMIZATION OF ...  

E-print Network

May 17, 2002 ... Multigrid methods, optimization of systems governed by differential ... The nonlinear optimization problems have the form ..... so this Krylov subspace is a discrete approximation to ... conjugate gradient method to the minimization of the second-order ..... We apply the forward-time, backward-space scheme.

2002-05-17

107

Convex Bayes decision theory  

Microsoft Academic Search

The basic concepts of Levi's epistemic utility theory and credal convexity are presented. Epistemic utility, in addition to penalizing error as is done with traditional Bayesian decision methodology, permits a unit of informational value to be distributed among the hypotheses of a decision problem. Convex Bayes decision theory retains the conditioning structure of probability-based inference, but addresses many of the

W. C. Stirling; D. R. Morrell

1991-01-01

108

Tracking local optimality for cost parameterized optimization problems  

NASA Astrophysics Data System (ADS)

In this paper, a procedure for computing local optimal solution curves of the cost parameterized optimization problem is presented. We recast the problem to a parameterized nonlinear equation derived from its Lagrange function and show that the point where the positive definiteness of the projected Hessian matrix vanishes must be a bifurcation point on the solution curve of the equation. Based on this formulation, the local optimal curves can be traced by the continuation method, coupled with the testing of singularity of the Jacobian matrix. Using the proposed procedure, we successfully compute the energy diagram of rotating Bose-Einstein condensates.

Kuo, Yueh-Cheng; Lee, Tsung-Lin

2014-02-01

109

Random generation of structured linear optimization problems  

SciTech Connect

We describe the on-going development of a random generator for linear optimization problems (LPs) founded on the concept of block structure. The general LP: minimize z = cx subject to Ax = b, x {ge} 0 can take a variety of special forms determined (primarily) by predefined structures on the matrix A of constraint coefficients. The authors have developed several random problem generators which provide instances of LPs having such structure; in particular (i) general (non-structured) problems, (ii) generalized upper bound (GUB) constraints, (iii) minimum cost network flow problems, (iv) transportation and assignment problems, (v) shortest path problems, (vi) generalized network flow problems, and (vii) multicommodity network flow problems. This paper discusses the general philosophy behind the construction of these generators. In addition, the task of combining the generators into a single generator -- in which the matrix A can contain various blocks, each of a prescribed structure from those mentioned above -- is described.

Arthur, J.; Frendewey, J. Jr.

1994-12-31

110

Solving constrained optimization problems with hybrid particle swarm optimization  

NASA Astrophysics Data System (ADS)

Constrained optimization problems (COPs) are very important in that they frequently appear in the real world. A COP, in which both the function and constraints may be nonlinear, consists of the optimization of a function subject to constraints. Constraint handling is one of the major concerns when solving COPs with particle swarm optimization (PSO) combined with the Nelder-Mead simplex search method (NM-PSO). This article proposes embedded constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, as a special operator in NM-PSO for dealing with constraints. Experiments using 13 benchmark problems are explained and the NM-PSO results are compared with the best known solutions reported in the literature. Comparison with three different meta-heuristics demonstrates that NM-PSO with the embedded constraint operator is extremely effective and efficient at locating optimal solutions.

Zahara, Erwie; Hu, Chia-Hsin

2008-11-01

111

Hierarchical particle swarm optimizer for minimizing the non-convex potential energy of molecular structure.  

PubMed

The stable conformation of a molecule is greatly important to uncover the secret of its properties and functions. Generally, the conformation of a molecule will be the most stable when it is of the minimum potential energy. Accordingly, the determination of the conformation can be solved in the optimization framework. It is, however, not an easy task to achieve the only conformation with the lowest energy among all the potential ones because of the high complexity of the energy landscape and the exponential computation increasing with molecular size. In this paper, we develop a hierarchical and heterogeneous particle swarm optimizer (HHPSO) to deal with the problem in the minimization of the potential energy. The proposed method is evaluated over a scalable simplified molecular potential energy function with up to 200 degrees of freedom and a realistic energy function of pseudo-ethane molecule. The experimental results are compared with other six PSO variants and four genetic algorithms. The results show HHPSO is significantly better than the compared PSOs with p-value less than 0.01277 over molecular potential energy function. PMID:25459763

Cheung, Ngaam J; Shen, Hong-Bin

2014-11-01

112

Approximate solutions to NP-optimization problems  

SciTech Connect

Most combinatorial optimization problems are NP-hard, and thus unlikely to be solvable to optimality in polynomial time. This tutorial is concerned with polynomial-time algorithms for the approximate solution of such problems. Such an algorithm is said to solve a problem within F(n) if, for every problem instance, it determines the optimal value within a multiplicative error of at most F(n). It has long been known that the knapsack and bin packing problems can be approximated within 1 + a for any positive a. We discuss recent advances in the construction of approximation algorithms for graph partitioning, multicommodity flow and Steiner tree problems. We also discuss negative results, showing that, unless P = NP, it is impossible to approximate the clique number or the chromatic number of a graph within the ratio n{sup b}, where b is a certain small positive number. These negative results stem from an unexpected connection between approximation algorithms and the theory of probabilistically checkable proofs, a branch of theoretical computer science related to cryptography. We also discuss problems such as vertex cover and maximum 2-sat that can be solved within a constant ratio, but not within an arbitrarily small constant ratio (unless P = NP).

Karp, R.

1994-12-31

113

Uncertainty on Multi-objective Optimization Problems  

NASA Astrophysics Data System (ADS)

In general, parameters in multi-objective optimization are assumed as deterministic with no uncertainty. However, uncertainty in the parameters can affect both variable and objective spaces. The corresponding Pareto optimal fronts, resulting from the disturbed problem, define a cloud of curves. In this work, the main objective is to study the resulting cloud of curves in order to identify regions of more robustness and, therefore, to assist the decision making process. Preliminary results, for a very limited set of problems, show that the resulting cloud of curves exhibits regions of less variation, which are, therefore, more robust to parameter uncertainty.

Costa, Lino; Santo, Isabel A. C. P. Espírito; Oliveira, Pedro

2011-09-01

114

Quadratic optimization in ill-posed problems  

NASA Astrophysics Data System (ADS)

Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.

Ben Belgacem, F.; Kaber, S.-M.

2008-10-01

115

Problem size, parallel architecture and optimal speedup  

NASA Technical Reports Server (NTRS)

The communication and synchronization overhead inherent in parallel processing can lead to situations where adding processors to the solution method actually increases execution time. Problem type, problem size, and architecture type all affect the optimal number of processors to employ. The numerical solution of an elliptic partial differential equation is examined in order to study the relationship between problem size and architecture. The equation's domain is discretized into n sup 2 grid points which are divided into partitions and mapped onto the individual processor memories. The relationships between grid size, stencil type, partitioning strategy, processor execution time, and communication network type are analytically quantified. In so doing, the optimal number of processors was determined to assign to the solution, and identified (1) the smallest grid size which fully benefits from using all available processors, (2) the leverage on performance given by increasing processor speed or communication network speed, and (3) the suitability of various architectures for large numerical problems.

Nicol, David M.; Willard, Frank H.

1987-01-01

116

A reverse convex programming for beamforming in cognitive multicast transmission  

Microsoft Academic Search

The cognitive beamforming problems are naturally formulated as indefinite quadratic (nonconvex) optimization programs. The typical methods for solving such optimization problems are to transform them into convex semi-definite programs (SDPs) with additional rank-one (nonconvex and discontinuous) constraints. The rank-one constraints are then dropped to obtain solvable SDP relaxed problems and randomization techniques are employed for seeking the feasible solutions to

A. H. Phan; H. D. Tuan; H. H. Kha; D. T. Ngo

2010-01-01

117

Ant Algorithms Solve Difficult Optimization Problems  

E-print Network

Ant Algorithms Solve Difficult Optimization Problems Marco Dorigo IRIDIA Universit´e Libre de Bruxelles 50 Avenue F. Roosevelt B-1050 Brussels, Belgium mdorigo@ulb.ac.be Abstract. The ant algorithms research field builds on the idea that the study of the behavior of ant colonies or other social insects

Libre de Bruxelles, Université

118

Creative dynamics approach to optimization problems  

Microsoft Academic Search

A type of dynamical system for solving optimization problems is introduced. The approach exploits a novel paradigm in nonlinear dynamics that is based upon the concept of terminal attractors and repellers. A class of dynamical systems-the unpredictable systems-is introduced and analyzed. These systems are represented in the form of coupled activation and learning dynamical equations whose ability to be spontaneously

Michail Zak; Nikzad Toomarian; Jacob Barhen

1990-01-01

119

Cooperative optimal path planning for herding problems  

E-print Network

of herding as another part of the performance index. The performance index J can be expressed in this form: J = w1 ?tf +w2 ? Z tf 0 (_x2p + _y2p)dt (2.3) In the above expression, w1 and w2 are the weights for time optimal and efiort optimal respectively... (t0 = 0) are randomly cho- sen: [xe(t0);ye(t0)] = [3;4] , [xp(t0);yp(t0)] = [4;4:6]. The flnal constraint at tf is [xe(tf);ye(tf)] = [0;0]. C. Dynamic Programming (SNOPT) Once the 1P1E herding problem is formulated as an optimal control problem...

Lu, Zhenyu

2009-05-15

120

Mathematical Optimization for Engineering Design Problems  

NASA Astrophysics Data System (ADS)

Applications in engineering design and the material sciences motivate the development of optimization theory in a manner that additionally draws from other branches of mathematics including the functional, complex, and numerical analyses. The first contribution, motivated by an automotive design application, extends multiobjective optimization theory under the assumption that the problem information is not available in its entirety to a single decision maker as traditionally assumed in the multiobjective optimization literature. Rather, the problem information and the design control are distributed among different decision makers. This requirement appears in the design of an automotive system whose subsystem components themselves correspond to highly involved design subproblems each of whose performance is measured by multiple criteria. This leads to a system/subsystem interaction requiring a coordination whose algorithmic foundation is developed and rigorously examined mathematically. The second contribution develops and analyzes a parameter estimation approach motivated from a time domain modeling problem in the material sciences. In addition to drawing from the theory of least-squares optimization and numerical analysis, the development of a mathematical foundation for comparing a baseline parameter estimation approach with an alternative parameter estimation approach relies on theory from both the functional and complex analyses. The application of the developed theory and algorithms associated with both contributions is also discussed.

Dandurand, Brian C.

121

Solving optimization problems on computational grids.  

SciTech Connect

Multiprocessor computing platforms, which have become more and more widely available since the mid-1980s, are now heavily used by organizations that need to solve very demanding computational problems. Parallel computing is now central to the culture of many research communities. Novel parallel approaches were developed for global optimization, network optimization, and direct-search methods for nonlinear optimization. Activity was particularly widespread in parallel branch-and-bound approaches for various problems in combinatorial and network optimization. As the cost of personal computers and low-end workstations has continued to fall, while the speed and capacity of processors and networks have increased dramatically, 'cluster' platforms have become popular in many settings. A somewhat different type of parallel computing platform know as a computational grid (alternatively, metacomputer) has arisen in comparatively recent times. Broadly speaking, this term refers not to a multiprocessor with identical processing nodes but rather to a heterogeneous collection of devices that are widely distributed, possibly around the globe. The advantage of such platforms is obvious: they have the potential to deliver enormous computing power. Just as obviously, however, the complexity of grids makes them very difficult to use. The Condor team, headed by Miron Livny at the University of Wisconsin, were among the pioneers in providing infrastructure for grid computations. More recently, the Globus project has developed technologies to support computations on geographically distributed platforms consisting of high-end computers, storage and visualization devices, and other scientific instruments. In 1997, we started the metaneos project as a collaborative effort between optimization specialists and the Condor and Globus groups. Our aim was to address complex, difficult optimization problems in several areas, designing and implementing the algorithms and the software infrastructure need to solve these problems on computational grids. This article describes some of the results we have obtained during the first three years of the metaneos project. Our efforts have led to development of the runtime support library MW for implementing algorithms with master-worker control structure on Condor platforms. This work is discussed here, along with work on algorithms and codes for integer linear programming, the quadratic assignment problem, and stochastic linear programmming. Our experiences in the metaneos project have shown that cheap, powerful computational grids can be used to tackle large optimization problems of various types. In an industrial or commercial setting, the results demonstrate that one may not have to buy powerful computational servers to solve many of the large problems arising in areas such as scheduling, portfolio optimization, or logistics; the idle time on employee workstations (or, at worst, an investment in a modest cluster of PCs) may do the job. For the optimization research community, our results motivate further work on parallel, grid-enabled algorithms for solving very large problems of other types. The fact that very large problems can be solved cheaply allows researchers to better understand issues of 'practical' complexity and of the role of heuristics.

Wright, S. J.; Mathematics and Computer Science

2001-05-01

122

Algorithms for nonlinear multicommodity network flow problems  

Microsoft Academic Search

This paper presents a class of algorithms for optimization of convex multi-commodity flow problems. The algorithms are based on the ideas of Gallager's methods for distributed optimization of delay in data communication networks [1],

Dimitri P. Bertsekas

123

Minimax optimization problem of structural design Elena Cherkaev *, Andrej Cherkaev  

E-print Network

Minimax optimization problem of structural design Elena Cherkaev *, Andrej Cherkaev University discusses a problem of robust optimal design of elastic structures when the loading is unknown on the structure and is subject of optimization. We formulate the problem of robust optimal design as a min

Cherkaev, Andrej

124

Optimization-Based Constrained Iterative Learning Control  

Microsoft Academic Search

We consider the problem of synthesis of iterative learning control (ILC) schemes for constrained linear systems executing a repetitive task. The ILC problem with affine constraints and quadratic objective functions is formulated as a convex quadratic program, for which there exist computationally efficient solvers. The key difference between standard convex optimization and the corresponding constrained ILC problem is that each

Sandipan Mishra; Ufuk Topcu; Masayoshi Tomizuka

2011-01-01

125

Optimal solutions of unobservable orbit determination problems  

NASA Astrophysics Data System (ADS)

The method of data augmentation, in the form ofa priori covariance information on the reference solution, as a means to overcome the effects of ill-conditioning in orbit determination problems has been investigated. Specifically, for the case when ill-conditioning results from parameter non-observability and an appropriatea priori covariance is unknown, methods by which thea priori covariance is optimally chosen are presented. In problems where an inaccuratea priori covariance is provided, the optimal weighting of this data set is obtained. The feasibility of these ‘ridge-type’ solution methods is demonstrated by their application to a non-observable gravity field recovery simulation. In the simulation, both ‘ridge-type’ and conventional solutions are compared. Substantial improvement in the accuracy of the conventional solution is realized by the use of these ridge-type solution methods. The solution techniques presented in this study are applicable to observable, but ill-conditioned problems as well as the unobservable problems directly addressed. For the case of observable problems, the ridge-type solutions provide an improvement in the accuracy of the ordinary least squares solutions.

Cicci, David A.; Tapley, Byron D.

1988-12-01

126

Combinatorial optimization problems in self-assembly  

Microsoft Academic Search

Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund

Leonard M. Adleman; Qi Cheng; Ashish Goel; Ming-Deh A. Huang; David Kempe; Pablo Moisset de Espanés; Paul Wilhelm Karl Rothemund

2002-01-01

127

User-guided segmentation of preterm neonate ventricular system from 3-d ultrasound images using convex optimization.  

PubMed

A three-dimensional (3-D) ultrasound (US) system has been developed to monitor the intracranial ventricular system of preterm neonates with intraventricular hemorrhage (IVH) and the resultant dilation of the ventricles (ventriculomegaly). To measure ventricular volume from 3-D US images, a semi-automatic convex optimization-based approach is proposed for segmentation of the cerebral ventricular system in preterm neonates with IVH from 3-D US images. The proposed semi-automatic segmentation method makes use of the convex optimization technique supervised by user-initialized information. Experiments using 58 patient 3-D US images reveal that our proposed approach yielded a mean Dice similarity coefficient of 78.2% compared with the surfaces that were manually contoured, suggesting good agreement between these two segmentations. Additional metrics, the mean absolute distance of 0.65 mm and the maximum absolute distance of 3.2 mm, indicated small distance errors for a voxel spacing of 0.22 × 0.22 × 0.22 mm(3). The Pearson correlation coefficient (r = 0.97, p < 0.001) indicated a significant correlation of algorithm-generated ventricular system volume (VSV) with the manually generated VSV. The calculated minimal detectable difference in ventricular volume change indicated that the proposed segmentation approach with 3-D US images is capable of detecting a VSV difference of 6.5 cm(3) with 95% confidence, suggesting that this approach might be used for monitoring IVH patients' ventricular changes using 3-D US imaging. The mean segmentation times of the graphics processing unit (GPU)- and central processing unit-implemented algorithms were 50 ± 2 and 205 ± 5 s for one 3-D US image, respectively, in addition to 120 ± 10 s for initialization, less than the approximately 35 min required by manual segmentation. In addition, repeatability experiments indicated that the intra-observer variability ranges from 6.5% to 7.5%, and the inter-observer variability is 8.5% in terms of the coefficient of variation of the Dice similarity coefficient. The intra-class correlation coefficient for ventricular system volume measurements for each independent observer ranged from 0.988 to 0.996 and was 0.945 for three different observers. The coefficient of variation and intra-class correlation coefficient revealed that the intra- and inter-observer variability of the proposed approach introduced by the user initialization was small, indicating good reproducibility, independent of different users. PMID:25542486

Qiu, Wu; Yuan, Jing; Kishimoto, Jessica; McLeod, Jonathan; Chen, Yimin; de Ribaupierre, Sandrine; Fenster, Aaron

2015-02-01

128

LDRD Final Report: Global Optimization for Engineering Science Problems  

SciTech Connect

For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.

HART,WILLIAM E.

1999-12-01

129

Directionally differentiable multiobjective optimization involving discrete inclusions  

Microsoft Academic Search

This paper is devoted to multiobjective optimization problems involving discrete inclusions. The objective functions are assumed to be directionally differentiable and the domination structure is defined by a closed convex cone. The directional derivatives are not assumed to be linear or convex. Several concepts of optimal solutions are analyzed, and the corresponding necessary conditions are obtained as well in maximum

Y. Ishizuka; H. D. Tuan

1996-01-01

130

Honey Bees Mating Optimization for the location routing problem  

Microsoft Academic Search

This paper introduces a new hybrid algorithmic nature inspired approach based on honey bees mating optimization, for solving successfully one of the most popular supply chain management problems, the location routing problem (LRP). The proposed algorithm for the solution of the location routing problem, the hybrid honey bees mating optimization (HBMO-LRP), combines a honey bees mating optimization (HBMO) algorithm, the

Yannis Marinakis; Magdalene Marinaki; Nikolaos Matsatsinis

2008-01-01

131

Optimal Control Problems with Control and State Constraints Numrical Method: Discretize and Optimize Theory of Optimal C Tutorial on Control and State Constrained Optimal  

E-print Network

and Optimize Theory of Optimal C Tutorial on Control and State Constrained Optimal Control Problems ­ Part 2 Problems with Control and State Constraints Numrical Method: Discretize and Optimize Theory of Optimal C and Optimize 3 Theory of Optimal Control Problems with Mixed Control-State Constraints 4 Example: Rayleigh

Boyer, Edmond

132

Automatic segmentation for brain MR images via a convex optimized segmentation and bias field correction coupled model.  

PubMed

Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results. PMID:24832358

Chen, Yunjie; Zhao, Bo; Zhang, Jianwei; Zheng, Yuhui

2014-09-01

133

Hybrid intelligent optimization methods for engineering problems  

NASA Astrophysics Data System (ADS)

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles.

Pehlivanoglu, Yasin Volkan

134

Design of Fractional Delay Filters Using Convex Optimization William Putnam ( putnam@ccrma.stanford.edu)  

E-print Network

In Music and Acoustics (CCRMA) Stanford University Stanford, CA 94305­8180 ABSTRACT Fractional sample delay arrays [1], [2], delay lines for physical models of musical instruments [3] [4], and time delay estimation[5]. This paper addresses the design of finite impulse response (FIR) FD filters. The problem

Smith III, Julius Orion

135

Design of Fractional Delay Filters Using Convex Optimization William Putnam ( putnam@ccrma.stanford.edu)  

E-print Network

In Music and Acoustics (CCRMA) Stanford University Stanford, CA 94305-8180 ABSTRACT Fractional sample delay arrays [1], [2], delay lines for physical models of musical instruments [3] [4], and time delay estimation[5]. This paper addresses the design of finite impulse response (FIR) FD filters. The problem

Smith III, Julius Orion

136

Advanced global optimization algorithms for parameterized LMIs  

Microsoft Academic Search

Parameterized linear matrix inequalities (PLMIs) frequently arise in analysis and synthesis problems of robust control theory. However, in contrast to linear matrix inequalities (LMIs) which are convex optimization problems with available efficient polynomial-time interior-point methods, PLMIs are highly nonconvex and thus are very hard to solve. In this paper, we exploit partial convexity properties of PLMIs that are useful for

H. D. Tuan; P. Apkarian; H. Tuy

1999-01-01

137

Solving ptychography with a convex relaxation  

E-print Network

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the current standard algorithm for ptychographic reconstruction...

Horstmeyer, Roarke; Ou, Xiaoze; Ames, Brendan; Tropp, Joel A; Yang, Changhuei

2014-01-01

138

Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems  

Microsoft Academic Search

Whether or not the general asymmetric variational inequality problem can be formulated as a differentiable optimization problem has been an open question. This paper gives an affirmative answer to this question. We provide a new optimization problem formulation of the variational inequality problem, and show that its objective function is continuously differentiable whenever the mapping involved in the latter problem

Masao Fukushima

1992-01-01

139

Group Search Optimizer for the Mobile Location Management Problem  

PubMed Central

We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach. PMID:25180199

Wang, Dan; Xiong, Congcong; Huang, Wei

2014-01-01

140

EFFICIENT SOLUTION OF OPTIMAL CONTROL PROBLEMS USING HYBRID SYSTEMS  

E-print Network

the synthesis of optimal controls for continuous feedback systems by recasting the problem to a hybrid optimal of a computationally appealing technique for synthesizing optimal controls for continuous feedback systems x = f(x, u is minimized, for each initial condition in a specified set Rn . Casting the problem as a hybrid control

Broucke, Mireille E.

141

Finding Globally Optimum Solutions in Antenna Optimization Problems  

E-print Network

as the optimization variables. This is particularly useful in designing on-chip smart antennas, where thousands in designing smart antennas. Description of the Problem Let us consider the problem in Figure 1, where a dipoleFinding Globally Optimum Solutions in Antenna Optimization Problems Aydin Babakhani*, Javad Lavaei

Hajimiri, Ali

142

LMI characterization for the convex hull of trigonometric curves and applications  

Microsoft Academic Search

In this paper, we develop a new linear matrix inequality (LMI) technique, which is practical for solutions of the general trigonometric semi-infinite linear constraint (TSIC) of competitive orders. Based on the new full LMI characterization for the convex hull of a trigonometric curve, it is shown that the semi-infinite optimization problem involving TSIC can be solved by an LMI optimization

H. D. Tuan; T. T. Son; B. Vo; T. Q. Nguyen

2005-01-01

143

Some optimization problems in power system reliability analysis  

E-print Network

This dissertation aims to address two optimization problems involving power system reliabilty analysis, namely multi-area power system adequacy planning and transformer maintenance optimization. A new simulation method for power system reliability...

Jirutitijaroen, Panida

2009-05-15

144

Dynkin stopping game for Merton's portfolio optimization problem  

Microsoft Academic Search

In this note, we consider a two-player, zero-sum Dynkin stopping game associated with Merton's portfolio optimization problem, for which the optimal strategies are made explicit under certain conditions.

Cloud Makasu

145

Existence of classical solutions to a free boundary problem for the pLaplace operator: (II) the interior convex case  

E-print Network

) the interior convex case Antoine HENROT \\Lambda Equipe de Math'ematiques, UMR CNRS Universit'e de Franche­Comt of Mathematics Royal Institute of Technology 100 44 Stockholm SWEDEN email henriks@math.kth.se August 11, 1999

Shahgholian, Henrik

146

A Simple But Effective Evolutionary Algorithm for Complicated Optimization Problems  

E-print Network

A simple but effective evolutionary algorithm is proposed in this paper for solving complicated optimization problems. The new algorithm presents two hybridization operations incorporated with the conventional genetic ...

Xu, Y.G.

147

Direct Transcription Solution of Optimal Control Problems with Control Delays  

NASA Astrophysics Data System (ADS)

The numerical solution of optimal control problems is important in many areas. Often the models for these problems have delays. Direct transcription is a popular approach for the numerical solution of optimal control problems in industry. However, much less work has been done on the direct transcription solution of optimal control problems with delays. This talk will describe progress and challenges in developing a general purpose industrial grade direct transcription code that can handle problems with delays. Of special interest will be the more challenging case of control delays.

Betts, John T.; Campbell, Stephen L.; Thompson, Karmethia C.

2011-09-01

148

Artificial Bee Colony (ABC) Optimization Algorithm for Solving Constrained Optimization Problems  

Microsoft Academic Search

This paper presents the comparison results on the performance of the Artificial Bee Colony (ABC) algorithm for constrained\\u000a optimization problems. The ABC algorithm has been firstly proposed for unconstrained optimization problems and showed that\\u000a it has superior performance on these kind of problems. In this paper, the ABC algorithm has been extended for solving constrained\\u000a optimization problems and applied to

Dervis Karaboga; Bahriye Basturk

2007-01-01

149

The Traveling Salesman Problem: A Case Study in Local Optimization  

Microsoft Academic Search

This is a preliminary version of a chapter that appeared in the book Local Search in Combinatorial Optimization, E. H. L. Aarts and J. K. Lenstra (eds.), John Wiley and Sons, London, 1997, pp. 215-310. The traveling salesman problem (TSP) has been an early proving ground for many approaches to combinatorial optimization, including clas- sical local optimization techniques as well

David S. Johnson; Lyle A. McGeoch

1977-01-01

150

Nonlinear classes of problems of environmental activity optimal control  

Microsoft Academic Search

We consider a set of optimization problems for dynamic models concerned with natural protection activity of enterprises (as environmental polluters) and an administrative center. Some solution methods are proposed. It is based on nonlinear transformation of the corresponding complex models into auxiliary problems of optimal control which are easier for solving

A. A. Moskalenko; A. I. Moskalenko; S. N. Vassilyev

1998-01-01

151

Dynamic Visualization in Modelling and Optimization of Ill Defined Problems  

E-print Network

Dynamic Visualization in Modelling and Optimization of Ill Defined Problems Case Studies and Generalizations William F. Eddy and Audris Mockus Abstract We consider visualization as a decision optimization of prevention and control. The fourth problem may be referred to as visual indexing. We perform exploratory

152

A Genetic Algorithm for Minimax Optimization Problems Jeffrey W. Herrmann  

E-print Network

A Genetic Algorithm for Minimax Optimization Problems Jeffrey W. Herrmann Department of Mechanical-space genetic algorithm as a general technique to solve minimax optimization problems. This algorithm maintains of applications. To illustrate its potential, we use the two-space genetic algorithm to solve a parallel machine

Herrmann, Jeffrey W.

153

The Proportional Colouring Problem: Optimizing Buffers in Wireless Mesh Networks  

E-print Network

The Proportional Colouring Problem: Optimizing Buffers in Wireless Mesh Networks Florian Huc 1 I3S optimization: the proportional edge colouring problem. Given a graph G with positive weights associated to its edges, we want to find a proper edge colouring which assigns to each edge at least a proportion (given

Paris-Sud XI, Université de

154

Problems in large-scale structural optimization  

NASA Technical Reports Server (NTRS)

A general design optimization model for large complex systems is defined. Major features of the model that challenge various optimization algorithms are discussed. Requirements of a model optimization algorithm are identified. Objectives of the study of various algorithms are defined and a basis for conducting such a study is developed. Primal as well as transformation methods are analytically studied and a unified viewpoint of various methods is presented. Several numerical examples are solved using different methods to study their performance. Conclusions drawn from the study are presented and discussed. Areas of future research in nonlinear programming as well as structural optimization are identified and discussed.

Arora, J. S.; Belegundu, A. D.

1984-01-01

155

Properties of an interior embedding for solving nonlinear optimization problems  

Microsoft Academic Search

.   The paper presents an interior embedding of nonlinear optimization problems. This embedding satisfies a sufficient condition\\u000a for the success of pathfollowing algorithms with jumps being applied to one-parametric optimization problems.¶The one-parametric\\u000a problem obtained by the embedding is supposed to be regular in the sense of Jongen, Jonker and Twilt. This asumption is analyzed,\\u000a and its genericity is proved in

Walter Gómez Bofill

1999-01-01

156

introduction first problem two optimization problems in physiology  

E-print Network

proliferates in a diabetic organism? #12;introduction first problem compartmental analysis concept: compartment kinetics' descriptor: exchange coefficients data: FDG (micro)-PET images #12;introduction first problem (micro)-PET images mathematical model: the kinetic input is modeled by an input function which

Combettes, Patrick Louis

157

On optimization techniques for solving nonlinear inverse problems  

Microsoft Academic Search

This paper considers optimization techniques for the solution of nonlinear inverse problems where the forward problems, like those encountered in electromagnetics, are modelled by differential equations. Such problems are often solved by utilizing a Gauss-Newton method in which the forward model constraints are implicitly incorporated. Variants of Newton's method which use second-derivative information are rarely employed because their perceived disadvantage

Eldad Haber; Uri M. Ascher; Doug Oldenburg

2000-01-01

158

Spectral finite-element methods for parametric constrained optimization problems.  

SciTech Connect

We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.

Anitescu, M.; Mathematics and Computer Science

2009-01-01

159

Comparison of optimal design methods in inverse problems  

NASA Astrophysics Data System (ADS)

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

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

2011-07-01

160

A global optimization problem in portfolio selection  

E-print Network

34,44,47,. 19,20,31. Risk ? 0.744 & 50. From (1.9) (Q-N only). -. 8,12,15,. 1,17,19 .... [3] N.J. Jobst, M.D. Horniman, C.A. Lucas and G. Mitra, Computational Aspects ... [4] D.R.Jones, C.D. Perttunen and B.E. Stuckman, Lipschitzian Optimization.

2004-06-24

161

Parallel hybrid optimization methods for permutation based problems.  

E-print Network

??Solving efficiently large benchmarks of NP-hard permutation-based problems requires the development of hybrid methods combining different classes of optimization algorithms. The key challenge here is… (more)

Mehdi, Malika

2011-01-01

162

The tracial moment problem and trace-optimization of polynomials  

E-print Network

Abstract. The main topic addressed in this paper is trace-optimization of polynomials in .... quantum mechanical many particle systems one often investigates the statis- .... study a closely related instance of a semidefinite programming problem.

2011-04-29

163

Decomposition methods for large scale stochastic and robust optimization problems  

E-print Network

We propose new decomposition methods for use on broad families of stochastic and robust optimization problems in order to yield tractable approaches for large-scale real world application. We introduce a new type of a ...

Becker, Adrian Bernard Druke

2011-01-01

164

Consensus over Ring Networks as a Quadratic Optimal Control Problem  

E-print Network

Consensus over Ring Networks as a Quadratic Optimal Control Problem J. A. Rogge J. A. K. Suykens-mail: {jonathan.rogge,dirk.aeyels}@ugent.be) K. U. Leuven, ESAT-SCD, Kasteelpark Arenberg 10, B-3001 Leuven

165

Combinatorial optimization problems with concave costs  

E-print Network

In the first part, we study the problem of minimizing a separable concave function over a polyhedron. We assume the concave functions are nonnegative nondecreasing on R+, and the polyhedron is in RI' (these assumptions can ...

Stratila, Dan

2009-01-01

166

The Checkpoint Ordering Problem - Optimization Online  

E-print Network

Sep 16, 2014 ... It arises as the problem of ordering stations on a production line where the material flow ... 3. no empty space is allowed between the departments, ...... Algorithms, Software and Applications, International Series in Operations ...

2014-09-16

167

DC optimization approach to robust controls: the optimal scaling value problem  

Microsoft Academic Search

The optimal scaling problem (OSP) for constant scaling in output feedback control is an inherently difficult nonconvex problem for which existing local search algorithms can at best locate a local solution. Because of the presence of additional nonconvex constraints, OSP is a harder problem than the feasibility problem (FP) studied in Tuan et al. However, like FP, it can be

H. D. Tuan; S. Hosoe; H. Tuy

1997-01-01

168

Some Optimal Stochastic Control Problems in Neuroscience — a Review  

NASA Astrophysics Data System (ADS)

Nervous systems are probability machines and, as such, modeling their activities should incorporate stochastic processes. In this review, we present two examples of optimal stochastic control problems with an analytic methodology on how to find optimal signals. The first example deals with neuronal activity and the second example is concerned with a higher level task: arm movement. In both cases we find optimal signals for particular tasks and find our results in agreement with the experimental Fitts Law.

Feng, Jianfeng; Chen, Xiaojiang; Tuckwell, Henry C.; Vasilaki, Eleni

169

An optimization approach for process engineering problems under uncertainty  

Microsoft Academic Search

The problem of selecting an optimal design\\/plan for process models involving stochastic parameters is addressed in this paper. A classification of uncertainty is introduced depending on its sources and mathematical model structure. A combined multiperiod\\/stochastic optimization formulation is then proposed along with a decomposition-based algorithmic procedure for its solution. The approach is illustrated with a process synthesis\\/planning example problem.

M. G. Ierapetritou; J. Acevedo; E. N. Pistikopoulos

1996-01-01

170

Robust stability and contraction analysis of nonlinear systems via semidefinite optimization  

E-print Network

A wide variety of stability and performance problems for linear and certain classes of nonlinear dynamical systems can be formulated as convex optimization problems involving linear matrix inequalities (LMIs). These ...

Aylward, Erin M

2006-01-01

171

V International Conference on Inverse Problems, Control and Shape Optimization  

E-print Network

V International Conference on Inverse Problems, Control and Shape Optimization Cartagena (Spain and internal control. We use a Galerkin approximation of the optimal control operator of the continuous model) April 7-9, 2010 Experimental Study of the HUM Control Operator for Linear Waves Gilles Lebeau1 , Ma

Boyer, Edmond

172

GENETIC ALGORITHMS APPLIED TO REAL TIME MULTIOBJECTIVE OPTIMIZATION PROBLEMS  

E-print Network

-to-air missions, air defense suppression missions, reconnaissance, anti­tactical ballistic missile, and air refueling. This software automatically plans military moves and actions in a rule-based manner. It also optimization method with some additional rules. To find solutions to this kind of optimization problem, one

Coello, Carlos A. Coello

173

Strong Equivalence of Qualitative Optimization Problems Wolfgang Faber  

E-print Network

settings is an important research area for knowledge representation and qualitative decision theoryStrong Equivalence of Qualitative Optimization Problems Wolfgang Faber University of Calabria faber of Technology woltran@dbai.tuwien.ac.at Abstract We introduce the framework of qualitative optimization prob

Faber, Wolfgang

174

Optimal boundary control problems related to high-lift configurations  

E-print Network

functions belonging to L2 ( ) under an integral state constraint. We de- rive optimality conditions. Here, a linear- quadratic integral functional expressing the lift is to be maximized under an integral, 11, 12, 13, 14, 32, 34]. Optimal flow control problems with state constraints were studied in [10, 24

Tröltzsch, Fredi

175

Finding Optimal Gains In Linear-Quadratic Control Problems  

NASA Technical Reports Server (NTRS)

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

176

Solving the discrete network design problem to optimality  

SciTech Connect

The network design problem has various applications, such as construction of new links in transportation networks, topological design of computer communication networks and planning of empty freight car transportation on railways. The problem is a multicommodity minimal cost network flow problem with fixed costs on the arcs, i.e. a structured linear mixed-integer programming problem. We discuss solution methods for finding the exact optimal solution of the problem. Encouraging computational results are given for a Lagrangean heuristic within a branch-and-bound framework for the uncapacitated network design problem with single origins and destinations for each commodity (the simplest problem in this class, but still NP-hard). The Lagrangean heuristic uses a Lagrangean relaxation as subproblem, solving the Lagrange dual with subgradient optimization, combined with a primal heuristic (here the Benders subproblem) yielding primal feasible solutions.

Holmberg, K.; Hellstrand, J.

1994-12-31

177

The Expanded Invasive Weed Optimization Metaheuristic for Solving Continuous and Discrete Optimization Problems  

PubMed Central

This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature. PMID:24955420

Josi?ski, Henryk; Michalczuk, Agnieszka; ?wito?ski, Adam

2014-01-01

178

The expanded invasive weed optimization metaheuristic for solving continuous and discrete optimization problems.  

PubMed

This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature. PMID:24955420

Josi?ski, Henryk; Kostrzewa, Daniel; Michalczuk, Agnieszka; Swito?ski, Adam

2014-01-01

179

Chapter 4: Unconstrained Optimization Unconstrained optimization problem minx F(x) or maxx F(x)  

E-print Network

Chapter 4: Unconstrained Optimization · Unconstrained optimization problem minx F(x) or maxx F(x) · Constrained optimization problem min x F(x) or max x F(x) subject to g(x) = 0 and/or h(x) x) > 0 Example: minimize the outer area of a cylinder subject to a fixed volume. Objective function F(x) = 2r2

Wu, Xiaolin

180

Exact Solution of Graph Coloring Problems via - Optimization Online  

E-print Network

Vehicle Routing Problem with Time Windows. Rousseau ... Urban Transit Crew Management .... Min–GCP is a challenging problem partially due to the high number of symmetric solutions. ..... the tailing-off effect, that is the very slow convergence towards the optimal solution of the relaxation, due ...... COG-rd-

2011-09-21

181

An interactive global optimization algorithm for geological problems  

Microsoft Academic Search

A number of problems in geology can be formulated so that they consist of optimizing a real-valued function (termed the objective function) on some interval or over some region. Many methods are available for solution if the function is unimodal within the domain of interest. Direct methods, involving only function evaluations, are particularly useful in geological problems where the objective

Paul Schiffelbein

1985-01-01

182

Optimization of the multiple retailer supply chain management problem  

Microsoft Academic Search

With stock surpluses and shortages representing one of the greatest elements of risk to wholesalers, a solution to the multi- retailer supply chain management problem would result in tremendous economic benefits. In this problem, a single wholesaler with multiple retailer customers must find an optimal balance of quantities ordered from suppliers and acceptable lead time costs, while taking into account

Caio Soares; Gerry V. Dozier; Emmett Lodree; Jared Phillips; Katie Nobles; Yong Won Park

2008-01-01

183

BSDE representations for optimal switching problems with controlled volatility  

E-print Network

positive cost given by the function c. Of course, one of the mode of production may possibly consist the entirely probabilistic schemes presented in [3] or [7]. Key words: Stochastic control, Switching problems to the obtention of a probabilistic representation for a general form of continuous optimal switching problems

Paris-Sud XI, Université de

184

NEOS and Condor: solving optimization problems over the Internet  

Microsoft Academic Search

We discuss the use of Condor, a distributed resource management system, as a provider of computational resources for NEOS, an environment for solving optimization problems over the Internet. We also describe how problems are submitted and processed by NEOS, and then scheduled and solved by Condor on available (idle) workstations

Michael C. Ferris; Michael P. Mesnier; Jorge J. Moré

2000-01-01

185

Neos And Condor: Solving Optimization Problems Over The Internet  

Microsoft Academic Search

We discuss the use of Condor, a distributed resource management system, as aprovider of computational resources for NEOS, an environment for solving optimizationproblems over the Internet. We also describe how problems are submitted and processedby NEOS, and then scheduled and solved by Condor on available (idle) workstations.1 IntroductionThe NEOS Server [8] is a novel environment for solving optimization problems over

Jorge J. Mor'e; Michael C. Ferris; Michael P. Mesnier

1998-01-01

186

STATE-CONSTRAINED OPTIMAL CONTROL PROBLEMS OF IMPULSIVE DIFFERENTIAL EQUATIONS  

E-print Network

STATE-CONSTRAINED OPTIMAL CONTROL PROBLEMS OF IMPULSIVE DIFFERENTIAL EQUATIONS NICOLAS FORCADEL by measure driven differential systems and in presence of state constraints. The first result shows a reparametrized control problem of absolutely continuous trajectories but with time-dependent state

Paris-Sud XI, Université de

187

Good solution for multi-objective optimization problem  

NASA Astrophysics Data System (ADS)

Multi-objective optimization problems have been solved widely by determination of a Pareto optimal set. Practically, the decision-makers need to choose only one solution to implement on their system, which is a challenge for them especially when the number of solutions in the Pareto set is large. In this paper, new method has been proposed to get a good solution for multi-objective optimization problem. The method consists of two stages; the first stage used the Multi Objective Simulated Annealing algorithm to find the Pareto set that contains the non-dominated solutions, whereas the second stage used the optimal computing allocation technique to reduce the number of solutions in the Pareto set to one solution that depends on ranking the preferences of the objective functions. To validate this method, multi-objective 01 knapsack problem was analyzed.

Abubaker, Ahmad; Baharum, Adam; Alrefaei, Mahmoud

2014-07-01

188

Analysis, estimation and controller design of parameter-dependent systems using convex optimization based on linear matrix inequalities  

NASA Astrophysics Data System (ADS)

In this thesis, we outline three contributions in robust control. The first is the efficient computation of a lower bound on the robust stability margin (RSM) of uncertain systems. A lower bound on the RSM can be derived using the framework of integral quadratic constraints (IQCs). Current techniques for numerically computing this lower bound use a bisection scheme. We show how this bisection can be avoided altogether by reformulating the lower bound computation problem as a single generalized eigenvalue minimization problem, which can be solved very efficiently using standard algorithms. For the second contribution, we focus on linear systems affected by parametric uncertainties. For these systems, we present sufficient conditions for robust stability. We also derive conditions for the existence of a robustly stabilizing gain-scheduled controller when the system has time-varying parametric uncertainties that can be measured in real time. Our approach is proven to be in general less conservative than existing methods. Our third contribution is on the robust estimation of systems having parametric uncertainties. For systems with mixed deterministic and stochastic uncertainties, we design two optimized steady state filters: (i) the first filter minimizes an upper bound on the worst-case gain in the mean energy between the noise affecting the system and the estimation error; (ii) the second filter minimizes an upper bound on the worst-case asymptotic mean square estimation error when the plant is driven by a white noise process. For time-varying systems with stochastic uncertainties, we derive a robust adaptive Kalman filtering algorithm. This algorithm offers considerable improvement in performance when compared to the standard Kalman filtering techniques. We demonstrate the performance of these robust filters on numerical examples consisting of the design of equalizers for communication channels.

Wang, Fan

189

TSP based Evolutionary optimization approach for the Vehicle Routing Problem  

NASA Astrophysics Data System (ADS)

Vehicle Routing and Flexible Job Shop Scheduling Problems (VRP and FJSSP) are two common hard combinatorial optimization problems that show many similarities in their conceptual level [2, 4]. It was proved for both problems that solving techniques like exact methods fail to provide good quality solutions in a reasonable amount of time when dealing with large scale instances [1, 5, 14]. In order to overcome this weakness, we decide in the favour of meta heuristics and we focalize on evolutionary algorithms that have been successfully used in scheduling problems [1, 5, 9]. In this paper we investigate the common properties of the VRP and the FJSSP in order to provide a new controlled evolutionary approach for the CVRP optimization inspired by the FJSSP evolutionary optimization algorithms introduced in [10].

Kouki, Zoulel; Chaar, Besma Fayech; Ksouri, Mekki

2009-03-01

190

GloptiPoly: Global Optimization over Polynomials with Matlab and ...  

E-print Network

Feb 12, 2002 ... relaxations of (generally non-convex) global optimization problems with .... Then we invoke GloptiPoly with four input matrices: the first input matrix ...... in the near future. ... Proceedings of the European Control Conference, pp.

2002-02-12

191

The coral reefs optimization algorithm: a novel metaheuristic for efficiently solving optimization problems.  

PubMed

This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems. PMID:25147860

Salcedo-Sanz, S; Del Ser, J; Landa-Torres, I; Gil-López, S; Portilla-Figueras, J A

2014-01-01

192

The Coral Reefs Optimization Algorithm: A Novel Metaheuristic for Efficiently Solving Optimization Problems  

PubMed Central

This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems. PMID:25147860

Salcedo-Sanz, S.; Del Ser, J.; Landa-Torres, I.; Gil-López, S.; Portilla-Figueras, J. A.

2014-01-01

193

Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems  

NASA Technical Reports Server (NTRS)

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. During solution of the multidisciplinary problems several issues were encountered. This paper lists four issues and discusses the strategies adapted for their resolution: (1) The optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. (2) Optimum solutions obtained were infeasible for aircraft and air-breathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. (3) Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. (4) The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through six problems: (1) design of an engine component, (2) synthesis of a subsonic aircraft, (3) operation optimization of a supersonic engine, (4) design of a wave-rotor-topping device, (5) profile optimization of a cantilever beam, and (6) design of a cvlindrical shell. The combined effort of designers and researchers can bring the optimization method from academia to industry.

Patnaik, Suna N.; Coroneos, Rula M.; Hopkins, Dale A.; Lavelle, Thomas M.

2000-01-01

194

Sub-problem Optimization With Regression and Neural Network Approximators  

NASA Technical Reports Server (NTRS)

Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of sub-problems. For a multidisciplinary system, individual disciplines, accounting for coupling, can be considered as sub-problems. A sub-problem, if required, can be further broken down to accommodate sub-disciplines. The sub-problem strategy is being implemented into the NASA design optimization test bed, referred to as "CometBoards." Neural network and regression approximators are employed for reanalysis and sensitivity analysis calculations at the sub-problem level. The strategy has been implemented in sequential as well as parallel computational environments. This strategy, which attempts to alleviate algorithmic and reanalysis deficiencies, has the potential to become a powerful design tool. However, several issues have to be addressed before its full potential can be harnessed. This paper illustrates the strategy and addresses some issues.

Guptill, James D.; Hopkins, Dale A.; Patnaik, Surya N.

2003-01-01

195

Russian Doll Search for solving Constraint Optimization problems  

SciTech Connect

If the Constraint Satisfaction framework has been extended to deal with Constraint Optimization problems, it appears that optimization is far more complex than satisfaction. One of the causes of the inefficiency of complete tree search methods, like Depth First Branch and Bound, lies in the poor quality of the lower bound on the global valuation of a partial assignment, even when using Forward Checking techniques. In this paper, we introduce the Russian Doll Search algorithm which replaces one search by n successive searches on nested subproblems (n being the number of problem variables), records the results of each search and uses them later, when solving larger subproblems, in order to improve the lower bound on the global valuation of any partial assignment. On small random problems and on large real scheduling problems, this algorithm yields surprisingly good results, which greatly improve as the problems get more constrained and the bandwidth of the used variable ordering diminishes.

Verfaillie, G.; Lemaitre, M. [CERT/ONERA, Toulouse (France); Schiex, T. [INRA, Castanet Tolosan (France)

1996-12-31

196

Integrated network design and scheduling problems : optimization algorithms and applications.  

SciTech Connect

We consider the class of integrated network design and scheduling problems. These problems focus on selecting and scheduling operations that will change the characteristics of a network, while being speci cally concerned with the performance of the network over time. Motivating applications of INDS problems include infrastructure restoration after extreme events and building humanitarian distribution supply chains. While similar models have been proposed, no one has performed an extensive review of INDS problems from their complexity, network and scheduling characteristics, information, and solution methods. We examine INDS problems under a parallel identical machine scheduling environment where the performance of the network is evaluated by solving classic network optimization problems. We classify that all considered INDS problems as NP-Hard and propose a novel heuristic dispatching rule algorithm that selects and schedules sets of arcs based on their interactions in the network. We present computational analysis based on realistic data sets representing the infrastructures of coastal New Hanover County, North Carolina, lower Manhattan, New York, and a realistic arti cial community CLARC County. These tests demonstrate the importance of a dispatching rule to arrive at near-optimal solutions during real-time decision making activities. We extend INDS problems to incorporate release dates which represent the earliest an operation can be performed and exible release dates through the introduction of specialized machine(s) that can perform work to move the release date earlier in time. An online optimization setting is explored where the release date of a component is not known.

Nurre, Sarah G.; Carlson, Jeffrey J.

2014-01-01

197

Climate Intervention as an Optimization Problem  

NASA Astrophysics Data System (ADS)

Typically, climate models simulations of intentional intervention in the climate system have taken the approach of imposing a change (eg, in solar flux, aerosol concentrations, aerosol emissions) and then predicting how that imposed change might affect Earth's climate or chemistry. Computations proceed from cause to effect. However, humans often proceed from "What do I want?" to "How do I get it?" One approach to thinking about intentional intervention in the climate system ("geoengineering") is to ask "What kind of climate do we want?" and then ask "What pattern of radiative forcing would come closest to achieving that desired climate state?" This involves defining climate goals and a cost function that measures how closely those goals are attained. (An important next step is to ask "How would we go about producing these desired patterns of radiative forcing?" However, this question is beyond the scope of our present study.) We performed a variety of climate simulations in NCAR's CAM3.1 atmospheric general circulation model with a slab ocean model and thermodynamic sea ice model. We then evaluated, for a specific set of climate forcing basis functions (ie, aerosol concentration distributions), the extent to which the climate response to a linear combination of those basis functions was similar to a linear combination of the climate response to each basis function taken individually. We then developed several cost functions (eg, relative to the 1xCO2 climate, minimize rms difference in zonal and annual mean land temperature, minimize rms difference in zonal and annual mean runoff, minimize rms difference in a combination of these temperature and runoff indices) and then predicted optimal combinations of our basis functions that would minimize these cost functions. Lastly, we produced forward simulations of the predicted optimal radiative forcing patterns and compared these with our expected results. Obviously, our climate model is much simpler than reality and predictions from individual models do not provide a sound basis for action; nevertheless, our model results indicate that the general approach outlined here can lead to patterns of radiative forcing that make the zonal annual mean climate of a high CO2 world markedly more similar to that of a low CO2 world simultaneously for both temperature and hydrological indices, where degree of similarity is measured using our explicit cost functions. We restricted ourselves to zonally uniform aerosol concentrations distributions that can be defined in terms of a positive-definite quadratic equation on the sine of latitude. Under this constraint, applying an aerosol distribution in a 2xCO2 climate that minimized a combination of rms difference in zonal and annual mean land temperature and runoff relative to the 1xCO2 climate, the rms difference in zonal and annual mean temperatures was reduced by ~90% and the rms difference in zonal and annual mean runoff was reduced by ~80%. This indicates that there may be potential for stratospheric aerosols to diminish simultaneously both temperature and hydrological cycle changes caused by excess CO2 in the atmosphere. Clearly, our model does not include many factors (eg, socio-political consequences, chemical consequences, ocean circulation changes, aerosol transport and microphysics) so we do not argue strongly for our specific climate model results, however, we do argue strongly in favor of our methodological approach. The proposed approach is general, in the sense that cost functions can be developed that represent different valuations. While the choice of appropriate cost functions is inherently a value judgment, evaluating those functions for a specific climate simulation is a quantitative exercise. Thus, the use of explicit cost functions in evaluating model results for climate intervention scenarios is a clear way of separating value judgments from purely scientific and technical issues.

Caldeira, Ken; Ban-Weiss, George A.

2010-05-01

198

Microcanonical Optimization Applied to the Traveling Salesman Problem  

NASA Astrophysics Data System (ADS)

Optimization strategies based on simulated annealing and its variants have been extensively applied to the traveling salesman problem (TSP). Recently, there has appeared a new physics-based metaheuristic, called the microcanonical optimization algorithm (?O), which does not resort to annealing, and which has proven a superior alternative to the annealing procedures in various applications. Here we present the first performance evaluation of ?O as applied to the TSP. When compared to three annealing strategies (simulated annealing, microcanonical annealing and Tsallis annealing), and to a tabu search algorithm, the microcanonical optimization has yielded the best overall results for several instances of the euclidean TSP. This confirms ?O as a competitive approach for the solution of general combinatorial optimization problems.

Linhares, Alexandre; Torreão, José R. A.

199

Piercing Convex Sets and Daniel J. Kleitman  

E-print Network

Piercing Convex Sets Noga Alon and Daniel J. Kleitman Abstract A family of sets has the (p, q-pierceable if it can be split into k or fewer subsets, each having a nonempty intersection. The piercing number of H general problem of studying the piercing numbers of families F of compact, convex sets in Rd that satisfy

Shamir, Ron

200

Optimal Price Decision Problem for Simultaneous Multi-article Auction and Its Optimal Price Searching Method by Particle Swarm Optimization  

NASA Astrophysics Data System (ADS)

We propose a method for solving optimal price decision problems for simultaneous multi-article auctions. An auction problem, originally formulated as a combinatorial problem, determines both every seller's whether or not to sell his/her article and every buyer's which article(s) to buy, so that the total utility of buyers and sellers will be maximized. Due to the duality theory, we transform it equivalently into a dual problem in which Lagrange multipliers are interpreted as articles' transaction price. As the dual problem is a continuous optimization problem with respect to the multipliers (i.e., the transaction prices), we propose a numerical method to solve it by applying heuristic global search methods. In this paper, Particle Swarm Optimization (PSO) is used to solve the dual problem, and experimental results are presented to show the validity of the proposed method.

Masuda, Kazuaki; Aiyoshi, Eitaro

201

Nonconvex Problems of Global Optimization: Linear-Quadratic Control Problems with Quadratic Constraints  

Microsoft Academic Search

In this paper, we study a class of optimization problems,which are of certain interest for control theory. These problemsare of global constrained optimization and may be nonconvex ingeneral. A simple approach to their solution is presented. Aspecial attention is paid to the case when the objective andconstraints functions are quadratic functionals on a Hilbertspace. As an example of an application

A. Matveev; V. Yakubovich

1997-01-01

202

Ant colony optimization for solving university facility layout problem  

NASA Astrophysics Data System (ADS)

Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ? 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).

Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin

2013-04-01

203

Hybrid optimization schemes for simulation-based problems.  

SciTech Connect

The inclusion of computer simulations in the study and design of complex engineering systems has created a need for efficient approaches to simulation-based optimization. For example, in water resources management problems, optimization problems regularly consist of objective functions and constraints that rely on output from a PDE-based simulator. Various assumptions can be made to simplify either the objective function or the physical system so that gradient-based methods apply, however the incorporation of realistic objection functions can be accomplished given the availability of derivative-free optimization methods. A wide variety of derivative-free methods exist and each method has both advantages and disadvantages. Therefore, to address such problems, we propose a hybrid approach, which allows the combining of beneficial elements of multiple methods in order to more efficiently search the design space. Specifically, in this paper, we illustrate the capabilities of two novel algorithms; one which hybridizes pattern search optimization with Gaussian Process emulation and the other which hybridizes pattern search and a genetic algorithm. We describe the hybrid methods and give some numerical results for a hydrological application which illustrate that the hybrids find an optimal solution under conditions for which traditional optimal search methods fail.

Fowler, Katie (Clarkson University, NY); Gray, Genetha Anne; Griffin, Joshua D. (SAS Institute, NC)

2010-05-01

204

A Discrete Lagrangian Algorithm for Optimal Routing Problems  

SciTech Connect

The ideas of discrete Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton's principle of stationary action Lagrangian and specifically on the direct discretization of the Lagrange-Hamilton principle for a conservative system. Since, in contrast to the differential equations, the discrete Euler-Lagrange equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.

Kosmas, O. T.; Vlachos, D. S.; Simos, T. E. [University of Peloponnese, 22100 Tripoli (Greece)

2008-11-06

205

Optimality problem of network topology in stocks market analysis  

NASA Astrophysics Data System (ADS)

Since its introduction fifteen years ago, minimal spanning tree has become an indispensible tool in econophysics. It is to filter the important economic information contained in a complex system of financial markets' commodities. Here we show that, in general, that tool is not optimal in terms of topological properties. Consequently, the economic interpretation of the filtered information might be misleading. To overcome that non-optimality problem, a set of criteria and a selection procedure of an optimal minimal spanning tree will be developed. By using New York Stock Exchange data, the advantages of the proposed method will be illustrated in terms of the power-law of degree distribution.

Djauhari, Maman Abdurachman; Gan, Siew Lee

2015-02-01

206

Application of clustering global optimization to thin film design problems.  

PubMed

Refinement techniques usually calculate an optimized local solution, which is strongly dependent on the initial formula used for the thin film design. In the present study, a clustering global optimization method is used which can iteratively change this initial formula, thereby progressing further than in the case of local optimization techniques. A wide panel of local solutions is found using this procedure, resulting in a large range of optical thicknesses. The efficiency of this technique is illustrated by two thin film design problems, in particular an infrared antireflection coating, and a solar-selective absorber coating. PMID:24663856

Lemarchand, Fabien

2014-03-10

207

Numerical Solution of Some Types of Fractional Optimal Control Problems  

PubMed Central

We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches. PMID:24385874

Sweilam, Nasser Hassan; Al-Ajami, Tamer Mostafa; Hoppe, Ronald H. W.

2013-01-01

208

State-Constrained Optimal Control Problems of Impulsive Differential Equations  

SciTech Connect

The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.

Forcadel, Nicolas, E-mail: forcadel@ceremade.dauphine.fr [Universite Paris-Dauphine, Ceremade (France); Rao Zhiping, E-mail: Zhiping.Rao@ensta-paristech.fr; Zidani, Hasnaa, E-mail: Hasnaa.Zidani@ensta-paristech.fr [ENSTA ParisTech and INRIA-Saclay, Equipe COMMANDS (France)

2013-08-01

209

Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization.  

PubMed

Reducing scanning time is significantly important for MRI. Compressed sensing has shown promising results by undersampling the k-space data to speed up imaging. Sparsity of an image plays an important role in compressed sensing MRI to reduce the image artifacts. Recently, the method of patch-based directional wavelets (PBDW) which trains geometric directions from undersampled data has been proposed. It has better performance in preserving image edges than conventional sparsifying transforms. However, obvious artifacts are presented in the smooth region when the data are highly undersampled. In addition, the original PBDW-based method does not hold obvious improvement for radial and fully 2D random sampling patterns. In this paper, the PBDW-based MRI reconstruction is improved from two aspects: 1) An efficient non-convex minimization algorithm is modified to enhance image quality; 2) PBDW are extended into shift-invariant discrete wavelet domain to enhance the ability of transform on sparsifying piecewise smooth image features. Numerical simulation results on vivo magnetic resonance images demonstrate that the proposed method outperforms the original PBDW in terms of removing artifacts and preserving edges. PMID:23992629

Ning, Bende; Qu, Xiaobo; Guo, Di; Hu, Changwei; Chen, Zhong

2013-11-01

210

An optimized finite-difference scheme for wave propagation problems  

NASA Technical Reports Server (NTRS)

Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.

Zingg, D. W.; Lomax, H.; Jurgens, H.

1993-01-01

211

Convex Graph Invariants  

E-print Network

Dec 2, 2010 ... tion; robust optimization; graph deconvolution; graph sampling; graph hypothesis testing ..... problem, which involves identifying hidden cliques embedded ... work setting, transcriptional regulatory networks of bacteria have ...

2010-12-02

212

On destination optimality in asymmetric distance Fermat-Weber problems  

Microsoft Academic Search

This paper introduces skewed norms, i.e. norms perturbed by a linear function, which are useful for modelling asymmetric distance\\u000a measures. The Fermat-Weber problem with mixed skewed norms is then considered. Using subdifferential calculus we derive exact\\u000a conditions for a destination point to be optimal, thereby correcting and completing some recent work on asymmetric distance\\u000a location problems. Finally the classical dominance

Frank Plastria

1992-01-01

213

A New Local Search Based Ant Colony Optimization Algorithm for Solving Combinatorial Optimization Problems  

NASA Astrophysics Data System (ADS)

Ant Colony Optimization (ACO) algorithms are a new branch of swarm intelligence. They have been applied to solve different combinatorial optimization problems successfully. Their performance is very promising when they solve small problem instances. However, the algorithms' time complexity increase and solution quality decrease for large problem instances. So, it is crucial to reduce the time requirement and at the same time to increase the solution quality for solving large combinatorial optimization problems by the ACO algorithms. This paper introduces a Local Search based ACO algorithm (LSACO), a new algorithm to solve large combinatorial optimization problems. The basis of LSACO is to apply an adaptive local search method to improve the solution quality. This local search automatically determines the number of edges to exchange during the execution of the algorithm. LSACO also applies pheromone updating rule and constructs solutions in a new way so as to decrease the convergence time. The performance of LSACO has been evaluated on a number of benchmark combinatorial optimization problems and results are compared with several existing ACO algorithms. Experimental results show that LSACO is able to produce good quality solutions with a higher rate of convergence for most of the problems.

Hassan, Md. Rakib; Islam, Md. Monirul; Murase, Kazuyuki

214

A Sparse Representation-Based Deployment Method for Optimizing the Observation Quality of Camera Networks  

PubMed Central

Deployment is a critical issue affecting the quality of service of camera networks. The deployment aims at adopting the least number of cameras to cover the whole scene, which may have obstacles to occlude the line of sight, with expected observation quality. This is generally formulated as a non-convex optimization problem, which is hard to solve in polynomial time. In this paper, we propose an efficient convex solution for deployment optimizing the observation quality based on a novel anisotropic sensing model of cameras, which provides a reliable measurement of the observation quality. The deployment is formulated as the selection of a subset of nodes from a redundant initial deployment with numerous cameras, which is an ?0 minimization problem. Then, we relax this non-convex optimization to a convex ?1 minimization employing the sparse representation. Therefore, the high quality deployment is efficiently obtained via convex optimization. Simulation results confirm the effectiveness of the proposed camera deployment algorithms. PMID:23989826

Wang, Chang; Qi, Fei; Shi, Guangming; Wang, Xiaotian

2013-01-01

215

Optimizing Value and Avoiding Problems in Building Schools.  

ERIC Educational Resources Information Center

This report describes school design and construction delivery processes used by the School Board of Brevard County (Cocoa, Florida) that help optimize value, avoid problems, and eliminate the cost of maintaining a large facility staff. The project phases are examined from project definition through design to construction. Project delivery…

Brevard County School Board, Cocoa, FL.

216

To the optimization problem in minority game model  

SciTech Connect

The article presents the research results of the optimization problem in minority game model to a gaussian approximation using replica symmetry breaking by one step (1RSB). A comparison to replica symmetry approximation (RS) and the results from literary sources received using other methods has been held.

Yanishevsky, Vasyl [Drogobych Ivan Franko University, 36 Ivan Franko St., 82100 (Ukraine)

2009-12-14

217

Complementarity Formulations of l0-norm Optimization Problems  

E-print Network

Sep 25, 2013 ... conditions, as well as local and global optimality. ... A simple example of such a problem is that of finding a solution to a system of linear inequalities ... usually for the convergence analysis of standard NLP algorithms, such as constraint qualifications. ... support of xi; we call 1n ? ? the support vector of x.

2013-09-25

218

AIAA-2002-5573 GLOBAL OPTIMIZATION OF PROBLEMS WITH DISCONNECTED  

E-print Network

MODELING Michael Sasena , Panos Papalambros , Pierre Goovaerts University of Michigan, Ann Arbor, MI 48109 an infill sampling criterion (ISC) as the objective function for an auxiliary optimization problem that selects the next design point to eval- uate. The kriging models are iteratively updated with the new

Papalambros, Panos

219

SEARCHING PARETO OPTIMAL SOLUTIONS FOR THE PROBLEM OF FORMING AND  

E-print Network

, a multi-agent system is made up of several homogeneous or heterogeneous agents which communicate betweenSEARCHING PARETO OPTIMAL SOLUTIONS FOR THE PROBLEM OF FORMING AND RESTRUCTURING COALITIONS IN MULTI-AGENT and multi-agent systems. Current multi-agent coalition formation methods present two limits: First

Paris-Sud XI, Université de

220

Modulus of convexity for operator convex functions  

E-print Network

Given an operator convex function $f(x)$, we obtain an operator-valued lower bound for $cf(x) + (1-c)f(y) - f(cx + (1-c)y)$, $c \\in [0,1]$. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is shown to be false for functions that are convex but not operator convex.

Isaac H. Kim

2014-07-08

221

Finding the optimal metric in classification problems with ordinal features  

NASA Astrophysics Data System (ADS)

A method for finding the optimal distance function for the classification problem with two classes in which the objects are specified by vectors of their ordinal features is proposed. An optimal distance function is sought by the minimization of the weighted difference of the average intraclass and interclass distances. It is assumed that a specific distance function is given for each feature, which is defined on the Cartesian product of the set of integer numbers in the range from 0 to N - 1 and takes values from 0 to M. Distance functions satisfy modified metric properties. The number of admissible distance functions is calculated, which enables one to significantly reduce the complexity of the problem. To verify the appropriateness of metric optimization and to perform experiments, the nearest neighbor algorithm is used.

Iofina, G. V.

2010-03-01

222

Binary optimization for source localization in the inverse problem of ECG.  

PubMed

The goal of ECG-imaging (ECGI) is to reconstruct heart electrical activity from body surface potential maps. The problem is ill-posed, which means that it is extremely sensitive to measurement and modeling errors. The most commonly used method to tackle this obstacle is Tikhonov regularization, which consists in converting the original problem into a well-posed one by adding a penalty term. The method, despite all its practical advantages, has however a serious drawback: The obtained solution is often over-smoothed, which can hinder precise clinical diagnosis and treatment planning. In this paper, we apply a binary optimization approach to the transmembrane voltage (TMV)-based problem. For this, we assume the TMV to take two possible values according to a heart abnormality under consideration. In this work, we investigate the localization of simulated ischemic areas and ectopic foci and one clinical infarction case. This affects only the choice of the binary values, while the core of the algorithms remains the same, making the approximation easily adjustable to the application needs. Two methods, a hybrid metaheuristic approach and the difference of convex functions (DC), algorithm were tested. For this purpose, we performed realistic heart simulations for a complex thorax model and applied the proposed techniques to the obtained ECG signals. Both methods enabled localization of the areas of interest, hence showing their potential for application in ECGI. For the metaheuristic algorithm, it was necessary to subdivide the heart into regions in order to obtain a stable solution unsusceptible to the errors, while the analytical DC scheme can be efficiently applied for higher dimensional problems. With the DC method, we also successfully reconstructed the activation pattern and origin of a simulated extrasystole. In addition, the DC algorithm enables iterative adjustment of binary values ensuring robust performance. PMID:25008005

Potyagaylo, Danila; Cortés, Elisenda Gil; Schulze, Walther H W; Dössel, Olaf

2014-09-01

223

Approximating convex Pareto surfaces in multiobjective radiotherapy planning  

SciTech Connect

Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable dimension. The set of all such plans is called the Pareto optimal surface. This article presents an algorithm for computing well distributed points on the (convex) Pareto optimal surface of a multiobjective programming problem. The algorithm is applied to intensity-modulated radiation therapy inverse planning problems, and results of a prostate case and a skull base case are presented, in three and four dimensions, investigating tradeoffs between tumor coverage and critical organ sparing.

Craft, David L.; Halabi, Tarek F.; Shih, Helen A.; Bortfeld, Thomas R. [Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114 (United States)

2006-09-15

224

Neural network for constrained nonsmooth optimization using Tikhonov regularization.  

PubMed

This paper presents a one-layer neural network to solve nonsmooth convex optimization problems based on the Tikhonov regularization method. Firstly, it is shown that the optimal solution of the original problem can be approximated by the optimal solution of a strongly convex optimization problems. Then, it is proved that for any initial point, the state of the proposed neural network enters the equality feasible region in finite time, and is globally convergent to the unique optimal solution of the related strongly convex optimization problems. Compared with the existing neural networks, the proposed neural network has lower model complexity and does not need penalty parameters. In the end, some numerical examples and application are given to illustrate the effectiveness and improvement of the proposed neural network. PMID:25590563

Qin, Sitian; Fan, Dejun; Wu, Guangxi; Zhao, Lijun

2015-03-01

225

Minimizing separable convex functions subject to simple chain constraints  

SciTech Connect

We show in the present paper that it is possible to minimize a separable convex function subject to simple chain constraints by a {open_quotes}Pool Adjacent Violators{close_quotes} algorithm. Our result unifies and extends some results previously obtained in the context of statistics and inventory control. We further show that a modified version of the algorithm determines the set of all optimal solutions to the problem. Finally, we show that yet another modified version solves an integer version of the problem.

Chakravarti, M.; Best, M.; Ubhaya, V.

1994-12-31

226

Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method  

NASA Astrophysics Data System (ADS)

Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

Vasant, Pandian

2011-06-01

227

Statistical physics of hard combinatorial optimization: Vertex cover problem  

NASA Astrophysics Data System (ADS)

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

Zhao, Jin-Hua; Zhou, Hai-Jun

2014-07-01

228

Heuristic Optimization for the Discrete Virtual Power Plant Dispatch Problem  

SciTech Connect

We consider a virtual power plant, which is given the task of dispatching a fluctuating power supply to a portfolio of flexible consumers. The flexible consumers are modeled as discrete batch processes, and the associated optimization problem is denoted the discrete virtual power plant dispatch problem (DVPPDP). First, the nondeterministic polynomial time (NP)-completeness of the discrete virtual power plant dispatch problem is proved formally. We then proceed to develop tailored versions of the meta-heuristic algorithms hill climber and greedy randomized adaptive search procedure (GRASP). The algorithms are tuned and tested on portfolios of varying sizes. We find that all the tailored algorithms perform satisfactorily in the sense that they are able to find sub-optimal, but usable, solutions to very large problems (on the order of 105 units) at computation times on the scale of just 10 s, which is far beyond the capabilities of the optimal algorithms we have tested. In particular, GRASP sorted shows with the most promising performance, as it is able to find solutions that are both agile (sorted) and well balanced, and consistently yields the best numerical performance among the developed algorithms.

Petersen, Mette K.; Hansen, Lars H.; Bendtsen, Jan; Edlund, Kristian; Stoustrup, Jakob

2014-10-17

229

Near-optimal deterministic algorithms for volume computation via M-ellipsoids  

PubMed Central

We give a deterministic algorithm for computing an M-ellipsoid of a convex body, matching a known lower bound. This leads to a nearly optimal deterministic algorithm for estimating the volume of a convex body and improved deterministic algorithms for fundamental lattice problems under general norms.

Dadush, Daniel; Vempala, Santosh S.

2013-01-01

230

Exact multiplicity of positive solutions for concave-convex and convex-concave nonlinearities  

NASA Astrophysics Data System (ADS)

This note gives an unified treatment of the exact multiplicity results for both S-shaped and reversed S-shaped bifurcation for positive solutions of the two-point problem u?+?f(u)=0, for -1convex and convex-concave nonlinearities f(u).

Korman, Philip; Li, Yi

2014-11-01

231

Cores of convex games  

Microsoft Academic Search

The core of ann-person game is the set of feasible outcomes that cannot be improved upon by any coalition of players. A convex game is defined as one that is based on a convex set function. In this paper it is shown that the core of a convex game is not empty and that it has an especially regular structure.

Lloyd S. Shapley

1971-01-01

232

Compensated optimal grids for elliptic boundary-value problems  

PubMed Central

A method is proposed which allows to efficiently treat elliptic problems on unbounded domains in two and three spatial dimensions in which one is only interested in obtaining accurate solutions at the domain boundary. The method is an extension of the optimal grid approach for elliptic problems, based on optimal rational approximation of the associated Neumann-to-Dirichlet map in Fourier space. It is shown that, using certain types of boundary discretization, one can go from second-order accurate schemes to essentially spectrally accurate schemes in two-dimensional problems, and to fourth-order accurate schemes in three-dimensional problems without any increase in the computational complexity. The main idea of the method is to modify the impedance function being approximated to compensate for the numerical dispersion introduced by a small finite-difference stencil discretizing the differential operator on the boundary. We illustrate how the method can be efficiently applied to nonlinear problems arising in modeling of cell communication. PMID:19802366

Posta, F.; Shvartsman, S. Y.; Muratov, C. B.

2008-01-01

233

Optimal Solutions for Frequency Assignment Problems via Tree Decomposition  

Microsoft Academic Search

In this paper we describe a computational study to solve hard frequency assignment problems (FAPs) to optimality using a tree\\u000a decomposition of the graph that models interference constraints. We present a dynamic programming algorithm which solves FAPs\\u000a based on this tree decomposition. With the use of several dominance and bounding techniques it is possible to solve small\\u000a and medium-sized real-life

Arie M. C. A. Koster; Stan P. M. Van Hoesel; Antoon W. J. Kolen

1999-01-01

234

Second-order adjoints for solving PDE-constrained optimization problems  

Microsoft Academic Search

Inverse problems are of the utmost importance in many fields of science and engineering. In the variational approach, inverse problems are formulated as partial differential equation-constrained optimization problems, where the optimal estimate of the uncertain parameters is the minimizer of a certain cost functional subject to the constraints posed by the model equations. The numerical solution of such optimization problems

Alexandru Cioaca; Mihai Alexe; Adrian Sandu

2012-01-01

235

Second-order adjoints for solving PDE-constrained optimization problems  

Microsoft Academic Search

Inverse problems are of the utmost importance in many fields of science and engineering. In the variational approach, inverse problems are formulated as partial differential equation-constrained optimization problems, where the optimal estimate of the uncertain parameters is the minimizer of a certain cost functional subject to the constraints posed by the model equations. The numerical solution of such optimization problems

Alexandru Cioaca; Mihai Alexe; Adrian Sandu

2011-01-01

236

Linear Programming (LP) Formulation Problems Math 364: Principles of Optimization, Lecture 6  

E-print Network

Linear Programming (LP) Formulation Problems Math 364: Principles of Optimization, Lecture 6 Haijun Problems Staffing Problem: Linear Programming Formulation Haijun Li Math 364: Principles of Optimization;Linear Programming (LP) Formulation Problems Haijun Li Math 364: Principles of Optimization, Lecture 6

Li, Haijun

237

Issues and Strategies in Solving Multidisciplinary Optimization Problems  

NASA Technical Reports Server (NTRS)

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Patnaik, Surya

2013-01-01

238

Robust output-feedback controller design via local BMI optimization  

Microsoft Academic Search

The problem of designing a globally optimal full-order output-feedback controller for polytopic uncertain systems is known to be a non-convex NP-hard optimization problem, that can be represented as a bilinear matrix inequality optimization problem for most design objectives. In this paper a new approach is proposed to the design of locally optimal controllers. It is iterative by nature, and starting

S. Kanev; C. Scherer; Michel Verhaegen; Bart De Schutter

2004-01-01

239

Lagrange's principle in extremum problems with constraints  

NASA Astrophysics Data System (ADS)

In this paper a general result concerning Lagrange's principle for so-called smoothly approximately convex problems is proved which encompasses necessary extremum conditions for mathematical and convex programming, the calculus of variations, Lyapunov problems, and optimal control problems with phase constraints. The problem of local controllability for a dynamical system with phase constraints is also considered. In an appendix, results are presented that relate to the development of a 'Lagrangian approach' to problems where regularity is absent and classical approaches are meaningless. Bibliography: 33 titles.

Avakov, E. R.; Magaril-Il'yaev, G. G.; Tikhomirov, V. M.

2013-06-01

240

A self-learning particle swarm optimizer for global optimization problems.  

PubMed

Particle swarm optimization (PSO) has been shown as an effective tool for solving global optimization problems. So far, most PSO algorithms use a single learning pattern for all particles, which means that all particles in a swarm use the same strategy. This monotonic learning pattern may cause the lack of intelligence for a particular particle, which makes it unable to deal with different complex situations. This paper presents a novel algorithm, called self-learning particle swarm optimizer (SLPSO), for global optimization problems. In SLPSO, each particle has a set of four strategies to cope with different situations in the search space. The cooperation of the four strategies is implemented by an adaptive learning framework at the individual level, which can enable a particle to choose the optimal strategy according to its own local fitness landscape. The experimental study on a set of 45 test functions and two real-world problems show that SLPSO has a superior performance in comparison with several other peer algorithms. PMID:22067435

Li, Changhe; Yang, Shengxiang; Nguyen, Trung Thanh

2012-06-01

241

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows  

PubMed Central

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C2, C3, C4,…. It is known that C2 can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing Ck (k > 2) require solving a linear program. In this paper we prove that C3 can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}n, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596

Wang, Di; Kleinberg, Robert D.

2009-01-01

242

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.  

PubMed

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596

Wang, Di; Kleinberg, Robert D

2009-11-28

243

On Several Fundamental Problems of Optimization, Estimation, and Scheduling in Wireless Communications  

NASA Astrophysics Data System (ADS)

For both the conventional radio frequency and the comparably recent optical wireless communication systems, extensive effort from the academia had been made in improving the network spectrum efficiency and/or reducing the error rate. To achieve these goals, many fundamental challenges such as power efficient constellation design, nonlinear distortion mitigation, channel training design, network scheduling and etc. need to be properly addressed. In this dissertation, novel schemes are proposed accordingly to deal with specific problems falling in category of these challenges. Rigorous proofs and analyses are provided for each of our work to make a fair comparison with the corresponding peer works to clearly demonstrate the advantages. The first part of this dissertation considers a multi-carrier optical wireless system employing intensity modulation (IM) and direct detection (DD). A block-wise constellation design is presented, which treats the DC-bias that conventionally used solely for biasing purpose as an information basis. Our scheme, we term it MSM-JDCM, takes advantage of the compactness of sphere packing in a higher dimensional space, and in turn power efficient constellations are obtained by solving an advanced convex optimization problem. Besides the significant power gains, the MSM-JDCM has many other merits such as being capable of mitigating nonlinear distortion by including a peak-to-power ratio (PAPR) constraint, minimizing inter-symbol-interference (ISI) caused by frequency-selective fading with a novel precoder designed and embedded, and further reducing the bit-error-rate (BER) by combining with an optimized labeling scheme. The second part addresses several optimization problems in a multi-color visible light communication system, including power efficient constellation design, joint pre-equalizer and constellation design, and modeling of different structured channels with cross-talks. Our novel constellation design scheme, termed CSK-Advanced, is compared with the conventional decoupled system with the same spectrum efficiency to demonstrate the power efficiency. Crucial lighting requirements are included as optimization constraints. To control non-linear distortion, the optical peak-to-average-power ratio (PAPR) of LEDs can be individually constrained. With a SVD-based pre-equalizer designed and employed, our scheme can achieve lower BER than counterparts applying zero-forcing (ZF) or linear minimum-mean-squared-error (LMMSE) based post-equalizers. Besides, a binary switching algorithm (BSA) is applied to improve BER performance. The third part looks into a problem of two-phase channel estimation in a relayed wireless network. The channel estimates in every phase are obtained by the linear minimum mean squared error (LMMSE) method. Inaccurate estimate of the relay to destination (RtD) channel in phase 1 could affect estimate of the source to relay (StR) channel in phase 2, which is made erroneous. We first derive a close-form expression for the averaged Bayesian mean-square estimation error (ABMSE) for both phase estimates in terms of the length of source and relay training slots, based on which an iterative searching algorithm is then proposed that optimally allocates training slots to the two phases such that estimation errors are balanced. Analysis shows how the ABMSE of the StD channel estimation varies with the lengths of relay training and source training slots, the relay amplification gain, and the channel prior information respectively. The last part deals with a transmission scheduling problem in a uplink multiple-input-multiple-output (MIMO) wireless network. Code division multiple access (CDMA) is assumed as a multiple access scheme and pseudo-random codes are employed for different users. We consider a heavy traffic scenario, in which each user always has packets to transmit in the scheduled time slots. If the relay is scheduled for transmission together with users, then it operates in a full-duplex mode, where the packets previously collected from users are transmitted to the destination

Gao, Qian

244

Optimal Parametric Discrete Event Control: Problem and Solution  

SciTech Connect

We present a novel optimization problem for discrete event control, similar in spirit to the optimal parametric control problem common in statistical process control. In our problem, we assume a known finite state machine plant model $G$ defined over an event alphabet $\\Sigma$ so that the plant model language $L = \\LanM(G)$ is prefix closed. We further assume the existence of a \\textit{base control structure} $M_K$, which may be either a finite state machine or a deterministic pushdown machine. If $K = \\LanM(M_K)$, we assume $K$ is prefix closed and that $K \\subseteq L$. We associate each controllable transition of $M_K$ with a binary variable $X_1,\\dots,X_n$ indicating whether the transition is enabled or not. This leads to a function $M_K(X_1,\\dots,X_n)$, that returns a new control specification depending upon the values of $X_1,\\dots,X_n$. We exhibit a branch-and-bound algorithm to solve the optimization problem $\\min_{X_1,\\dots,X_n}\\max_{w \\in K} C(w)$ such that $M_K(X_1,\\dots,X_n) \\models \\Pi$ and $\\LanM(M_K(X_1,\\dots,X_n)) \\in \\Con(L)$. Here $\\Pi$ is a set of logical assertions on the structure of $M_K(X_1,\\dots,X_n)$, and $M_K(X_1,\\dots,X_n) \\models \\Pi$ indicates that $M_K(X_1,\\dots,X_n)$ satisfies the logical assertions; and, $\\Con(L)$ is the set of controllable sublanguages of $L$.

Griffin, Christopher H [ORNL

2008-01-01

245

CONVEXIFICATION OF GENERALIZED NETWORK FLOW PROBLEM WITH APPLICATION TO POWER SYSTEMS  

E-print Network

CONVEXIFICATION OF GENERALIZED NETWORK FLOW PROBLEM WITH APPLICATION TO POWER SYSTEMS SOMAYEH to flows may not be unique. A primary application of this work is in optimization over power networks. Recent work on the optimal power flow (OPF) problem has shown that this non-convex problem can be solved

Shepard, Kenneth

246

Adaptive Evolutionary Monte Carlo for Heuristic Optimization: With Applications to Sensor Placement Problems  

E-print Network

This dissertation presents an algorithm to solve optimization problems with "black-box" objective functions, i.e., functions that can only be evaluated by running a computer program. Such optimization problems often arise in engineering applications...

Ren, Yuan

2010-01-14

247

Optimality conditions for a two-stage reservoir operation problem  

NASA Astrophysics Data System (ADS)

This paper discusses the optimality conditions for standard operation policy (SOP) and hedging rule (HR) for a two-stage reservoir operation problem using a consistent theoretical framework. The effects of three typical constraints, i.e., mass balance, nonnegative release, and storage constraints under both certain and uncertain conditions are analyzed. When all nonnegative constraints and storage constraints are unbinding, HR results in optimal reservoir operation following the marginal benefit (MB) principle (the MB is equal over current and future stages. However, if any of those constraints are binding, SOP results in the optimal solution, except in some special cases which need to carry over water in the current stage to the future stage, when extreme drought is certain and a higher marginal utility exists for the second stage. Furthermore, uncertainty complicates the effects of the various constraints. A higher uncertainty level in the future makes HR more favorable as water needs to be reserved to defend against the risk caused by uncertainty. Using the derived optimality conditions, an algorithm for solving a numerical model is developed and tested with the Miyun Reservoir in China.

Zhao, Jianshi; Cai, Ximing; Wang, Zhongjing

2011-08-01

248

On the robust optimization to the uncertain vaccination strategy problem  

SciTech Connect

In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.

Chaerani, D., E-mail: d.chaerani@unpad.ac.id; Anggriani, N., E-mail: d.chaerani@unpad.ac.id; Firdaniza, E-mail: d.chaerani@unpad.ac.id [Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Padjadjaran Indonesia, Jalan Raya Bandung Sumedang KM 21 Jatinangor Sumedang 45363 (Indonesia)

2014-02-21

249

On the robust optimization to the uncertain vaccination strategy problem  

NASA Astrophysics Data System (ADS)

In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.

Chaerani, D.; Anggriani, N.; Firdaniza

2014-02-01

250

New attitude penalty functions for spacecraft optimal control problems  

SciTech Connect

A solution of a spacecraft optimal control problem, whose cost function relies on an attitude description, usually depends on the choice of attitude coordinates used. A problem could be solved using 3-2-1 Euler angles or using classical Rodriguez parameters and yield two different ``optimal`` solutions, unless the performance index in invariant with respect to the attitude coordinate choice. Another problem arising with many attitude coordinates is that they have no sense of when a body has tumbled beyond 180{degrees} from the reference attitude. In many such cases it would be easier (i.e. cost less) to let the body complete the revolution than to force it to reverse the rotation and return to the desired attitude. This paper develops a universal attitude penalty function g() whose value is independent of the attitude coordinates chosen to represent it. Furthermore, this function will achieve its maximum value only when a principal rotation of {plus_minus}180{degrees} from the target state is performed. This will implicitly permit the g() function to sense the shortest rotational distance back to the reference state. An attitude penalty function which depends on the Modified Rodriguez Parameters (MRP) will also be presented. These recently discovered MRPs are a non-singular three-parameter set which can describe any three-attitude. This MRP penalty function is simpler than the attitude coordinate independent g() function, but retains the useful property of avoiding lengthy principal rotations of more than {plus_minus}180{degrees}.

Schaub, H.; Junkins, J.L. [Texas A and M Univ., College Station, TX (United States). Dept. of Aerospace Engineering; Robinett, R.D. [Sandia National Labs., Albuquerque, NM (United States)

1996-03-01

251

Relaxing the Optimality Conditions of Box QP  

E-print Network

Oct 23, 2007 ... ming, which incorporate the first- and second-order necessary optimality conditions ... Critical to any global optimization method for (1) is the ability to relax (1) into a convex ...... future, this technique may be extended to other problems, e.g., ... In Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.

2007-10-26

252

Hybrid Particle Swarm Optimization for Vehicle Routing Problem with Reverse Logistics  

Microsoft Academic Search

The vehicle routing problem (VRP) is a well-known combinatorial optimization problem, holds a central place in logistics management. This paper proposes an hybrid particle swarm optimization (PSO) for VRP with reverse logistics, which possesses a new strategy to represent the solution of the problem, and in the evolution of PSO, SA algorithm is used to optimize the sequence of the

Yang Peng

2009-01-01

253

Solving the Attribute Reduction Problem with Ant Colony Optimization  

NASA Astrophysics Data System (ADS)

Attribute reduction is an important process in rough set theory. More minimal attribute reductions are expected to help clients make decisions in some cases, though the minimal attribute reduction problem (MARP) is proved to be an NP-hard problem. In this paper, we propose a new heuristic approach for solving the MARP based on the ant colony optimization (ACO) metaheuristic. We first model the MARP as finding an assignment which minimizes the cost in a graph. Afterward, we introduce a preprocessing step that removes the redundant data in a discernibility matrix through the absorption operator and the cutting operator, the goal of which is to favor a smaller exploration of the search space at a lower cost. We then develop a new algorithm R-ACO for solving the MARP. Finally, the simulation results show that our approach can find more minimal attribute reductions more efficiently in most cases.

Yu, Hong; Wang, Guoyin; Lan, Fakuan

254

Peritoneal dialysis catheter implantation: avoiding problems and optimizing outcomes.  

PubMed

The success of peritoneal dialysis (PD) as renal replacement therapy is dependent upon the patient having a functional long-term peritoneal access. There are a number of identified best practices that must be adhered to during PD catheter placement to achieve a durable and infection-resistant access. The clinical setting, available resources, and the employed catheter insertion method may not always permit complete adherence to these practices; however, an attempt should be made to comply with them as closely as possible. Although omission of any one of the practices can lead to catheter loss, departures from some are committed more frequently, manifesting as commonly occurring clinical problems, such as drain pain, catheter tip migration, omental entrapment, pericatheter leaks and hernias, and poor exit-site location. Understanding the technical pitfalls in PD catheter placement that lead to these problems, enable the provider to modify practice habits to avoid them and optimize outcomes. PMID:25338661

Crabtree, John H

2015-01-01

255

Using pareto-optimality for solving multi-objective unequal area facility layout problem  

Microsoft Academic Search

A lot of optimal and heuristic algorithms for solving facility layout problem (FLP) have been developed in the past few decades. The majority of these approaches adopt a problem formulation known as the quadratic assignment problem (QAP) that is particularly suitable for equal area facilities. Unequal area FLP comprises a class of extremely difficult and widely applicable optimization problems arising

Kazi Shah Nawaz Ripon; Kashif Nizam Khan; Kyree Glette; Mats Hovin; Jim Torresen

2011-01-01

256

Algorithms for bilevel optimization  

NASA Technical Reports Server (NTRS)

General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multi-criteria optimization problems. Here, for clarity in displaying our ideas, we restrict ourselves to general bi-level optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easily extended to handle the general multilevel problem. We make no convexity assumptions, but we do assume that the problem has a nondegenerate feasible set. We consider necessary optimality conditions for the bi-level problem formulations and discuss results that can be extended to obtain multilevel optimization formulations with constraints at each level.

Alexandrov, Natalia; Dennis, J. E., Jr.

1994-01-01

257

Optimal order multilevel preconditioners for regularized ill-posed problems  

NASA Astrophysics Data System (ADS)

In this article we design and analyze multilevel preconditioners for linear systems arising from regularized inverse problems. Using a scale-independent distance function that measures spectral equivalence of operators, it is shown that these preconditioners approximate the inverse of the operator to optimal order with respect to the spatial discretization parameter h . As a consequence, the number of preconditioned conjugate gradient iterations needed for solving the system will decrease when increasing the number of levels, with the possibility of performing only one fine-level residual computation if h is small enough. The results are based on the previously known two-level preconditioners of Rieder (1997) (see also Hanke and Vogel (1999)), and on applying Newton-like methods to the operator equation X^{-1} - A = 0 . We require that the associated forward problem has certain smoothing properties; however, only natural stability and approximation properties are assumed for the discrete operators. The algorithm is applied to a reverse-time parabolic equation, that is, the problem of finding the initial value leading to a given final state. We also present some results on constructing restriction operators with preassigned approximating properties that are of independent interest.

Draganescu, Andrei; Dupont, Todd F.

2008-12-01

258

Left ventricle segmentation in MRI via convex relaxed distribution matching.  

PubMed

A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm requires about 3.87 s for a typical cardiac MRI volume, a speed-up of about five times compared to a standard implementation. We report a performance evaluation over 400 volumes acquired from 20 subjects, which shows that the obtained 3D surfaces correlate with independent manual delineations. We further demonstrate experimentally that (1) the performance of the algorithm is not significantly affected by the choice of the training subject and (2) the shape description we use does not change significantly from one subject to another. These results support the fact that a single subject is sufficient for training the proposed algorithm. PMID:23851075

Nambakhsh, Cyrus M S; Yuan, Jing; Punithakumar, Kumaradevan; Goela, Aashish; Rajchl, Martin; Peters, Terry M; Ayed, Ismail Ben

2013-12-01

259

Human opinion dynamics: An inspiration to solve complex optimization problems  

PubMed Central

Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making. PMID:24141795

Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan

2013-01-01

260

Power Mutation Embedded Modified PSO for Global Optimization Problems  

NASA Astrophysics Data System (ADS)

In the present study we propose a simple and modified framework for Particle Swarm Optimization (PSO) algorithm by incorporating in it a newly defined operator based on Power Mutation (PM). The resulting PSO variants are named as (Modified Power Mutation PSO) MPMPSO and MPMPSO 1 which differs from each other in the manner of implementation of mutation operator. In MPMPSO, PM is applied stochastically in conjugation with basic position update equation of PSO and in MPMPSO 1, PM is applied on the worst particle of swarm at each iteration. A suite of ten standard benchmark problems is employed to evaluate the performance of the proposed variations. Experimental results show that the proposed MPMPSO outperforms the existing method on most of the test functions in terms of convergence and solution quality.

Chauhan, Pinkey; Deep, Kusum; Pant, Millie

261

Optimal Control Problem of Feeding Adaptations of Daphnia and Neural Network Simulation  

NASA Astrophysics Data System (ADS)

A neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints and open final time. The optimal control problem is transcribed into nonlinear programming problem, which is implemented with adaptive critic neural network [9] and recurrent neural network for solving nonlinear proprojection equations [10]. The proposed simulation methods is illustrated by the optimal control problem of feeding adaptation of filter feeders of Daphnia. Results show that adaptive critic based systematic approach and neural network solving of nonlinear equations hold promise for obtaining the optimal control with control and state constraints and open final time.

Kmet', Tibor; Kmet'ov, Mria

2010-09-01

262

One-Dimensional Infinite Horizon Nonconcave Optimal Control Problems Arising in Economic Dynamics  

SciTech Connect

We study the existence of optimal solutions for a class of infinite horizon nonconvex autonomous discrete-time optimal control problems. This class contains optimal control problems without discounting arising in economic dynamics which describe a model with a nonconcave utility function.

Zaslavski, Alexander J., E-mail: ajzasl@tx.technion.ac.il [Technion-Israel Institute of Technology, Department of Mathematics (Israel)

2011-12-15

263

A scatter learning particle swarm optimization algorithm for multimodal problems.  

PubMed

Particle swarm optimization (PSO) has been proved to be an effective tool for function optimization. Its performance depends heavily on the characteristics of the employed exemplars. This necessitates considering both the fitness and the distribution of exemplars in designing PSO algorithms. Following this idea, we propose a novel PSO variant, called scatter learning PSO algorithm (SLPSOA) for multimodal problems. SLPSOA contains some new algorithmic features while following the basic framework of PSO. It constructs an exemplar pool (EP) that is composed of a certain number of relatively high-quality solutions scattered in the solution space, and requires particles to select their exemplars from EP using the roulette wheel rule. By this means, more promising solution regions can be found. In addition, SLPSOA employs Solis and Wets' algorithm as a local searcher to enhance its fine search ability in the newfound solution regions. To verify the efficiency of the proposed algorithm, we test it on a set of 16 benchmark functions and compare it with six existing typical PSO algorithms. Computational results demonstrate that SLPSOA can prevent premature convergence and produce competitive solutions. PMID:24108491

Ren, Zhigang; Zhang, Aimin; Wen, Changyun; Feng, Zuren

2014-07-01

264

Improved Particle Swarm Optimization with a Collective Local Unimodal Search for Continuous Optimization Problems  

PubMed Central

A new local search technique is proposed and used to improve the performance of particle swarm optimization algorithms by addressing the problem of premature convergence. In the proposed local search technique, a potential particle position in the solution search space is collectively constructed by a number of randomly selected particles in the swarm. The number of times the selection is made varies with the dimension of the optimization problem and each selected particle donates the value in the location of its randomly selected dimension from its personal best. After constructing the potential particle position, some local search is done around its neighbourhood in comparison with the current swarm global best position. It is then used to replace the global best particle position if it is found to be better; otherwise no replacement is made. Using some well-studied benchmark problems with low and high dimensions, numerical simulations were used to validate the performance of the improved algorithms. Comparisons were made with four different PSO variants, two of the variants implement different local search technique while the other two do not. Results show that the improved algorithms could obtain better quality solution while demonstrating better convergence velocity and precision, stability, robustness, and global-local search ability than the competing variants. PMID:24723827

Arasomwan, Martins Akugbe; Adewumi, Aderemi Oluyinka

2014-01-01

265

Multiagent optimization system for solving the traveling salesman problem (TSP).  

PubMed

The multiagent optimization system (MAOS) is a nature-inspired method, which supports cooperative search by the self-organization of a group of compact agents situated in an environment with certain sharing public knowledge. Moreover, each agent in MAOS is an autonomous entity with personal declarative memory and behavioral components. In this paper, MAOS is refined for solving the traveling salesman problem (TSP), which is a classic hard computational problem. Based on a simplified MAOS version, in which each agent manipulates on extremely limited declarative knowledge, some simple and efficient components for solving TSP, including two improving heuristics based on a generalized edge assembly recombination, are implemented. Compared with metaheuristics in adaptive memory programming, MAOS is particularly suitable for supporting cooperative search. The experimental results on two TSP benchmark data sets show that MAOS is competitive as compared with some state-of-the-art algorithms, including the Lin-Kernighan-Helsgaun, IBGLK, PHGA, etc., although MAOS does not use any explicit local search during the runtime. The contributions of MAOS components are investigated. It indicates that certain clues can be positive for making suitable selections before time-consuming computation. More importantly, it shows that the cooperative search of agents can achieve an overall good performance with a macro rule in the switch mode, which deploys certain alternate search rules with the offline performance in negative correlations. Using simple alternate rules may prevent the high difficulty of seeking an omnipotent rule that is efficient for a large data set. PMID:19095545

Xie, Xiao-Feng; Liu, Jiming

2009-04-01

266

High-order entropy-based closures for linear transport in slab geometry II: A computational study of the optimization problem  

SciTech Connect

We present a numerical algorithm to implement entropy-based (M{sub N}) moment models in the context of a simple, linear kinetic equation for particles moving through a material slab. The closure for these models - as is the case for all entropy-based models - is derived through the solution of constrained, convex optimization problem. The algorithm has two components. The first component is a discretization of the moment equations which preserves the set of realizable moments, thereby ensuring that the optimization problem has a solution (in exact arithmetic). The discretization is a second-order kinetic scheme which uses MUSCL-type limiting in space and a strong-stability-preserving, Runge-Kutta time integrator. The second component of the algorithm is a Newton-based solver for the dual optimization problem, which uses an adaptive quadrature to evaluate integrals in the dual objective and its derivatives. The accuracy of the numerical solution to the dual problem plays a key role in the time step restriction for the kinetic scheme. We study in detail the difficulties in the dual problem that arise near the boundary of realizable moments, where quadrature formulas are less reliable and the Hessian of the dual objection function is highly ill-conditioned. Extensive numerical experiments are performed to illustrate these difficulties. In cases where the dual problem becomes 'too difficult' to solve numerically, we propose a regularization technique to artificially move moments away from the realizable boundary in a way that still preserves local particle concentrations. We present results of numerical simulations for two challenging test problems in order to quantify the characteristics of the optimization solver and to investigate when and how frequently the regularization is needed.

Hauck, Cory D [ORNL; Alldredge, Graham [University of Maryland; Tits, Andre [University of Maryland

2012-01-01

267

Tomographic data selection as wave-based optimization problem  

NASA Astrophysics Data System (ADS)

Albert Tarantola devised the exploitation of full waveforms in both forward and inverse modeling almost 3 decades ago. Powerful numerical techniques and improved hardware capabilities have finally materialized this vision more recently and we now enjoy various methodological options to tackle these problems. Meanwhile, efforts to increase data coverage (e.g. USArray) have enjoyed a similar surge such that constructing a problem-specific database may require delicate selection and significant time investment. To enhance robustness and resolution of imaging capabilities for a given region of interest, we strive to quantify and automate some of the data selection processes for large-scale tomographic inversions by analyzing the nature and parameter dependencies of seismic sensitivity kernels. This is achieved by formulating an optimization problem for 3D region V(x), and computing spatio-temporal seismic sensitivity K(xs,x_r,x,t) for seismograms u(xr,t) upon an earthquake located at xs as a function of source frequency and depth, radiation pattern, receiver component, epicentral distance, azimuth, time windows of the seismogram, misfit parameters (e.g. traveltime versus waveforms), and model parameterization (wavespeeds versus elastic moduli). We sample the corresponding multi-dimensional parameter space discretely using a method described in Nissen-Meyer et al. (2007), which only requires a limited number of forward solutions to yield the full time- and frequency-dependent sensitivity of the waveform, thereby permitting a rather comprehensive sensitivity study. As an illustrative example, we consider the specific case of lowermost mantle phases, and discuss various trade-offs that may help in improving coverage and selecting appropriate data.

Nissen-Meyer, T.; Fournier, A.

2010-12-01

268

Goedel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements  

Microsoft Academic Search

An old dream of computer scientists is to build an optimally efficient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Godel's celebrated self-referential formulas (1931). Our Godel machine's initial software includes an axiomatic description of: the Godel machine's hardware, the problem-specific utility function (such as the expected future reward of

Juergen Schmidhuber

2003-01-01

269

On the Hamming distance in combinatorial optimization problems on hypergraph matchings  

E-print Network

On the Hamming distance in combinatorial optimization problems on hypergraph matchings Alla the properties of the Hamming distance in combinatorial optimization problems on hypergraph matchings, also known as multidimensional assignment problems. It is shown that the Hamming distance between feasible solutions

Krokhmal, Paul

270

The Inverse Newsvendor Problem: Choosing an Optimal Demand Portfolio for Capacitated Resources  

Microsoft Academic Search

The classical newsvendor problem is one of optimally choosing a level of capacity to respond to a known demand distribution. The inverse newsvendor problem is one of optimally choosing a demand distribution with fixed capacity. The applications of the inverse problem include industrial settings where demand management is relatively less costly than capacity adjustments. Demand distributions are chosen from an

Scott Carr; William Lovejoy

2000-01-01

271

Inverse Problems, Design and Optimization Symposium Jo~ao Pessoa, Brazil, August 25-27, 2010  

E-print Network

Inverse Problems, Design and Optimization Symposium Jo~ao Pessoa, Brazil, August 25-27, 2010 and Optimization Symposium Jo~ao Pessoa, Brazil, August 25-27, 2010 ## # # Thermocouples Heat source x y z Figure 1

Walker, D. Greg

272

A sparse superlinearly convergent SQP with applications to two-dimensional shape optimization.  

SciTech Connect

Discretization of optimal shape design problems leads to very large nonlinear optimization problems. For attaining maximum computational efficiency, a sequential quadratic programming (SQP) algorithm should achieve superlinear convergence while preserving sparsity and convexity of the resulting quadratic programs. Most classical SQP approaches violate at least one of the requirements. We show that, for a very large class of optimization problems, one can design SQP algorithms that satisfy all these three requirements. The improvements in computational efficiency are demonstrated for a cam design problem.

Anitescu, M.

1998-04-15

273

CONTINUOUS CONVEX SETS AND ZERO DUALITY GAP FOR ...  

E-print Network

euclidean spaces, like Gale & Klee's boundary rays and asymptotes of ... gardless of the value of the constraints and respectively of the objective ... Key words and phrases. constrained optimization, recession analysis, convex programs,.

2011-11-12

274

Geodesic Convexity and Chordal Graphs  

Microsoft Academic Search

A convexity on a flnite set X is a family C of subsets of X (each such set called a convex set), which is closed under intersection and which contains both X and the empty set. The pair (X;C) is called a convexity space. A (flnite) graph convexity space is a pair (G;C), formed by a flnite connected graph G

Ignacio M. Pelayo

275

Stochastic optimal LQR control with integral quadratic constraints and indefinite control weights  

Microsoft Academic Search

A standard assumption in traditional (deterministic and stochastic) optimal (minimizing) linear quadratic regulator (LQR) theory is that the control weighting matrix in the cost functional is strictly positive definite. In the deterministic case, this assumption is in fact necessary for the problem to be well-posed because positive definiteness is required to make it a convex optimization problem. However, it has

Andrew E. B. Lim; Xun Yu Zhou

1999-01-01

276

Chance-Constrained Guidance With Non-Convex Constraints  

NASA Technical Reports Server (NTRS)

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

Ono, Masahiro

2011-01-01

277

Weakly Convex Discontinuity Adaptive Regularization for Microwave Imaging  

E-print Network

1 Weakly Convex Discontinuity Adaptive Regularization for Microwave Imaging Funing Bai, Member develop a new class of weakly convex discontinuity adaptive (WCDA) models as a regularization and receivers than available in the database. Index Terms--Inverse problem, discontinuity adaptive regular

Pizurica, Aleksandra

278

Necessary Optimality Conditions for Some Control Problems of Elliptic Equations with Venttsel Boundary Conditions  

SciTech Connect

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constraint on the solution of the state equation is also considered.

Luo Yousong, E-mail: yluo@rmit.edu.a [RMIT University, School of Mathematical and Geospatial Sciences (Australia)

2010-06-15

279

Advancement and analysis of Gauss pseudospectral transcription for optimal control problems  

E-print Network

As optimal control problems become increasingly complex, innovative numerical methods are needed to solve them. Direct transcription methods, and in particular, methods involving orthogonal collocation have become quite ...

Huntington, Geoffrey Todd, 1979-

2007-01-01

280

Finite element approximation of an optimal control problem for the von Karman equations  

NASA Technical Reports Server (NTRS)

This paper is concerned with optimal control problems for the von Karman equations with distributed controls. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Finally we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations.

Hou, L. Steven; Turner, James C.

1994-01-01

281

On large scale unconstrained optimization problems and higher ...  

E-print Network

In: Nonlinear Optimization, M. J. D. Powell (Ed.), Academic Press, New York, NY, pp. 301–312. ... Algorithms, Addison-Wesley. [13] Bagirov, A.M. ... [19] Schwefel, H. P., 1981, Numerical Optimization of Computer Models, John Wiley and Sons,.

2008-08-29

282

Dinkelbach's Algorithm as an Efficient Method for Solving a Class of MINLP Models for Large-Scale Cyclic Scheduling Problems  

Microsoft Academic Search

In this paper we consider the solution methods for mixed-integer linear fractional programming (MILFP) models, which arise in cyclic process scheduling problems. We first discuss convexity properties of MILFP problems, and then investigate the capability of solving MILFP problems with MINLP methods. Dinkelbach's algorithm is introduced as an efficient method for solving large scale MILFP problems for which its optimality

Pedro M. Castro; Ignacio E. Grossmann

283

Cellular Neural-Like Algorithms with Heuristics for Solving Combinatorial Optimization Problems  

Microsoft Academic Search

We study a heuristic paradigm of neural network algorithms for solving combinatorial optimization problems in a cellular architecture. As an illustration, we present a cellular neural-like algorithm for solving approximately the maximum independent set problem.

S. M. Achasova

1997-01-01

284

Aircraft Routing -A Global Optimization Problem Michael C Bartholomew-Biggs  

E-print Network

Aircraft Routing - A Global Optimization Problem Michael C Bartholomew-Biggs matqmb@herts.ac.uk University of Hertfordshire, England This paper deals with the problem of calculating aircraft flight paths

Neumaier, Arnold

285

Solving Three-objective Optimization Problems Using Evolutionary Dynamic Weighted  

E-print Network

the definition function in the pa- rameter space that defines a Pareto-optimal front or the boundary of a Pareto- tionary optimization, the weights drift randomly during optimization. A method that explicitly uses random weights during selection for genetic algorithms has been suggested in [2]: wi = randomi/(random1

Jin, Yaochu

286

Elastic energy of a convex body Chiara Bianchini, Antoine Henrot, Takeo Takahashi  

E-print Network

of planar convex bodies is considered. More precisely we give a description of set E := (x, y) R2 , x = 4A Appendix 25 1 Introduction For a regular planar convex body , that is a planar convex compact set, we, in kinematics (the ball-plate problem), in numerical analysis (non-linear splines), in computer vision

Boyer, Edmond

287

Distributionally Robust Convex Optimization - Optimization Online  

E-print Network

2College of Management and Technology, École Polytechnique Fédérale de ... 0 [v(x, ˜z) ? w] ? 1 ? ? based on the identity Q0 [v(x, ˜z) ? w] = EQ. 0 ...... future liability v(x, ˜z) into a fraction ? that is paid today and a remainder v(x, ˜z) ? ? that is .... Instead, the newsvendor has access to a limited number of i.i.d. samples of ˜

2013-09-22

288

A faster optimization method based on support vector regression for aerodynamic problems  

NASA Astrophysics Data System (ADS)

In this paper, a new strategy for optimal design of complex aerodynamic configuration with a reasonable low computational effort is proposed. In order to solve the formulated aerodynamic optimization problem with heavy computation complexity, two steps are taken: (1) a sequential approximation method based on support vector regression (SVR) and hybrid cross validation strategy, is proposed to predict aerodynamic coefficients, and thus approximates the objective function and constraint conditions of the originally formulated optimization problem with given limited sample points; (2) a sequential optimization algorithm is proposed to ensure the obtained optimal solution by solving the approximation optimization problem in step (1) is very close to the optimal solution of the originally formulated optimization problem. In the end, we adopt a complex aerodynamic design problem, that is optimal aerodynamic design of a flight vehicle with grid fins, to demonstrate our proposed optimization methods, and numerical results show that better results can be obtained with a significantly lower computational effort than using classical optimization techniques.

Yang, Xixiang; Zhang, Weihua

2013-09-01

289

A Cascade Optimization Strategy for Solution of Difficult Multidisciplinary Design Problems  

NASA Technical Reports Server (NTRS)

A research project to comparatively evaluate 10 nonlinear optimization algorithms was recently completed. A conclusion was that no single optimizer could successfully solve all 40 problems in the test bed, even though most optimizers successfully solved at least one-third of the problems. We realized that improved search directions and step lengths, available in the 10 optimizers compared, were not likely to alleviate the convergence difficulties. For the solution of those difficult problems we have devised an alternative approach called cascade optimization strategy. The cascade strategy uses several optimizers, one followed by another in a specified sequence, to solve a problem. A pseudorandom scheme perturbs design variables between the optimizers. The cascade strategy has been tested successfully in the design of supersonic and subsonic aircraft configurations and air-breathing engines for high-speed civil transport applications. These problems could not be successfully solved by an individual optimizer. The cascade optimization strategy, however, generated feasible optimum solutions for both aircraft and engine problems. This paper presents the cascade strategy and solutions to a number of these problems.

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.; Berke, Laszlo

1996-01-01

290

A Synergistic Approach of Desirability Functions and Metaheuristic Strategy to Solve Multiple Response Optimization Problems  

NASA Astrophysics Data System (ADS)

Ensuring quality of a product is rarely based on observations of a single quality characteristic. Generally, it is based on observations of family of properties, so-called `multiple responses'. These multiple responses are often interacting and are measured in variety of units. Due to presence of interaction(s), overall optimal conditions for all the responses rarely result from isolated optimal condition of individual response. Conventional optimization techniques, such as design of experiment, linear and nonlinear programmings are generally recommended for single response optimization problems. Applying any of these techniques for multiple response optimization problem may lead to unnecessary simplification of the real problem with several restrictive model assumptions. In addition, engineering judgements or subjective ways of decision making may play an important role to apply some of these conventional techniques. In this context, a synergistic approach of desirability functions and metaheuristic technique is a viable alternative to handle multiple response optimization problems. Metaheuristics, such as simulated annealing (SA) and particle swarm optimization (PSO), have shown immense success to solve various discrete and continuous single response optimization problems. Instigated by those successful applications, this chapter assesses the potential of a Nelder-Mead simplex-based SA (SIMSA) and PSO to resolve varied multiple response optimization problems. The computational results clearly indicate the superiority of PSO over SIMSA for the selected problems.

Bera, Sasadhar; Mukherjee, Indrajit

2010-10-01

291

CONVEX BACKSCATTERING SUPPORT IN ELECTRIC IMPEDANCE TOMOGRAPHY  

E-print Network

CONVEX BACKSCATTERING SUPPORT IN ELECTRIC IMPEDANCE TOMOGRAPHY MARTIN HANKE, NUUTTI HYV ¨ONEN of the method. Key words. Electric impedance tomography, inclusions, backscattering, backscattering support for the inverse obstacle problem in impedance tomography. Under mild restrictions on the topological prop- erties

Hanke-Bourgeois, Martin

292

Coarse-grained parallel genetic algorithm applied to a nuclear reactor core design optimization problem  

Microsoft Academic Search

This work extends the research related to genetic algorithms (GA) in core design optimization problems, which basic investigations were presented in previous work. Here we explore the use of the Island Genetic Algorithm (IGA), a coarse-grained parallel GA model, comparing its performance to that obtained by the application of a traditional non-parallel GA. The optimization problem consists on adjusting several

Cláudio M. N. A. Pereira; Celso M. F. Lapa

2003-01-01

293

On Some Optimal Control Problems for Electric Circuits Kristof Altmann, Simon Stingelin, and Fredi Troltzsch  

E-print Network

On Some Optimal Control Problems for Electric Circuits Kristof Altmann, Simon Stingelin, and Fredi to be expected in such processes, we study here simplified models for electrical circuits based on ordinary's equations. We shall study different types of electrical circuits and associated optimal control problems

Tröltzsch, Fredi

294

20.18 Optimization Problems in Air Pollution Modeling Ivan Dimov, and Zahari Zlatev  

E-print Network

20.18 Optimization Problems in Air Pollution Modeling Ivan Dimov, and Zahari Zlatev ABSTRACT. The appearance of optimization problems in the field of air pollution modeling and their importance arising in air pollution modeling will be considered. We shall present a review of some approaches

Dimov, Ivan

295

Two adaptive mutation operators for optima tracking in dynamic optimization problems with evolution strategies  

Microsoft Academic Search

The dynamic optimization problem concerns finding an op- timum in a changing environment. In the tracking problem, the optimizer should be able to follow the optimum's changes over time. In this paper we present two adaptive muta- tion operators designed to improve the following of a time- changing optimum, under the assumption that the changes follow a non-random law. Such

Claudio Rossi; Antonio Barrientos; Jaime Del Cerro

2007-01-01

296

A Honey-bee Mating Optimization Algorithm for Educational Timetabling Problems  

E-print Network

1 A Honey-bee Mating Optimization Algorithm for Educational Timetabling Problems Nasser R. Sabar1 of the Honey-bee Mating Optimization Algorithm for solv- ing educational timetabling problems. The honey-bee algorithm is a nature inspired algorithm which sim- ulates the process of real honey-bees mating

Qu, Rong

297

A global optimization approach for the BMI problem  

Microsoft Academic Search

The biaffine matrix inequality (BMI) is a potentially very flexible new framework for approaching complex robust control system synthesis problems with multiple plants, multiple objectives and controller order constraints. The BMI problem may be viewed as the nondifferentiable biconvex programming problem of minimizing the maximum eigenvalue of a biaffine combination of symmetric matrices. The BMI problem is non-local-global in general,

K.-C. Goh; M. G. Safonovt; G. P. Papavassilopoulos

1994-01-01

298

Optimal Conditions for the Control Problem Associated to a Biomedical Process  

NASA Astrophysics Data System (ADS)

This paper considers a mathematical model of infectious disease of SIS type. We will analyze the problem of minimizing the cost of diseases trough medical treatment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon. The necessary conditions for optimality are given. Using the optimality conditions we prove the existence, uniqueness and stability of the steady state for a differential equations system.

Bund?u, O.; Juratoni, A.; Chevere?an, A.

2010-09-01

299

Domain decomposition methods for advection dominated linear-quadratic elliptic optimal control problems.  

SciTech Connect

We present an optimization-level domain decomposition (DD) preconditioner for the solution of advection dominated elliptic linear-quadratic optimal control problems. The DD preconditioner is based on a decomposition of the optimality conditions for the elliptic linear-quadratic optimal control problem into smaller subdomain optimality conditions with Dirichlet boundary conditions for the states and the adjoints on the subdomain interfaces. These subdomain optimality conditions are coupled through Robin transmission conditions for the states and the adjoints. The parameters in the Robin transmission condition depend on the advection. This decomposition leads to a Schur complement system in which the unknowns are the state and adjoint variables on the subdomain interfaces. The Schur complement operator is the sum of subdomain Schur complement operators, the application of which is shown to correspond to the solution of subdomain optimal control problems, which are essentially smaller copies of the original optimal control problem. We show that, under suitable conditions, the application of the inverse of the subdomain Schur complement operators requires the solution of a subdomain elliptic linear-quadratic optimal control problem with Robin boundary conditions for the state. Numerical tests for problems with distributed and with boundary control show that the dependence of the preconditioners on mesh size and subdomain size is comparable to its counterpart applied to a single advection dominated equation. These tests also show that the preconditioners are insensitive to the size of the control regularization parameter.

Heinkenschloss, Matthias (Rice University, Houston, TX); Bartlett, Roscoe Ainsworth; Van Bloeman Waanders, Paul; Ridzal, Denis (Rice University, Houston, TX)

2005-04-01

300

Hybrid genetic algorithm research and its application in problem optimization  

Microsoft Academic Search

There is a lot of research in genetic algorithm about structural optimization. But as far as the large multi-goal program is concerned, it limits the application of genetic algorithm for the reason of its specialty and large calculation. In order to explore a new resolution, the author proposed a combining algorithm for structural optimization, which is based on genetic algorithm

Weijin Jiang I; Dingti Luol; Yusheng Xu; Xingming Sun

2004-01-01

301

An asymptotically optimal algorithm for pickup and delivery problems  

E-print Network

Pickup and delivery problems (PDPs), in which objects or people have to be transported between specific locations, are among the most common combinatorial problems in real-world operations. One particular PDP is the Stacker ...

Pavone, Marco

302

Continuous Blooming of Convex Polyhedra  

E-print Network

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number ...

Demaine, Erik D.

303

A particle swarm optimization for wind energy control problem  

Microsoft Academic Search

The control problem of a wind turbine involves the determination of rotor speed and tip-speed ratio to maximize power and energy capture from the wind. The problem can be formulated as a nonlinear programming problem with the annual energy generation as the objective function. The wind speed distribution is modeled as the Weibull distribution. The Weibull shape and scale parameters

C. Kongnam; S. Nuchprayoon

2010-01-01

304

Convex Geometry and Stoichiometry  

E-print Network

We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of "mixtures" to explain multiple stoichiometry, and the half-reaction for balancing redox actions all yield nice convex geometric interpretations. We also relate some natural questions on reaction mechanisms with the enumeration of lattice points in polytopes. Lastly, it is known that a given reaction mechanism imposes linear constraints on observed stoichiometries. We consider the inverse question of deducing reaction mechanism consistent with a given set of linear stoichiometric restrictions.

Jer-Chin,

2011-01-01

305

Convex Quantum Logic  

E-print Network

In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of propositions of quantum logic is shown. This new structure is suitable for the study of compound systems and shows new differences between quantum and classical mechanics. This differences are linked to the nontrivial correlations which appear when quantum systems interact. They are reflected in the new propositional structure, and do not have a classical analogue. This approach is also suitable for an algebraic characterization of entanglement.

F. Holik; C. Massri; N. Ciancaglini

2010-08-24

306

Discrete Bat Algorithm for Optimal Problem of Permutation Flow Shop Scheduling  

PubMed Central

A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem. PMID:25243220

Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang

2014-01-01

307

Multi-agent Optimization Design for Multi-resource Job Shop Scheduling Problems  

NASA Astrophysics Data System (ADS)

As a practical generalization of the job shop scheduling problem, multi-resource job shop scheduling problem (MRJSSP) is discussed in this paper. In this problem, operations may be processed by a type of resources and jobs have individual deadlines. How to design and optimize this problem with DSAFO, a novel multi-agent algorithm, is introduced in detail by a case study, including problem analysis, agent role specification, and parameter selection. Experimental results show the effectiveness and efficiency of designing and optimizing MRJSSPs with multi-agent.

Xue, Fan; Fan, Wei

308

Singular optimal control and the identically non-regular problem in the calculus of variations  

NASA Technical Reports Server (NTRS)

A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.

Menon, P. K. A.; Kelley, H. J.; Cliff, E. M.

1985-01-01

309

A hybrid Honey Bees Mating Optimization algorithm for the Probabilistic Traveling Salesman Problem  

Microsoft Academic Search

The probabilistic traveling salesman problem is a variation of the classic traveling salesman problem and one of the most significant stochastic routing problems. In this paper, a new hybrid algorithmic nature inspired approach based on honey bees mating optimization (HBMO), greedy randomized adaptive search procedure (GRASP) and expanding neighborhood search strategy (ENS) is proposed for the solution of the probabilistic

Yannis Marinakis; Magdalene Marinaki

2009-01-01

310

Large scale hydrothermal optimal power flow problems based on interior point nonlinear programming  

Microsoft Academic Search

This paper presents an interior point algorithm for hydrothermal optimal power flow problems (HTOPF) which is derived from the perturbed KKT conditions of the primal problem. Moreover, the algorithm is extended successfully to solve approximate HTOPF problems (A-HTOPF) to find a suboptimal solution with much less execution time. For large scale systems, A-HTOPF can reduce CPU time by half and

Hau Wei; Hiroshi Sasaki; Junji Kubokawa; Ryuichi Yokoyama

2000-01-01

311

A steady-state solution for the optimal pavement resurfacing problem  

Microsoft Academic Search

This paper presents a solution approach for the problem of optimising the frequency and intensity of pavement resurfacing, under steady-state conditions. If the pavement deterioration and improvement models are deterministic and follow the Markov property, it is possible to develop a simple but exact solution method. This method removes the need to solve the problem as an optimal control problem,

Yuwei Li; Samer Madanat

2002-01-01

312

A comparison of optimization-based approaches for solving the aerodynamic design problem  

NASA Technical Reports Server (NTRS)

Three optimization-based methods for solving aerodynamic design problems are compared. The Euler equations for one-dimensional duct flow was used as a model problem, and the three methods are compared for efficiency, robustness, and implementation difficulty. The smoothness of the design problem with respect to different shock-capturing finite difference schemes, and in the presence of grid refinement, is investigated.

Frank, Paul D.; Shubin, Gregory R.

1990-01-01

313

6.893 Approximability of Optimization Problems October 4, 1999 Lecturer: Madhu Sudan Scribe: Leonid Reyzin  

E-print Network

6.893 Approximability of Optimization Problems October 4, 1999 Lecture 8 Lecturer: Madhu Sudan to decision problems are ``verification gap problems.'' For example, define GapSAT g as follows: YES = f(c 1 ; : : : ; c m ; k)j9 assignment satisfying at least k clauses g and NO = f(c 1 ; : : : ; c m ; k)j8

Goldwasser, Shafi

314

Computing Large Sparse Multivariate Optimization Problems with an Application in Biophysics  

E-print Network

Computing Large Sparse Multivariate Optimization Problems with an Application in Biophysics for the analysis of a biophysics problem, which is representative for a large class of problems in the physical, chosen from the field of biophysics, is analytical ultracentrifugation (AUC) [1, 2, 3]. AUC is a powerful

Boppana, Rajendra V.

315

Reducing computation time in DFP (Davidon, Fletcher & Powell) update method for solving unconstrained optimization problems  

NASA Astrophysics Data System (ADS)

Solving the unconstrained optimization problems is not easy and DFP update method is one of the methods that we can work with to solve the problems. In unconstrained optimization, the time computing needed by the method's algorithm to solve the problems is very vital and because of that, we proposed a hybrid search direction for DFP update method in order to reduce the computation time needed for solving unconstrained optimization problems. Some convergence analysis and numerical results of the hybrid search direction were analyzed and the results showed that the proposed hybrid search direction strictly reduce the computation time needed by DFP update method and at the same time increase the method's efficiency which is sometimes fail for some complicated unconstrained optimization problems.

Sofi, A. Z. M.; Mamat, M.; Ibrahim, M. A. H.

2013-04-01

316

Convex Hull Algorithms  

NSDL National Science Digital Library

An applet that demonstrates some algorithms for computing the convex hull of points in three dimensions. See the points from different viewpoints; see how the Incremental algorithm constructs the hull, face by face; while it's playing, look at it from different directions; see how the gift-wrapping or divide-and-conquer algorithms construct the hull; look at animations of Delaunay triangulation algorithms.

Tim Lambert

317

Optimizing material properties of composite plates for sound transmission problem  

NASA Astrophysics Data System (ADS)

To calculate the specific transmission loss (TL) of a composite plate, the conjugate gradient optimization method is utilized to estimate and optimize material properties of the composite plate in this study. For an n-layer composite plate, a nonlinear dynamic stiffness matrix based on the thick plate theory is formulated. To avoid huge computational efforts due to the combination of different composite material plates, a transfer matrix approach is proposed to restrict the dynamic stiffness matrix of the composite plate to a 4×4 matrix. Moreover, the transfer matrix approach has also been used to simplify the complexity of the objective function gradient for the optimization method. Numerical simulations are performed to validate the present algorithm by comparing the TL of the optimal composite plate with that of the original plate. Small number of iterations required during convergence tests illustrates the efficiency of the optimization method. The results indicate that an excellent estimation for the composite plate can be obtained for the desired sound transmission.

Tsai, Yu-Ting; Pawar, S. J.; Huang, Jin H.

2015-01-01

318

Algorithms for discrete, non-linear and robust optimization problems with applications in scheduling and service operations  

E-print Network

This thesis presents efficient algorithms that give optimal or near-optimal solutions for problems with non-linear objective functions that arise in discrete, continuous and robust optimization. First, we present a general ...

Mittal, Shashi, Ph. D. Massachusetts Institute of Technology

2011-01-01

319

Algebraic Optimization: The Fermat-Weber Location Problem  

Microsoft Academic Search

The Fermat-Weber location problem is to find a point in Rn that minimizes the sum of the (weighted) Euclidean distances fromm given points in Rn. In this work we discuss some relevant complexity and algorithmic issues. First, using Tarski's theory on solvability over real closed fields we argue that there is an infinite scheme to solve the problem, where the

R. Chandrasekaran; Arie Tamir

1990-01-01

320

Nonlinear switched capacitor `neural' networks for optimization problems  

Microsoft Academic Search

A systematic approach is presented for the design of analog neural nonlinear programming solvers using switched-capacitor (SC) integrated circuit techniques. The method is based on formulating a dynamic gradient system whose state evolves in time toward the solution point of the corresponding programming problem. A neuron cell for the linear and the quadratic problem suitable for monolithic implementation is introduced.

A. Rodriguez-Vazquez; R. Dominguez-Castro; A. Rueda; J. L. Huertas; E. Sanchez-Sinencio

1990-01-01

321

Hybrid genetic algorithm for optimization problems with permutation property  

Microsoft Academic Search

Permutation property has been recognized as a common but challenging feature in combinatorial problems. Because of their complexity, recent research has turned to genetic algorithms to address such problems. Although genetic algorithms have been proven to facilitate the entire space search, they lack in fine-tuning capability for obtaining the global optimum. Therefore, in this study a hybrid genetic algorithm was

Hsiao-fan Wang; Kuang-yao Wu

2004-01-01

322

A Finite Horizon Optimal Multiple Switching Problem Boualem Djehiche,  

E-print Network

, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem and solved using probabilistic tools to questions related to the structural profitability of an investment project or an industry whose production

Di Girolami, Cristina

323

Adding Multiple Cost Constraints to Combinatorial Optimization Problems,  

E-print Network

to Multicommodity Flows David Karger \\Lambda Serge Plotkin y Abstract Minimum cost multicommodity flow is an instance of a simpler problem (multicommodity flow) to which a cost constraint has been added algorithm for approximately solving the minimum­ cost multicommodity flow problem. Our algorithm finds a (1

324

Finite dimensional approximation of a class of constrained nonlinear optimal control problems  

NASA Technical Reports Server (NTRS)

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Gunzburger, Max D.; Hou, L. S.

1994-01-01

325

Hybrid functions approach for nonlinear constrained optimal control problems  

NASA Astrophysics Data System (ADS)

In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrix of integration is introduced. This matrix is then utilized to reduce the solution of the nonlinear constrained optimal control to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Mashayekhi, S.; Ordokhani, Y.; Razzaghi, M.

2012-04-01

326

Solution of transient optimization problems by using an algorithm based on nonlinear programming  

NASA Technical Reports Server (NTRS)

An algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.

Teren, F.

1977-01-01

327

Computational and statistical tradeoffs via convex relaxation  

PubMed Central

Modern massive datasets create a fundamental problem at the intersection of the computational and statistical sciences: how to provide guarantees on the quality of statistical inference given bounds on computational resources, such as time or space. Our approach to this problem is to define a notion of “algorithmic weakening,” in which a hierarchy of algorithms is ordered by both computational efficiency and statistical efficiency, allowing the growing strength of the data at scale to be traded off against the need for sophisticated processing. We illustrate this approach in the setting of denoising problems, using convex relaxation as the core inferential tool. Hierarchies of convex relaxations have been widely used in theoretical computer science to yield tractable approximation algorithms to many computationally intractable tasks. In the current paper, we show how to endow such hierarchies with a statistical characterization and thereby obtain concrete tradeoffs relating algorithmic runtime to amount of data. PMID:23479655

Chandrasekaran, Venkat; Jordan, Michael I.

2013-01-01

328

Computational and statistical tradeoffs via convex relaxation.  

PubMed

Modern massive datasets create a fundamental problem at the intersection of the computational and statistical sciences: how to provide guarantees on the quality of statistical inference given bounds on computational resources, such as time or space. Our approach to this problem is to define a notion of "algorithmic weakening," in which a hierarchy of algorithms is ordered by both computational efficiency and statistical efficiency, allowing the growing strength of the data at scale to be traded off against the need for sophisticated processing. We illustrate this approach in the setting of denoising problems, using convex relaxation as the core inferential tool. Hierarchies of convex relaxations have been widely used in theoretical computer science to yield tractable approximation algorithms to many computationally intractable tasks. In the current paper, we show how to endow such hierarchies with a statistical characterization and thereby obtain concrete tradeoffs relating algorithmic runtime to amount of data. PMID:23479655

Chandrasekaran, Venkat; Jordan, Michael I

2013-03-26

329

A BARRIER ALGORITHM FOR LARGE NONLINEAR OPTIMIZATION PROBLEMS  

E-print Network

to the scientific computing and computational mathematics program and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy in scientific's upbeat attitude and depth of knowledge of optimization was the backbone that made this thesis possible. I

Stanford University

330

Global Optimization of MINLP Problems in Process Synthesis and Design  

Microsoft Academic Search

Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear BB, SMIN- BB, and the General structure Mixed Integer Nonlinear BB, GMIN- BB, are presented. Their theoretical foundations provide guarantees that the global optimum solution of MINLPs involving twice-differentiable nonconvex functions in the continuous variables can be identified. The conditions imposed on the functionality

C. S. Adjiman; I. P. Androulakis; C. A. Floudas

1997-01-01

331

Strategies for Solving High-Fidelity Aerodynamic Shape Optimization Problems  

E-print Network

) models used for evaluating aircraft performance. As the computational time for a given CFD model reduces proven to be particularly effective. This enables aircraft designers to shorten design cycle times calculation. There are several possible ways to reduce the overall optimization time. One way is to reduce

Papalambros, Panos

332

Problems of optimal choice on posets and generalizations of acyclic colourings  

E-print Network

Problems of optimal choice on posets and generalizations of acyclic colourings Bryn Garrod Department of Pure Mathematics and Mathematical Statistics Trinity College University of Cambridge This dissertation is submitted for the degree of Doctor...

Garrod, Bryn James

333

The Megawatt-Frequency Control Problem: A New Approach Via Optimal Control Theory  

Microsoft Academic Search

This paper records the development of a state variable model of the megawatt-frequency control problem of multiarea electric energy systems. The model is in a mathematical form necessary for application of theorems of modem optimal control theory.

CHARLES E. FOSHA; Olle Elgerd

1970-01-01

334

Application of Particle Swarm Optimization Algorithm in the Heating System Planning Problem  

PubMed Central

Based on the life cycle cost (LCC) approach, this paper presents an integral mathematical model and particle swarm optimization (PSO) algorithm for the heating system planning (HSP) problem. The proposed mathematical model minimizes the cost of heating system as the objective for a given life cycle time. For the particularity of HSP problem, the general particle swarm optimization algorithm was improved. An actual case study was calculated to check its feasibility in practical use. The results show that the improved particle swarm optimization (IPSO) algorithm can more preferably solve the HSP problem than PSO algorithm. Moreover, the results also present the potential to provide useful information when making decisions in the practical planning process. Therefore, it is believed that if this approach is applied correctly and in combination with other elements, it can become a powerful and effective optimization tool for HSP problem. PMID:23935429

Ma, Rong-Jiang; Yu, Nan-Yang; Hu, Jun-Yi

2013-01-01

335

Second-order analysis of optimal control problems with control and ...  

E-print Network

quadratic growth condition, for optimal control problems of ordinary differential equations with constraints on initial-final state, as well as control constraints satisfying the ..... to some integral of difference of Hamiltonian functions. For µ ? Rr? ...

2008-10-30

336

6.893 Approximability of Optimization Problems December 6, 1999 Lecturer: Madhu Sudan Scribe: Prahladh Harsha  

E-print Network

6.893 Approximability of Optimization Problems December 6, 1999 Lecture 24 Lecturer: Madhu Sudan the hardness of approximating Max­Sat and the c=s ratio for Clique, we shall employ MIP with 2 provers

Goldwasser, Shafi

337

Optimization technique for problems with an inequality constraint  

NASA Technical Reports Server (NTRS)

General technique uses a modified version of an existing technique termed the pattern search technique. New procedure called the parallel move strategy permits pattern search technique to be used with problems involving a constraint.

Russell, K. J.

1972-01-01

338

Optimal control for problems with a general variational inequality  

E-print Network

inequality is introduced 1988 b* *y Noor [16]. Such problems arise frequently for example in shape the following papers Ben-El-Mechaiekh and Isac [4], Xui, Zhang and Noor [21], X* *ui and Zhang [23] and Noor

339

Seismic Source Inversion As A Multiple-Objective Optimization Problem  

Microsoft Academic Search

Combining independent seismic observations helps produce better solutions to inverse problems. Successful examples include the combination of teleseismic and strong-motion seismograms with geodetic data to constrain fault rupture processes, and the joint inversion of surface-wave dispersion with receiver-function observations. In practice however, each observation brings a set of modeling assumptions and problems, such as sensitivity to un-modeled aspects of earth

C. J. Ammon

2002-01-01

340

Variational stability of optimal control problems involving subdifferential operators  

SciTech Connect

This paper is concerned with the problem of minimizing an integral functional with control-nonconvex integrand over the class of solutions of a control system in a Hilbert space subject to a control constraint given by a phase-dependent multivalued map with closed nonconvex values. The integrand, the subdifferential operators, the perturbation term, the initial conditions and the control constraint all depend on a parameter. Along with this problem, the paper considers the problem of minimizing an integral functional with control-convexified integrand over the class of solutions of the original system, but now subject to a convexified control constraint. By a solution of a control system we mean a 'trajectory-control' pair. For each value of the parameter, the convexified problem is shown to have a solution, which is the limit of a minimizing sequence of the original problem, and the minimal value of the functional with the convexified integrand is a continuous function of the parameter. This property is commonly referred to as the variational stability of a minimization problem. An example of a control parabolic system with hysteresis and diffusion effects is considered. Bibliography: 24 titles.

Tolstonogov, Aleksandr A [Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk (Russian Federation)

2011-04-30

341

Optimal spread spectrum watermark embedding via a multistep feasibility formulation.  

PubMed

We consider optimal formulations of spread spectrum watermark embedding where the common requirements of watermarking, such as perceptual closeness of the watermarked image to the cover and detectability of the watermark in the presence of noise and compression, are posed as constraints while one metric pertaining to these requirements is optimized. We propose an algorithmic framework for solving these optimal embedding problems via a multistep feasibility approach that combines projections onto convex sets (POCS) based feasibility watermarking with a bisection parameter search for determining the optimum value of the objective function and the optimum watermarked image. The framework is general and can handle optimal watermark embedding problems with convex and quasi-convex formulations of watermark requirements with assured convergence to the global optimum. The proposed scheme is a natural extension of set-theoretic watermark design and provides a link between convex feasibility and optimization formulations for watermark embedding. We demonstrate a number of optimal watermark embeddings in the proposed framework corresponding to maximal robustness to additive noise, maximal robustness to compression, minimal frequency weighted perceptual distortion, and minimal watermark texture visibility. Experimental results demonstrate that the framework is effective in optimizing the desired characteristic while meeting the constraints. The results also highlight both anticipated and unanticipated competition between the common requirements for watermark embedding. PMID:19131302

Altun, H Oktay; Orsdemir, Adem; Sharma, Gaurav; Bocko, Mark F

2009-02-01

342

ANTI-ANGIOGENIC THERAPY IN CANCER TREATMENT AS AN OPTIMAL CONTROL PROBLEM  

E-print Network

ANTI-ANGIOGENIC THERAPY IN CANCER TREATMENT AS AN OPTIMAL CONTROL PROBLEM URSZULA LEDZEWICZ AND HEINZ SCH¨ATTLER Abstract. Anti-angiogenic therapy is a novel treatment approach in cancer therapy. Key words. optimal control, geometric methods, cancer treatment, anti-angiogenic therapy AMS subject

Schaettler, Heinz

343

Optimization of Polling Systems and Dynamic Vehicle Routing Problems on Networks  

E-print Network

We consider the problem of optimizing a polling system, i.e., of optimally sequencing a server in a multi-class queueing system with switch-over times in order to minimize a linear objective function of the waiting times. ...

Bertsimas, Dimitris J.

344

The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots  

E-print Network

The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots of Minnesota Minneapolis, MN 55455 Email: {hjmin|npapas}@cs.umn.edu Abstract-- This work presents a novel multi-robot coverage scheme for an unknown number of robots; it focuses on optimizing the number of robots and each

Minnesota, University of

345

A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems  

Microsoft Academic Search

Several extensions to evolutionary algorithms (EAs) and particle swarm optimization (PSO) have been suggested during the last decades offering improved performance on selected benchmark problems. Recently, another search heuristic termed differential evolution (DE) has shown superior performance in several real-world applications. In this paper, we evaluate the performance of DE, PSO, and EAs regarding their general applicability as numerical optimization

J. Vesterstrom; R. Thomsen

2004-01-01

346

UFO: Uncertainty Feature Optimization, an Implicit Paradigm for Problems with Noisy Data  

Microsoft Academic Search

Optimization problems due to noisy data are usually solved using stochastic programming or robust optimization approaches. Both requiring the explicit characterization of an uncertainty set that models the nature of the noise. Such approaches tightly depend on the modeling of the uncertainty set. In this paper, we introduce a framework that implicitly models the uncertain data. We define the general

Niklaus Eggenberg; Matteo Salani; Michel Bierlaire

2008-01-01

347

NUMERICAL SOLUTION OF HYBRID OPTIMAL CONTROL PROBLEMS WITH APPLICATIONS IN ROBOTICS  

E-print Network

. Two solution techniques for obtaining suboptimal solutions are presented (both based on numerical: Hybrid optimal control, mechatronics, underactuated robots. 1. INTRODUCTION Solutions to nonlinear optimal control problems play a key role in modern mechatronics and robotics and particularly in the area

Stryk, Oskar von

348

Generate Pareto optimal solutions of scheduling problems using normal boundary intersection technique  

Microsoft Academic Search

The problem of short-term scheduling under uncertainty is addressed in this paper through a multiobjective optimization framework that incorporates economic expectation, robustness, and flexibility in terms of demand satisfaction. In order to be able to identify Pareto optimal solutions, a new approach is applied which is based on normal boundary intersection (NBI) technique. The main advantage of this technique is

Zhenya Jia; Marianthi G. Ierapetritou

2007-01-01

349

Edinburgh Research Explorer Local solutions of the optimal power flow problem  

E-print Network

local optimization techniques are shown to converge to these local optima if started close enough in power systems. This problem was first introduced by Carpentier [1] in 1962. The objective of OPF optimization techniques as applied to OPF over the last 30 years is given in [3], [4]. None of these methods

Millar, Andrew J.

350

Optimal anisotropic three-phase conducting composites: Plane problem  

E-print Network

The paper establishes tight lower bound for effective conductivity tensor $K_*$ of two-dimensional three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed that three materials are mixed with fixed volume fractions and that the conductivity of one of the materials is infinite. The bound expands the Hashin-Shtrikman and Translation bounds to multiphase structures, it is derived using the technique of {\\em localized polyconvexity} that is a combination of Translation method and additional inequalities on the fields in the materials; similar technique was used by Nesi (1995) and Cherkaev (2009) for isotropic multiphase composites. This paper expands the bounds to the anisotropic composites. The lower bound of conductivity (G-closure) is a piece-wise analytic function of eigenvalues of $K_*$, that depends only on conductivities of components and their volume fractions. Also, we find optimal microstructures that realize the bounds, developing the technique suggested earlier by Albin Cherkaev and Nesi (2007) and Cherkaev (2009). The optimal microstructures are laminates of some rank for all regions. The found structures match the bounds in all but one region of parameters; we discuss the reason for the gap and numerically estimate it.

Andrej Cherkaev; and Yuan Zhang

2010-09-15

351

Evaluation of Genetic Algorithm Concepts using Model Problems. Part 1; Single-Objective Optimization  

NASA Technical Reports Server (NTRS)

A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.

Holst, Terry L.; Pulliam, Thomas H.

2003-01-01

352

Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System  

E-print Network

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order. We establish a first global theory of existence and regularity for this shock diffraction problem. In particular, we establish that the optimal regularity for the solution is $C^{0,1}$ across the degenerate sonic boundary. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.

Gui-Qiang G. Chen; Xuemei Deng; Wei Xiang

2012-02-04

353

Evaluation of Genetic Algorithm Concepts Using Model Problems. Part 2; Multi-Objective Optimization  

NASA Technical Reports Server (NTRS)

A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.

Holst, Terry L.; Pulliam, Thomas H.

2003-01-01

354

A DECOMPOSITION ALGORITHM FOR NESTED RESOURCE ALLOCATION PROBLEMS  

E-print Network

, portfolio selection, energy optimization, sample allocation in stratified sampling, capital budgeting, mass continuous or integer variables. No assumption of strict convexity or differentiability is needed. The method method achieves a higher performance than previous algorithms, addressing all problems with up to one

Jaillet, Patrick

355

Solving fractional packing problems in O ast (1\\/?) iterations  

Microsoft Academic Search

We adapt a method proposed by Nesterov [16] to design an algorithm that computes ?-optimal solutions to fractional packing problems by solving O*(?-1 ?Kn) separable convex quadratic programs, where K is the maximum number of non-zeros per row and n is the number of variables. We also show that the quadratic program can be approximated to any degree of accuracy

Daniel Bienstock; Garud Iyengar

2004-01-01

356

Automated Knowledge Elicitation and Flowchart Optimization for Problem Diagnosis  

Microsoft Academic Search

The established procedure for problem diag- nosis in a wide variety of systems is often em- bodied in a ?owchart or decision tree. These procedures are usually authored manually, which is extremely expensive and results in ?owcharts that are di-cult to maintain and often quite ine-cient. A better diagnostic procedure would be one that automatically modifles itself in response to

Alina Beygelzimer; Mark Brodie; Jonathan Lenchner; Irina Rish

357

New numerical methods for open-loop and feedback solutions to dynamic optimization problems  

NASA Astrophysics Data System (ADS)

The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.

Ghosh, Pradipto

358

Study on Parameter Optimization for Support Vector Regression in Solving the Inverse ECG Problem  

PubMed Central

The typical inverse ECG problem is to noninvasively reconstruct the transmembrane potentials (TMPs) from body surface potentials (BSPs). In the study, the inverse ECG problem can be treated as a regression problem with multi-inputs (body surface potentials) and multi-outputs (transmembrane potentials), which can be solved by the support vector regression (SVR) method. In order to obtain an effective SVR model with optimal regression accuracy and generalization performance, the hyperparameters of SVR must be set carefully. Three different optimization methods, that is, genetic algorithm (GA), differential evolution (DE) algorithm, and particle swarm optimization (PSO), are proposed to determine optimal hyperparameters of the SVR model. In this paper, we attempt to investigate which one is the most effective way in reconstructing the cardiac TMPs from BSPs, and a full comparison of their performances is also provided. The experimental results show that these three optimization methods are well performed in finding the proper parameters of SVR and can yield good generalization performance in solving the inverse ECG problem. Moreover, compared with DE and GA, PSO algorithm is more efficient in parameters optimization and performs better in solving the inverse ECG problem, leading to a more accurate reconstruction of the TMPs. PMID:23983808

Jiang, Mingfeng; Jiang, Shanshan; Zhu, Lingyan; Wang, Yaming; Huang, Wenqing; Zhang, Heng

2013-01-01

359

A Domain Decomposition Method for the Helmholtz Equation and Related Optimal Control Problems  

Microsoft Academic Search

We present an iterative domain decomposition method to solve the Helmholtz equation and related optimal control problems. The proof of convergence of this method relies on energy techniques. This method leads to efficient algorithms for the numerical resolution of harmonic wave propagation problems in homogeneous and heterogeneous media.

Jean-David Benamou; Bruno Desprès

1997-01-01

360

The Finite Horizon Optimal Multi-Modes Switching Problem: The Viscosity Solution Approach  

SciTech Connect

In this paper we show existence and uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is in relation with the valuation of firms in a financial market.

El Asri, Brahim, E-mail: brahim.el_Asri@univ-lemans.fr; Hamadene, Said [Universite du Maine, Dept. de Mathematiques, Equipe Stat. et Processus (France)], E-mail: hamadene@univ-lemans.fr

2009-10-15

361

A well-posed optimal spectral element approximation for the Stokes problem  

NASA Technical Reports Server (NTRS)

A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.

Maday, Y.; Patera, A. T.; Ronquist, E. M.

1987-01-01

362

An Ant Colony Optimization Algorithm for the 2D HP Protein Folding Problem  

E-print Network

An Ant Colony Optimization Algorithm for the 2D HP Protein Folding Problem Alena Shmygelska, Rosal, the two dimensional hydrophobic-polar (2D HP) protein folding problem. We introduce an ant colony algorithm closely approaches that of specialised, state-of-the methods for 2D HP protein folding. 1

Hoos, Holger H.

363

Optimizing for Transfers in a Multi-Vehicle Collection and Delivery Problem  

E-print Network

Optimizing for Transfers in a Multi-Vehicle Collection and Delivery Problem Brian Coltin and Manuela Veloso Abstract We address the Collection and Delivery Problem (CDP) with multiple ve- hicles, such that each collects a set of items at different locations and delivers them to a dropoff point. The goal

Veloso, Manuela M.

364

The Proportional Coloring Problem: Optimizing Buffers in Radio Mesh Networks 1  

E-print Network

The Proportional Coloring Problem: Optimizing Buffers in Radio Mesh Networks 1 Florian Huc 2 problem to model call scheduling op- timization issues in wireless mesh networks: the proportional a proportional coloring is pseudo-polynomial while de- termining its proportional chromatic index is NP-hard. We

Paris-Sud XI, Université de

365

Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control Problems  

E-print Network

Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control, 2007 Abstract In this paper, we consider numerous inventory control problems for which the base. In this paper, we analyze stochastic approximation methods for several inventory control problems for which

Topaloglu, Huseyin

366

Contribution to optimal flow in networks. A experimental multiprocessor for asynchronous iteration implementation  

NASA Astrophysics Data System (ADS)

The problem of optimal flow determination is considered in relation with packet-switched communication networks. For linear cost problems, a unifying presentation of classical methods is done, enabling graphic interpretations. For convex cost, a dual approach which incorporates an iteration control mechanism and stopping test based on a comparison between the dual function and the associated primal cost is derived. An extension to optimal multicommodity network flow problems is proposed. Parallelism and asynchronous iterations are also discussed.

Authie, Gerard

1987-12-01

367

An Improved Lagrangian Relaxation Method for VLSI Combinational Circuit Optimization  

E-print Network

-objectives and proven to reach optimal solution under continuous solution space. However, it is more complex to use Lagrangian relaxation under discrete solution space. The Lagrangian dual problem is non-convex and previously a sub-gradient method was used to solve it...

Huang, Yi-Le

2012-02-14

368

OPTIMAL MAGNETIC SHIELD DESIGN WITH SECOND-ORDER CONE PROGRAMMING  

E-print Network

of the MAGLEV train, a new bullet train under development in Japan, is formulated as the continuous convex words. second-order cone programming, interior-point methods, magnetic shielding, MAGLEV train, optimal as similar problems with different linear equality constraints [15]. The bullet train, which is called MAGLEV

Tsuchiya, Takashi

369

SOME OPTIMIZATION PROBLEMS FOR p-LAPLACIAN TYPE LEANDRO M. DEL PEZZO AND JULIAN FERNANDEZ BONDER  

E-print Network

is the (unique) solution to the nonlinear membrane problem with load f (1.1) -pu + |u|p-2 u = 0 in , | u|p-2 u´ANDEZ BONDER Abstract. In this paper we study some optimization problems for nonlinear elastic membranes. More admissible class of loads f where u is the (unique) solution to the problem -pu + |u|p-2u = 0 in with | u

Bonder, Julián Fernández

370

Exact solution of multicommodity network optimization problems with general step cost functions  

Microsoft Academic Search

We describe an exact solution procedure, based on the use of standard LP software, for multicommodity network optimization problems with general discontinuous step-increasing cost functions. This class of problems includes the so-called single-facility and multiple-facility capacitated network loading problems as special cases. The proposed procedure may be viewed as a specialization of the well-known BENDERS partitioning procedure, leading to iteratively

Virginie Gabrel; Arnaud Knippel; Michel Minoux

1999-01-01

371

An Interactive Satisficing Method Based on Level Set Optimization for Fuzzy Random Multiobjective Linear Programming Problems  

NASA Astrophysics Data System (ADS)

This paper focuses on multiobjective linear programming problems involving fuzzy random variable coefficients. A new decision making model and Pareto optimal solution concept are proposed using ?-level cuts of membership function. It is shown that the problem including both randomness and fuzziness is equivalently transformed into a deterministic problem. An interactive algorithm is proposed in order to obtain a satisficing solution for a decision maker through interaction.

Katagiri, Hideki; Sakawa, Masatoshi; Kato, Kosuke; Nishizaki, Ichiro

2009-01-01

372

First and Second-Order Approximations as Derivatives of Mappings in Optimality Conditions for Nonsmooth Vector Optimization  

SciTech Connect

First and second-order approximations are used to establish both necessary and sufficient optimality conditions for local weak efficiency and local firm efficiency in nonsmooth set-constrained vector problems. Even continuity and relaxed convexity assumptions are not imposed. Compactness conditions are also relaxed. Examples are provided to show advantages of the presented results over recent existing ones.

Phan Quoc Khanh [International University of Hochiminh City, Department of Mathematics (Viet Nam)], E-mail: pqkhanh@hcmiu.edu.vn; Nguyen Dinh Tuan [University of Natural Sciences of Hochiminh City, Department of Mathematics (Viet Nam)], E-mail: ndtuan73@yahoo.com

2008-10-15

373

Optimizing Constrained Single Period Problem under Random Fuzzy Demand  

NASA Astrophysics Data System (ADS)

In this paper, we consider the multi-product multi-constraint newsboy problem with random fuzzy demands and total discount. The demand of the products is often stochastic in the real word but the estimation of the parameters of distribution function may be done by fuzzy manner. So an appropriate option to modeling the demand of products is using the random fuzzy variable. The objective function of proposed model is to maximize the expected profit of newsboy. We consider the constraints such as warehouse space and restriction on quantity order for products, and restriction on budget. We also consider the batch size for products order. Finally we introduce a random fuzzy multi-product multi-constraint newsboy problem (RFM-PM-CNP) and it is changed to a multi-objective mixed integer nonlinear programming model. Furthermore, a hybrid intelligent algorithm based on genetic algorithm, Pareto and TOPSIS is presented for the developed model. Finally an illustrative example is presented to show the performance of the developed model and algorithm.

Taleizadeh, Ata Allah; Shavandi, Hassan; Riazi, Afshin

2008-09-01

374

A novel algorithm for solving optimal path planning problems based on parametrization method and fuzzy aggregation  

NASA Astrophysics Data System (ADS)

In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. In this approach the path planning problems have some incompatible objectives such as the length of path that must be minimized, the distance between the path and obstacles that must be maximized and etc., then a multi-objective dynamic optimization problem (MODOP) is achieved. Considering the imprecise nature of decision maker's (DM) judgment, these multiple objectives are viewed as fuzzy variables. By determining intervals for the values of these fuzzy variables, flexible monotonic decreasing or increasing membership functions are determined as the degrees of satisfaction of these fuzzy variables on their intervals. Then, the optimal path planning policy is searched by maximizing the aggregated fuzzy decision values, resulting in a fuzzy multi-objective dynamic optimization problem (FMODOP). Using a suitable t-norm, the FMODOP is converted into a non-linear dynamic optimization problem (NLDOP). By using parametrization method and some calculations, the NLDOP is converted into the sequence of conventional non-linear programming problems (NLPP). It is proved that the solution of this sequence of the NLPPs tends to a Pareto optimal solution which, among other Pareto optimal solutions, has the best satisfaction of DM for the MODOP. Finally, the above procedure as a novel algorithm integrating parametrization method and fuzzy aggregation to solve the MODOP is proposed. Efficiency of our approach is confirmed by some numerical examples.

Zamirian, M.; Kamyad, A. V.; Farahi, M. H.

2009-09-01

375

Permutations Defining Convex Permutominoes  

NASA Astrophysics Data System (ADS)

A permutomino of size n is a polyomino determined by particular pairs (n_1,n_1) of permutations of size n, such that n_1(i) <> n_2i) for 1<=iconvex permutominoes. Using such a characterization, these permutations can be uniquely represented in terms of the so-called square permutations, introduced by Mansour and Severini. We provide a closed formula for the number of these permutations with size n.

Bernini, Antonio; Disanto, Filippo; Pinzani, Renzo; Rinaldi, Simone

2007-09-01

376

A New Evolutionary Search Strategy for Global Optimization of High-Dimensional Problems  

NASA Astrophysics Data System (ADS)

Global optimization of high-dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation. The weakness of randomization-based evolutionary algorithms in searching high-dimensional spaces is demonstrated in this paper. A new strategy, SCPCA (Shuffled Complex evolution with Principal Component Analysis), is developed to treat complexity caused by high dimensionalities. This strategy features a slope-based searching kernel and a scheme of maintaining the particle population’s capability of searching over the full search space. Examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that SCPCA surpasses two popular algorithms, Particle Swarm Optimizer (PSO) and Differential Evolution (DE), on high-dimensional problems. Experimental results also corroborate the argument that, in high-dimensional optimization, only problems with well-formative fitness landscapes are solvable, and slope-based schemes are preferable to randomization-based ones.

Chu, W.; Gao, X.; Sorooshian, S.

2010-12-01

377

Vortex generator design for aircraft inlet distortion as a numerical optimization problem  

NASA Technical Reports Server (NTRS)

Aerodynamic compatibility of aircraft/inlet/engine systems is a difficult design problem for aircraft that must operate in many different flight regimes. Takeoff, subsonic cruise, supersonic cruise, transonic maneuvering, and high altitude loiter each place different constraints on inlet design. Vortex generators, small wing like sections mounted on the inside surfaces of the inlet duct, are used to control flow separation and engine face distortion. The design of vortex generator installations in an inlet is defined as a problem addressable by numerical optimization techniques. A performance parameter is suggested to account for both inlet distortion and total pressure loss at a series of design flight conditions. The resulting optimization problem is difficult since some of the design parameters take on integer values. If numerical procedures could be used to reduce multimillion dollar development test programs to a small set of verification tests, numerical optimization could have a significant impact on both cost and elapsed time to design new aircraft.

Anderson, Bernhard H.; Levy, Ralph

1991-01-01

378

Using the PORS Problems to Examine Evolutionary Optimization of Multiscale Systems  

SciTech Connect

Nearly all systems of practical interest are composed of parts assembled across multiple scales. For example, an agrodynamic system is composed of flora and fauna on one scale; soil types, slope, and water runoff on another scale; and management practice and yield on another scale. Or consider an advanced coal-fired power plant: combustion and pollutant formation occurs on one scale, the plant components on another scale, and the overall performance of the power system is measured on another. In spite of this, there are few practical tools for the optimization of multiscale systems. This paper examines multiscale optimization of systems composed of discrete elements using the plus-one-recall-store (PORS) problem as a test case or study problem for multiscale systems. From this study, it is found that by recognizing the constraints and patterns present in discrete multiscale systems, the solution time can be significantly reduced and much more complex problems can be optimized.

Reinhart, Zachary [Ames Laboratory; Molian, Vaelan [Ames Laboratory; Bryden, Kenneth [Ames Laboratory

2013-01-01

379

Implementation and comparison of PSO-based algorithms for multi-modal optimization problems  

NASA Astrophysics Data System (ADS)

This paper aims to compare the global search capability and overall performance of a number of Particle Swarm Optimization (PSO) based algorithms in the context solving the Dynamic Economic Dispatch (DED) problem which takes into account the operation limitations of generation units such as valve-point loading effect as well as ramp rate limits. The comparative study uses six PSO-based algorithms including the basic PSO and hybrid PSO algorithms using a popular benchmark test IEEE power system which is 10-unit 24-hour system with non-smooth cost functions. The experimental results show that one of the hybrid algorithms that combines the PSO with both inertia weight and constriction factor, and the Gaussian mutation operator (CBPSO-GM) is promising in achieving the near global optimal of a non-linear multi-modal optimization problem, such as the DED problem under the consideration.

Sriyanyong, Pichet; Lu, Haiyan

2013-10-01

380

Solution of the boundary value problem for optimal escape in continuous stochastic systems and maps  

NASA Astrophysics Data System (ADS)

Topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps. A topological method is introduced that simplifies the solution of boundary value problems: The activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path. The method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps.

Beri, S.; Mannella, R.; Luchinsky, D. G.; Silchenko, A. N.; McClintock, P. V. E.

2005-09-01

381

Solution of a Sub-Riemannian Optimal Control Problem for a Quantum Spin System  

Microsoft Academic Search

Experiments in nuclear magnetic resonance (NMR) spectroscopy and NMR quantum computing require control of ensembles of quantum mechanical systems. The controlled transfer of coherence along a one-dimensional chain of spin systems plays a key role in NMR spectroscopy of proteins, and spin chains have also been proposed for NMR quantum information processing. The problem of time-optimal or energy-optimal control of

Amit K. Sanyal; Christopher Moseley; Anthony Bloch

382

Particle Swarm Optimization and Fitness Sharing to solve Multi-Objective Optimization Problems  

E-print Network

in the way birds travel when trying to find sources of food, or similarly the way a fish school will behave.e.rowe@cs.bham.ac.uk Abstract- The particle swarm optimization algorithm has been shown to be a competitive heuristic to solve developed by Kennedy and Eberhart [14], is basically inspired by bird flocking. The main idea is based

Coello, Carlos A. Coello

383

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression  

NASA Technical Reports Server (NTRS)

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

384

An approximation for the boundary optimal control problem of a heat equation defined in a variable domain  

NASA Astrophysics Data System (ADS)

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of the boundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming (SQP) algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.

Yu, Xin; Ren, Zhi-Gang; Xu, Chao

2014-04-01

385

The fuzzy clearing approach for a niching genetic algorithm applied to a nuclear reactor core design optimization problem  

Microsoft Academic Search

This article extends previous efforts on genetic algorithms (GAs) applied to a core design optimization problem. We introduce the application of a new Niching Genetic Algorithm (NGA) to this problem and compare its performance to these previous works. The optimization problem consists in adjusting several reactor cell parameters, such as dimensions, enrichment and materials, in order to minimize the average

Wagner F. Sacco; Marcelo D. Machado; Cláudio M. N. A. Pereira; Roberto Schirru

2004-01-01

386

Solving complex maintenance planning optimization problems using stochastic simulation and multi-criteria fuzzy decision making  

NASA Astrophysics Data System (ADS)

One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms of a suggested framework model based on discrete event simulation.

Tahvili, Sahar; Österberg, Jonas; Silvestrov, Sergei; Biteus, Jonas

2014-12-01

387

Solving optimization problem of space factor of multiple CPV trackers using "butterfly approach"  

NASA Astrophysics Data System (ADS)

Optimization of land use to multi-tracker CPV system is discussed by mathematical approach. Optimization problem using butterfly plot (Contour plot on the shading to adjacent tracker) is discussed to seek optimum allocation pattern. With initial solutions given by this optimum allocation pattern, numerical optimization calculation is done to obtain the optimum allocation including, skew angle to the North-South axis, aspect ratio between X and Y pitch and optimum panel aspect ratio. It is suggested that there are two candidate of optimum allocation pattern.

Araki, Kenji

2014-09-01

388

Solution to Electric Power Dispatch Problem Using Fuzzy Particle Swarm Optimization Algorithm  

NASA Astrophysics Data System (ADS)

This paper presents the application of fuzzy particle swarm optimization to constrained economic load dispatch (ELD) problem of thermal units. Several factors such as quadratic cost functions with valve point loading, ramp rate limits and prohibited operating zone are considered in the computation models. The Fuzzy particle swarm optimization (FPSO) provides a new mechanism to avoid premature convergence problem. The performance of proposed algorithm is evaluated on four test systems. Results obtained by proposed method have been compared with those obtained by PSO method and literature results. The experimental results show that proposed FPSO method is capable of obtaining minimum fuel costs in fewer numbers of iterations.

Chaturvedi, D. K.; Kumar, S.

2014-07-01

389

Study on Two Optimization Problems: Line Cover and Maximum Genus Embedding  

E-print Network

STUDY ON TWO OPTIMIZATION PROBLEMS: LINE COVER AND MAXIMUM GENUS EMBEDDING A Thesis by CHENG CAO Submitted to the O ce of Graduate Studies of Texas A&M University in partial ful llment of the requirements for the degree of MASTER OF SCIENCE... May 2012 Major Subject: Computer Science STUDY ON TWO OPTIMIZATION PROBLEMS: LINE COVER AND MAXIMUM GENUS EMBEDDING A Thesis by CHENG CAO Submitted to the O ce of Graduate Studies of Texas A&M University in partial ful llment...

Cao, Cheng

2012-07-16

390

Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints  

NASA Technical Reports Server (NTRS)

The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous design history, is tested in this paper on optimization problems with frequency constraints. The aim of the research is to verify the robustness and speed of convergence of the two point exponential approximation method when highly non-linear constraints are used.

Fadel, G. M.

1991-01-01

391

A comparison of optimization software for mesh shape-quality improvement problems.  

SciTech Connect

Simplicial mesh shape-quality can be improved by optimizing an objective function based on tetrahedral shape measures. If the objective function is formulated in terms of all elements in a given mesh rather than a local patch, one is confronted with a large-scale, nonlinear, constrained numerical optimization problem. We investigate the use of six general-purpose state-of-the-art solvers and two custom-developed methods to solve the resulting large-scale problem. The performance of each method is evaluated in terms of robustness, time to solution, convergence properties, and scalability on several two- and three-dimensional test cases.

Freitag, L.; Knupp, P.; Munson, T.; Shontz, S.

2002-08-19

392

Lipschitzian Regularity of Minimizers for Optimal Control Problems with Control-Affine Dynamics  

SciTech Connect

We study the Lagrange Problem of Optimal Control with a functional {integral}{sub a}{sup b}L(t,x(t),u(t)) dt and control-affine dynamics x-dot= f(t,x) + g(t,x)u and (a priori) unconstrained control u element of bf R{sup m}. We obtain conditions under which the minimizing controls of the problem are bounded-a fact which is crucial for the applicability of many necessary optimality conditions, like, for example, the Pontryagin Maximum Principle. As a corollary we obtain conditions for the Lipschitzian regularity of minimizers of the Basic Problem of the Calculus of Variations and of the Problem of the Calculus of Variations with higher-order derivatives.

Sarychev, A. V.; Torres, D. F. M. [Department of Mathematics, University of Aveiro, 3810 Aveiro (Portugal)], E-mail: ansar@mat.ua.pt; delfim@mat.ua.pt

2000-03-15

393

Using a modified invasive weed optimization algorithm for a personalized urban multi-criteria path optimization problem  

NASA Astrophysics Data System (ADS)

The personalized urban multi-criteria quasi-optimum path problem (PUMQPP) is a branch of multi-criteria shortest path problems (MSPPs) and it is classified as a NP-hard problem. To solve the PUMQPP, by considering dependent criteria in route selection, there is a need for approaches that achieve the best compromise of possible solutions/routes. Recently, invasive weed optimization (IWO) algorithm is introduced and used as a novel algorithm to solve many continuous optimization problems. In this study, the modified algorithm of IWO was designed, implemented, evaluated, and compared with the genetic algorithm (GA) to solve the PUMQPP in a directed urban transportation network. In comparison with the GA, the results have shown the significant superiority of the proposed modified IWO algorithm in exploring a discrete search-space of the urban transportation network. In this regard, the proposed modified IWO algorithm has reached better results in fitness function, quality metric and running-time values in comparison with those of the GA.

Pahlavani, Parham; Delavar, Mahmoud R.; Frank, Andrew U.

2012-08-01

394

Optimizing Constrained Mixed-Integer Nonlinear Programming Problems Using Nature Selection  

Microsoft Academic Search

Many practical engineering optimization problems involving real and integer\\/discrete design variables have been drawing much more attention from researchers. In this paper, an effective adaptive real-parameter simulated annealing genetic algorithm (ARSAGA) was proposed, applied to cope with constrained mixed-integer nonlinear programming problems. The performances of this proposed algorithm, including reliability and convergence speed are demonstrated by examples. It is noted

Rong-Song He

2009-01-01

395

Study of hybrid methods for approximating the Edgeworth-Pareto hull in nonlinear multicriteria optimization problems  

NASA Astrophysics Data System (ADS)

Methods for approximating the Edgeworth-Pareto hull (EPH) of the set of feasible criteria vectors in nonlinear multicriteria optimization problems are examined. The relative efficiency of two EPH approximation methods based on classical methods of searching for local extrema of convolutions of criteria is experimentally studied for a large-scale applied problem (with several hundred variables). A hybrid EPH approximation method combining classical and genetic approximation methods is considered.

Berezkin, V. E.; Lotov, A. V.; Lotova, E. A.

2014-06-01

396

A methodology to find the elementary landscape decomposition of combinatorial optimization problems.  

PubMed

A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of multiple elementary landscapes if the underlying neighborhood used is symmetric. This paper presents theoretical results that provide the foundation for algebraic methods that can be used to decompose the objective function of an arbitrary combinatorial optimization problem into a sum of subfunctions, where each subfunction is an elementary landscape. Many steps of this process can be automated, and indeed a software tool could be developed that assists the researcher in finding a landscape decomposition. This methodology is then used to show that the subset sum problem is a superposition of two elementary landscapes, and to show that the quadratic assignment problem is a superposition of three elementary landscapes. PMID:21469972

Chicano, Francisco; Whitley, L Darrell; Alba, Enrique

2011-01-01

397

Firefly algorithm for cardinality constrained mean-variance portfolio optimization problem with entropy diversity constraint.  

PubMed

Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results. PMID:24991645

Bacanin, Nebojsa; Tuba, Milan

2014-01-01

398

Firefly Algorithm for Cardinality Constrained Mean-Variance Portfolio Optimization Problem with Entropy Diversity Constraint  

PubMed Central

Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results. PMID:24991645

2014-01-01

399

Interior point algorithms: guaranteed optimality for fluence map optimization in IMRT  

NASA Astrophysics Data System (ADS)

One of the most widely studied problems of the intensity-modulated radiation therapy (IMRT) treatment planning problem is the fluence map optimization (FMO) problem, the problem of determining the amount of radiation intensity, or fluence, of each beamlet in each beam. For a given set of beams, the fluences of the beamlets can drastically affect the quality of the treatment plan, and thus it is critical to obtain good fluence maps for radiation delivery. Although several approaches have been shown to yield good solutions to the FMO problem, these solutions are not guaranteed to be optimal. This shortcoming can be attributed to either optimization model complexity or properties of the algorithms used to solve the optimization model. We present a convex FMO formulation and an interior point algorithm that yields an optimal treatment plan in seconds, making it a viable option for clinical applications.

Aleman, Dionne M.; Glaser, Daniel; Romeijn, H. Edwin; Dempsey, James F.

2010-09-01

400

Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective Lipschitz optimization to multidimensional problems  

NASA Astrophysics Data System (ADS)

A bi-objective optimization problem with Lipschitz objective functions is considered. An algorithm is developed adapting a univariate one-step optimal algorithm to multidimensional problems. The univariate algorithm considered is a worst-case optimal algorithm for Lipschitz functions. The multidimensional algorithm is based on the branch-and-bound approach and trisection of hyper-rectangles which cover the feasible region. The univariate algorithm is used to compute the Lipschitz bounds for the Pareto front. Some numerical examples are included.

Žilinskas, Antanas; Žilinskas, Julius

2015-04-01

401

On gauss-verifiability of optimal solutions in variational data assimilation problems with nonlinear dynamics  

NASA Astrophysics Data System (ADS)

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition. The optimal solution (analysis) error arises due to the errors in the input data (background and observation errors). Under the gaussian assumption the confidence region for the optimal solution error can be constructed using the analysis error covariance. Due to nonlinearity of the model equations the analysis pdf deviates from the gaussian. To a certain extent the gaussian confidence region built on a basis of a non-gaussian analysis pdf remains useful. In this case we say that the optimal solution is "gauss-verifiable". When the deviation from the gaussian further extends, the optimal solutions may still be partially (locally) gauss-verifiable. The aim of this paper is to develop a diagnostics to check gauss-verifiability of the optimal solution. We introduce a relevant measure and propose a method for computing decomposition of this measure into the sum of components associated to the corresponding elements of the control vector. This approach has the potential for implementation in realistic high-dimensional cases. Numerical experiments for the 1D Burgers equation illustrate and justify the presented theory

Gejadze, I. Yu.; Shutyaev, V.

2015-01-01

402

An optimal control approach to an inverse nonlinear elastic shell problem applied to car windscreen design  

Microsoft Academic Search

A numerical procedure to optimise the sag bending process for car windscreens is proposed. In particular a simplified elastic model with geometric nonlinearities is considered. The optimisation approach is based on the numerical resolution of an optimal control problem in nonlinear elasticity. The objective of the optimisation is to match a desired shape by controlling the temperature distribution and minimising

S. Manservisi

2000-01-01

403

An Efficient Monte Carlo Method for Optimal Control Problems with Uncertainty  

Microsoft Academic Search

A general framework is proposed for what we call the sensitivity derivative Monte Carlo (SDMC) solution of optimal control problems with a stochastic parameter. This method employs the residual in the first-order Taylor series expansion of the cost functional in terms of the stochastic parameter rather than the cost functional itself. A rigorous estimate is derived for the variance of

Yanzhao Cao; M. Y. Hussaini; T. A. Zang

2003-01-01

404

Genetic algorithms: An evolution from Monte Carlo methods for strongly non-linear geophysical optimization problems  

Microsoft Academic Search

In providing a method for solving non-linear optimization problems Monte Carlo techniques avoid the need for linearization but, in practice, are often prohibitive because of the large number of models that must be considered. A new class of methods known as Genetic Algorithms have recently been devised in the field of Artificial Intelligence. We outline the basic concept of genetic

Kerry Gallagher; Malcolm Sambridge; Guy Drijkoningen

1991-01-01

405

Explicit Speciation with few a priori Parameters for Dynamic Optimization Problems  

E-print Network

Explicit Speciation with few a priori Parameters for Dynamic Optimization Problems Christopher speciation cri­ terion. In a performance test on multiple stochastically moving fitness peaks speciation is generally advantageous because it enables the use of arbitrary (here generational) evolu

406

Reconstruction of silicon surfaces: A stochastic optimization problem Cristian V. Ciobanu1,2  

E-print Network

. STM has helped achieve remarkable successes in surface science such as finding the atomic structure. A commonly accepted strategy for identifying the atomic structure is to propose several possible models the view that finding the atomic structure of a surface is a problem of stochastic optimization, and we

Ciobanu, Cristian

407

Bifurcation of Singular Arcs in an Optimal Control Problem for Cancer Immune System Interactions under Treatment  

E-print Network

, 63130-4899, hms@wustl.edu Abstract-- A mathematical model for cancer treatment that includesBifurcation of Singular Arcs in an Optimal Control Problem for Cancer Immune System Interactions under Treatment Urszula Ledzewicz Dept. of Mathematics and Statistics, Southern Illinois University

Ledzewicz, Urszula

408

Neighboring Extremal Solution for Nonlinear Discrete-Time Optimal Control Problems With State Inequality Constraints  

Microsoft Academic Search

A neighboring extremal control method is proposed for discrete-time optimal control problems subject to a general class of inequality constraints. The approach is applicable to a broad class of systems with input and state constraints, including two special cases where the constraints depend only on states but not inputs and the constraints are over determined. A closed form solution for

Reza Ghaemi; Jing Sun; Ilya V. Kolmanovsky

2009-01-01

409

Partial conjugate gradient methods for a class of optimal control problems  

Microsoft Academic Search

In this paper, we examine the computational aspects of a certain class of discrete-time optimal control problems. We propose and analyze two partial conjugate gradient algorithms which operate in cycles ofs+1conjugate gradient steps (s leq n= state space dimension). The algorithms are motivated by the special form of the Hessian matrix of the cost functional. The first algorithm exhibits a

DIMITRI P. BERTSEKAS

1974-01-01

410

A multiobjective ant colony-based optimization algorithm for the bin packing problem with load balancing  

Microsoft Academic Search

This paper presents ABLA, a novel multiobjective ant colony-based optimization algorithm to address the bin packing problem with load balancing. ABLA incorporates (1) a new probabilistic decision rule that builds solutions by making use of individual pheromone matrices for each objective function; (2) a new pheromone updating approach in which ants deposit variable amounts of pheromone; (3) two new local

Oscar D. Lara; Miguel A. Labrador

2010-01-01

411

Hybrid optimization for a binary inverse problem Richard A. Krahenbuhl* and Yaoguo Li  

E-print Network

a hybrid optimization algorithm for inversion of gravity data using a binary formulation. The new algorithm utilizes the Genetic Algorithm (GA) as a global search tool, while implementing Quenched Simulated techniques for carrying out such discrete-variable minimization problems, namely, genetic algorithm (GA

412

A hybrid genetic algorithm for a class of global optimization problems with box constraints  

Microsoft Academic Search

In this paper, a new hybrid genetic algorithm is proposed, which combines the genetic algorithm with hill-climbing search steps differently from some former algorithms. The new algorithm can be widely applied to a class of global optimization problems for continuous functions with box constraints. Finally, numerical examples show that this algorithm can yield the global optimum with high efficiency.

Quan Yuan; Zhiqing He; Huinan Leng

2008-01-01

413

Strategic Planning in Air Traffic Control as a Multi-objective Stochastic Optimization Problem  

E-print Network

Strategic Planning in Air Traffic Control as a Multi-objective Stochastic Optimization Problem Ga a collaborative working plan during the strategic phase of air traffic control. The plan obtained via a new the so-called strategic phase of air traffic control. During this phase, flights can be scheduled

Paris-Sud XI, Université de

414

Optimal size and spacing of public facilities in metropolitan areas: The maximum covering location problem revisited  

Microsoft Academic Search

Two quite separate types of analyses have been used to explore the optimal size and spacing of public facilities in urban areas. One group of papers is economics oriented, theoretical, and provides an essentially qualitative analysis of the problem. The papers by Tiebout [10, pp. 79-96], Teitz [9], and Buchanan [2] are examples. The second set of analyses, developed primarily

William L. Holahan

1977-01-01

415

Exact analytical solutions for some popular benchmark problems in topology optimization III: L -shaped domains  

Microsoft Academic Search

In this paper exact, analytical solutions are derived for another highly popular benchmark problem, namely, L-shaped domains having a horizontal line support and one or several point loads. The optimal topologies are obtained in the\\u000a context of Michell structures, i.e., least-weight, stress, or compliance-controlled trusses with a single load condition.

T. Lewi?ski; G. I. N. Rozvany

2008-01-01

416

INVARIANTS FOR HOMOLOGY CLASSES WITH APPLICATION TO OPTIMAL SEARCH AND PLANNING PROBLEM IN ROBOTICS  

E-print Network

INVARIANTS FOR HOMOLOGY CLASSES WITH APPLICATION TO OPTIMAL SEARCH AND PLANNING PROBLEM IN ROBOTICS are of frequent occurrence as configuration spaces of robots, where O represent either physical obstacles that the robots need to avoid (e.g., walls, other robots, etc.) or illegal states (e.g., all legs off

Ghrist, Robert W.

417

Neuro-fuzzy Learning of Strategies for Optimal Control Problems Kaivan Kamali1  

E-print Network

systems such as adaptive network-based fuzzy inference system (ANFIS) [3], can be used to learn fuzzy ifNeuro-fuzzy Learning of Strategies for Optimal Control Problems Kaivan Kamali1 , Lijun Jiang2 of neuro-fuzzy systems which yields reusable knowledge in the form of fuzzy if-then rules. Ex- perimental

418

OPTIMALITY OF T-COERCIVITY FOR SCALAR INTERFACE PROBLEMS BETWEEN DIELECTRICS AND METAMATERIALS  

E-print Network

OPTIMALITY OF T-COERCIVITY FOR SCALAR INTERFACE PROBLEMS BETWEEN DIELECTRICS AND METAMATERIALS Anne are real-valued negative parameters when dissipa- tion is neglected. They are usually called metamaterials and a metamaterial, set in an open, bounded subset of Rd , with d = 2, 3. Our aim is to characterize occurences where

419

On the statistical mechanics of optimization problems of the travelling salesman type  

E-print Network

L-1145 On the statistical mechanics of optimization problems of the travelling salesman type J in an acceptable time. For several years, S. Kirkpatrick has advocated the use of statistical mechanics tools » in a way that closely follows the introduction of the canonical ensemble in statistical mechanics

Paris-Sud XI, Université de

420

Optimal constant in an L 2 extension problem and a proof of a conjecture of Ohsawa  

NASA Astrophysics Data System (ADS)

In this paper, we solve the optimal constant problem in the setting of Ohsawa's generalized $L^{2}$ extension theorem. As applications, we prove a conjecture of Ohsawa and the extended Suita conjecture, we also establish some relations between Bergman kernel and logarithmic capacity on compact and open Riemann surfaces.

Guan, Qi'An; Zhou, XiangYu

2015-01-01

421

6.893 Approximability of Optimization Problems November 15, 1999 Lecturer: Madhu Sudan Scribe: Adam Smith  

E-print Network

6.893 Approximability of Optimization Problems November 15, 1999 Lecture 18 Lecturer: Madhu Sudan , a degree d and a collection of constraints C 1 ; : : : ; C t . Each constraint is a set of k points in F m together with a small circuit constraining the values of p at those points, i.e. C j = (A j ; x (j) 1

Goldwasser, Shafi

422

6.893 Approximability of Optimization Problems October 6, 1999 Lecturer: Madhu Sudan Scribe: Nati Srebro  

E-print Network

6.893 Approximability of Optimization Problems October 6, 1999 Lecture 9 Lecturer: Madhu Sudan define the parametric complexity class PCP c;s [r(\\Delta); q(\\Delta)], where c; s are Completeness Queries quota as a function of the input word length. PCP c;s [r(\\Delta); q(\\Delta)] : = 8 ! : L ` \\Sigma

Goldwasser, Shafi

423

6.893 Approximability of Optimization Problems September 27, 1999 Lecturer: Madhu Sudan Scribe: Eric Lehman  

E-print Network

6.893 Approximability of Optimization Problems September 27, 1999 Lecture 6 Lecturer: Madhu Sudan. Let C(m; k) be the largest set cover produced by the greedy algorithm over all instances with universe at least one additional element, C(k; k) Ÿ k. Furthermore, there must be some set of size at least m

Goldwasser, Shafi

424

6.893 Approximability of Optimization Problems November 10, 1999 Lecturer: Madhu Sudan Scribe: Venkatesan Guruswami  

E-print Network

6.893 Approximability of Optimization Problems November 10, 1999 Lecture 17 Lecturer: Madhu Sudan satisfiability of certain polynomials of degree 3. Indeed one can arithmetize each clause C j of a 3SAT instance OE and obtain a degree 3 multivariate polynomial â?? C j over GF(2) such that C j (¯a) is true iff â?? C

Goldwasser, Shafi

425

6.893 Approximability of Optimization Problems October 13, 1999 Lecturer: Madhu Sudan Scribe: Chandra Boyapati  

E-print Network

6.893 Approximability of Optimization Problems October 13, 1999 Lecture 10 Lecturer: Madhu Sudan.2 Parameters of ECCs Let, C = A collection of strings (or vectors) over some q­ary alphabet. Let, Block length of the code = Length of the strings in C = n. Thus, C ` f0; :::; q \\Gamma 1g n . Let, Information content

Goldwasser, Shafi

426

6.893 Approximability of Optimization Problems September 15, 1999 Lecturer: Madhu Sudan Scribe: John Dunagan  

E-print Network

6.893 Approximability of Optimization Problems September 15, 1999 Lecture 3 Lecturer: Madhu Sudan) is an m by n matrix A, a vector ~ b of length m, and a vector ~c of length n. The goal is to find an n dimensional vector ~x maximizing ~c T \\Delta ~x while at the same time satisfying A~x Ÿ ~ b. It is also

Goldwasser, Shafi

427

6.893 Approximability of Optimization Problems November 8, 1999 Lecturer: Madhu Sudan Scribe: Yevgeniy Dodis  

E-print Network

6.893 Approximability of Optimization Problems November 8, 1999 Lecture 16 Lecturer: Madhu Sudan), and for each column x 2 H we are given a degree at most d ``column polynomial'' c x (y). Furthermore, assume that Pr x;y2H [r y (x) = c x (y)] â?? 1 \\Gamma ffi (1) for some (small) constant ffi . We would like

Goldwasser, Shafi

428

6.893 Approximability of Optimization Problems September 8, 1999 Lecturer: Madhu Sudan Scribe: Rocco Servedio  

E-print Network

6.893 Approximability of Optimization Problems September 8, 1999 Lecture 1 Lecturer: Madhu Sudan) and where each directed edge e 2 E has an associated nonnegative integer capacity c(e): A flow in G is a function f from E to the nonnegative real numbers which satisfies f(e) Ÿ c(e) for every edge e; and which

Goldwasser, Shafi

429

AN ANT COLONY OPTIMIZATION APPROACH FOR THE CAPACITATED VEHICLE ROUTING PROBLEM WITH  

E-print Network

in the sense that each unit consumes the same amount of vehicle capacity. Delivery and pick-up locations DELIVERY AND PICK-UP Bülent �atay1 Abstract. We propose an Ant Colony Optimization (ACO) algorithm to the NP- hard Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP). In VRPSDP

Yanikoglu, Berrin

430

Infinite Horizon Stochastic Optimal Control Problems with Degenerate Noise and Elliptic Equations in Hilbert Spaces  

SciTech Connect

Semilinear elliptic partial differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. These results are applied to a stochastic optimal control problem with infinite horizon. Applications to controlled stochastic heat and wave equations are given.

Masiero, Federica [Dipartimento Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 (Italy)], E-mail: masiero@mate.polimi.it

2007-05-15

431

THE PROBLEMS OF LIMIT LOAD ANALYSIS AND OPTIMIZATION USING EQUILIBRIUM FINITE ELEMENTS  

Microsoft Academic Search

The equilibrium dual discrete mathematical models of the problems of limit load analysis and optimization are investigated in the article. These models are presented in terms of static and kinematic formulation using equilibrium finite elements. In these mathematical models the possible discontinuities of displacement velocities are evaluated and the velocity of energy dissipation is estimated not only within the volume

S. Kalanta

1996-01-01

432

An algorithm for the weighting matrices in the sampled-data optimal linear regulator problem  

NASA Technical Reports Server (NTRS)

The sampled-data optimal linear regulator problem provides a means whereby a control designer can use an understanding of continuous optimal regulator design to produce a digital state variable feedback control law which satisfies continuous system performance specifications. A basic difficulty in applying the sampled-data regulator theory is the requirement that certain digital performance index weighting matrices, expressed as complicated functions of system matrices, be computed. Infinite series representations are presented for the weighting matrices of the time-invariant version of the optimal linear sampled-data regulator problem. Error bounds are given for estimating the effect of truncating the series expressions after a finite number of terms, and a method is described for their computer implementation. A numerical example is given to illustrate the results.

Armstrong, E. S.; Caglayan, A. K.

1976-01-01

433

Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods  

SciTech Connect

In this paper, we consider the optimal design of photonic crystal structures for two-dimensional square lattices. The mathematical formulation of the bandgap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized using the finite element method into a series of finite-dimensional eigenvalue problems for multiple values of the wave vector parameter. The resulting optimization problem is large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigenspaces, we reduce the large-scale non-convex optimization problem via reparametrization to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP solvers can be efficiently applied. Numerical results are presented for both transverse magnetic (TM) and transverse electric (TE) polarizations at several frequency bands. The optimized structures exhibit patterns which go far beyond typical physical intuition on periodic media design.

Men, H. [National University of Singapore, Center for Singapore-MIT Alliance, Singapore 117576 (Singapore)], E-mail: men@nus.edu.sg; Nguyen, N.C. [MIT Department of Aeronautics and Astronautics, 77 Massachusetts Ave., Cambridge, MA 02139 (United States)], E-mail: cuongng@mit.edu; Freund, R.M. [MIT Sloan School of Management, 50 Memorial Drive, Cambridge, MA 02142 (United States)], E-mail: rfreund@mit.edu; Parrilo, P.A. [MIT Department of Electrical Engineering and Computer Science, 77 Massachusetts Ave., Cambridge, MA 02139 (United States)], E-mail: parrilo@mit.edu; Peraire, J. [MIT Department of Aeronautics and Astronautics, 77 Massachusetts Ave., Cambridge, MA 02139 (United States)], E-mail: peraire@mit.edu

2010-05-20

434

Inverse optimization: functional and physiological considerations related to the force-sharing problem.  

PubMed

This paper is a review of the optimization techniques used for the solution of the force-sharing problem in biomechanics; that is, the distribution of the net joint moment to the force generating structures such as muscles and ligaments. The solution to this problem is achieved by the minimization (or maximization) of an objective function that includes the design variable (usually muscle forces) that are subject to certain constraints, and it is generally related to physiological or mechanical properties such as muscle stress, maximum force or moment, activation level, etc. The usual constraints require the sum of the exerted moments to be equal to the net joint moment and certain boundary conditions restrict the force solutions within physiologically acceptable limits. Linear optimization (objective and constraint functions are both linear relationships) has limited capabilities for the solution of the force sharing problem, although the use of appropriate constraints and physiologically realistic boundary conditions can improve the solution and lead to reasonable and functionally acceptable muscle force predictions. Nonlinear optimization provides more physiologically acceptable results, especially when the criteria used are related to the dynamics of the movement (e.g., instantaneous maximum force derived from muscle modeling based on length and velocity histories). The evaluation of predicted forces can be performed using direct measurements of forces (usually in animals), relationship with EMG patterns, comparisons with forces obtained from optimized forward dynamics, and by evaluating the results using analytical solutions of the optimal problem to highlight muscle synergism for example. Global objective functions are more restricting compared to local ones that are related to the specific objective of the movement at its different phases (e.g., maximize speed or minimize pain). In complex dynamic activities multiobjective optimization is likely to produce more realistic results. PMID:9505137

Tsirakos, D; Baltzopoulos, V; Bartlett, R

1997-01-01

435

Electronic neural network for solving traveling salesman and similar global optimization problems  

NASA Technical Reports Server (NTRS)

This invention is a novel high-speed neural network based processor for solving the 'traveling salesman' and other global optimization problems. It comprises a novel hybrid architecture employing a binary synaptic array whose embodiment incorporates the fixed rules of the problem, such as the number of cities to be visited. The array is prompted by analog voltages representing variables such as distances. The processor incorporates two interconnected feedback networks, each of which solves part of the problem independently and simultaneously, yet which exchange information dynamically.

Thakoor, Anilkumar P. (inventor); Moopenn, Alexander W. (inventor); Duong, Tuan A. (inventor); Eberhardt, Silvio P. (inventor)

1993-01-01

436

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

SciTech Connect

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

Haber, Eldad

2014-03-17

437

Inverse problems and optimal experiment design in unsteady heat transfer processes identification  

NASA Technical Reports Server (NTRS)

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

Artyukhin, Eugene A.

1991-01-01

438

Digital program for solving the linear stochastic optimal control and estimation problem  

NASA Technical Reports Server (NTRS)

A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.

Geyser, L. C.; Lehtinen, B.

1975-01-01

439

Multiview Stereo and Silhouette Consistency via Convex Functionals over Convex Domains  

E-print Network

Multiview Stereo and Silhouette Consistency via Convex Functionals over Convex Domains Daniel Cremers and Kalin Kolev Abstract--We propose a convex formulation for silhouette and stereo fusion in 3D of minimizing a convex functional, where the exact silhouette consistency is imposed as convex constraints

Cremers, Daniel

440

New Optimized Solution Method for Beamforming in Cognitive Multicast Transmission  

Microsoft Academic Search

The optimal beamforming for cognitive multicast transmission is nonconvex rank-one constrained optimization problem. For a solution, a popular method is the combination of relaxed convex semi-definite programming, where the rank-one constraint is dropped, and randomization. We show that in many cases, this method cannot give satisfactory solutions. As an initial step, we develop a simple alternative method, which gives much

Anh H. Phan; H. D. Tuan; Ha Hoang Kha

2010-01-01

441

Nonsmooth Optimization for Beamforming in Cognitive Multicast Transmission  

Microsoft Academic Search

It is well-known that the optimal beamforming problems for cognitive multicast transmission are indefinite quadratic (nonconvex) optimization programs. The conventional approach is to reformulate them as convex semi-definite programs (SDPs) with additional rank-one (nonconvex and discontinuous) constraints. The rank-one constraints are then dropped for relaxed solutions, and randomization techniques are employed for solution search. In many practical cases, this approach

Anh H. Phan; Hoang Duong Tuan; Ho Hong Kha; Duy T. Ngo

2010-01-01

442

Optimizing noisy funnel-like functions on the euclidean group with applications to protein docking  

Microsoft Academic Search

Formulated as an optimization problem, the final stages of protein docking can be viewed as optimizing a very noisy funnel-like function on the space of rigid body motions, the (special) Euclidean group SE(3). We have recently introduced a stochastic global optimization method, called semi-definite programming based underestimation (SDU) (Paschalidis et al., 2007), that constructs a convex quadratic under-estimator to the

Yang Shen; Pirooz Vakili; Sandor Vajda; I. C. Paschalidis

2007-01-01

443

A hybrid algorithm optimization approach for machine loading problem in flexible manufacturing system  

NASA Astrophysics Data System (ADS)

The production planning problem of flexible manufacturing system (FMS) concerns with decisions that have to be made before an FMS begins to produce parts according to a given production plan during an upcoming planning horizon. The main aspect of production planning deals with machine loading problem in which selection of a subset of jobs to be manufactured and assignment of their operations to the relevant machines are made. Such problems are not only combinatorial optimization problems, but also happen to be non-deterministic polynomial-time-hard, making it difficult to obtain satisfactory solutions using traditional optimization techniques. In this paper, an attempt has been made to address the machine loading problem with objectives of minimization of system unbalance and maximization of throughput simultaneously while satisfying the system constraints related to available machining time and tool slot designing and using a meta-hybrid heuristic technique based on genetic algorithm and particle swarm optimization. The results reported in this paper demonstrate the model efficiency and examine the performance of the system with respect to measures such as throughput and system utilization.

Kumar, Vijay M.; Murthy, ANN; Chandrashekara, K.

2012-05-01

444

A case study in the performance and scalability of optimization algorithms  

Microsoft Academic Search

We analyze the performance and scalabilty of algorithms for the solution of large optimization problems on high-performance parallel architectures. Our case study uses the GPCG (gradient projection, conjugate gradient) algorithm for solving bound-constrained convex quadratic problems. Our implementation of the GPCG algorithm within the Toolkit for Advanced Optimization (TAO) is available for a wide range of high-performance architectures and has

Steven J. Benson; Lois Curfman McInnes; Jorge J. Moré

2001-01-01

445

Determination of optimal self-drive tourism route using the orienteering problem method  

NASA Astrophysics Data System (ADS)

This paper was conducted to determine the optimal travel routes for self-drive tourism based on the allocation of time and expense by maximizing the amount of attraction scores assigned to each city involved. Self-drive tourism represents a type of tourism where tourists hire or travel by their own vehicle. It only involves a tourist destination which can be linked with a network of roads. Normally, the traveling salesman problem (TSP) and multiple traveling salesman problems (MTSP) method were used in the minimization problem such as determination the shortest time or distance traveled. This paper involved an alternative approach for maximization method which is maximize the attraction scores and tested on tourism data for ten cities in Kedah. A set of priority scores are used to set the attraction score at each city. The classical approach of the orienteering problem was used to determine the optimal travel route. This approach is extended to the team orienteering problem and the two methods were compared. These two models have been solved by using LINGO12.0 software. The results indicate that the model involving the team orienteering problem provides a more appropriate solution compared to the orienteering problem model.

Hashim, Zakiah; Ismail, Wan Rosmanira; Ahmad, Norfaieqah

2013-04-01

446

VeriQuickhull: fast sequential and parallel algorithms for computing the planar convex hull  

E-print Network

Computing the convex hull of a set of points in the plane is one of the most studied problems in computational geometry. The Quickhull algorithm is a popular convex hull algorithm. While the main structure of Quickhull is axed, many different...

Sambasivam, Mashilamani

1999-01-01

447

Fast Convex Closure for Efficient Predicate Detection Paul A.S. Ward and Dwight S. Bedasse  

E-print Network

Fast Convex Closure for Efficient Predicate Detection Paul A.S. Ward and Dwight S. Bedass´e Shoshin of the matching primitive events. In particular, the Xie and Taylor convex-closure algorithm forms the basis for hierarchical compound events. In this paper, we study the cause of the problems in the Xie and Taylor algo

Ward, Paul A.S.

448

Identifying Model Inaccuracies and Solution Uncertainties in Non-Invasive Activation-Based Imaging of Cardiac Excitation using Convex Relaxation  

PubMed Central

Noninvasive imaging of cardiac electrical function has begun to move towards clinical adoption. Here we consider one common formulation of the problem, in which the goal is to estimate the spatial distribution of electrical activation times during a cardiac cycle. We address the challenge of understanding the robustness and uncertainty of solutions to this formulation. This formulation poses a non-convex, non-linear least squares optimization problem. We show that it can be relaxed to be convex, at the cost of some degree of physiological realism of the solution set, and that this relaxation can be used as a framework to study model inaccuracy and solution uncertainty. We present two examples, one using data from a healthy human subject and the other synthesized with the ECGSIM software package. In the first case, we consider uncertainty in the initial guess and regularization parameter. In the second case, we mimic the presence of an ischemic zone in the heart in a way which violates a model assumption. We show that the convex relaxation allows understanding of spatial distribution of parameter sensitivity in the first case, and identification of model violation in the second. PMID:24710159

Erem, Burak; van Dam, Peter M.; Brooks, Dana H.

2014-01-01

449

Traveltime tomography and nonlinear constrained optimization  

SciTech Connect

Fermat's principle of least traveltime states that the first arrivals follow ray paths with the smallest overall traveltime from the point of transmission to the point of reception. This principle determines a definite convex set of feasible slowness models - depending only on the traveltime data - for the fully nonlinear traveltime inversion problem. The existence of such a convex set allows us to transform the inversion problem into a nonlinear constrained optimization problem. Fermat's principle also shows that the standard undamped least-squares solution to the inversion problem always produces a slowness model with many ray paths having traveltime shorter than the measured traveltime (an impossibility even if the trial ray paths are not the true ray paths). In a damped least-squares inversion, the damping parameter may be varied to allow efficient location of a slowness model on the feasibility boundary. 13 refs., 1 fig., 1 tab.

Berryman, J.G.

1988-10-01

450

Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods  

E-print Network

- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given, Electroencephalography, inverse problem, convex optimization, mixed-norms, structured sparsity, functional brain imaging fields measured by Magnetoencephalography (MEG) and Electroencephalography (EEG), which we will refer

Paris-Sud XI, Université de

451

Perspectives of matrix convex functions  

PubMed Central

In this paper, we generalize the main results of [Effros EG, (2009) Proc Natl Acad. Sci USA 106:1006–1008]. Namely, we provide the necessary and sufficient conditions for jointly convexity of perspective functions and generalized perspective functions.

Ebadian, Ali; Nikoufar, Ismail; Eshaghi Gordji, Madjid

2011-01-01

452

Model transitions and optimization problem in multi-flexible-body systems: Application to modeling molecular systems  

NASA Astrophysics Data System (ADS)

This paper presents an efficient algorithm for the simulation of multi-flexible-body systems undergoing discontinuous changes in model definition. The equations governing the dynamics of the transitions from a higher to a lower fidelity model and vice versa are formulated through imposing/removing certain constraints on/from the system model. The issue of the non-uniqueness of the results associated with the transition from a lower to a higher fidelity model may be handled by solving an optimization problem. This optimization problem is subjected to the satisfaction of the constraint imposed by the generalized impulse-momentum equations. The divide-and-conquer algorithm (DCA) is applied to formulate the jumps in the system states resulting from the model transition. The DCA formulation in its basic form is both time and processor optimal and results in linear and logarithmic complexity when implemented in serial and parallel with O(n) processors, respectively. As such, its application can reduce the effective computational cost of formulating and solving the optimization problem in the transitions to the finer models. The principal aspects of the mathematics for the algorithm implementation is developed and numerical examples are provided to validate the method.

Khan, I. M.; Poursina, M.; Anderson, K. S.

2013-07-01

453

Constraint Optimization Problem For The Cutting Of A Cobalt Chrome Refractory Material  

NASA Astrophysics Data System (ADS)

This paper shows a complete approach to solve a given problem, from the experimentation to the optimization of different cutting parameters. In response to an industrial problem of slotting FSX 414, a Cobalt-based refractory material, we have implemented a design of experiment to determine the most influent parameters on the tool life, the surface roughness and the cutting forces. After theses trials, an optimization approach has been implemented to find the lowest manufacturing cost while respecting the roughness constraints and cutting force limitation constraints. The optimization approach is based on the Response Surface Method (RSM) using the Sequential Quadratic programming algorithm (SQP) for a constrained problem. To avoid a local optimum and to obtain an accurate solution at low cost, an efficient strategy, which allows improving the RSM accuracy in the vicinity of the global optimum, is presented. With these models and these trials, we could apply and compare our optimization methods in order to get the lowest cost for the best quality, i.e. a satisfying surface roughness and limited cutting forces.

Lebaal, Nadhir; Schlegel, Daniel; Folea, Milena

2011-05-01

454

A linked simulation-optimization model for solving the unknown groundwater pollution source identification problems.  

PubMed

This study proposes a linked simulation-optimization model for solving the unknown groundwater pollution source identification problems. In the proposed model, MODFLOW and MT3DMS packages are used to simulate the flow and transport processes in the groundwater system. These models are then integrated with an optimization model which is based on the heuristic harmony search (HS) algorithm. In the proposed simulation-optimization model, the locations and release histories of the pollution sources are treated as the explicit decision variables and determined through the optimization model. Also, an implicit solution procedure is proposed to determine the optimum number of pollution sources which is an advantage of this model. The performance of the proposed model is evaluated on two hypothetical examples for simple and complex aquifer geometries, measurement error conditions, and different HS solution parameter sets. Identified results indicated that the proposed simulation-optimization model is an effective way and may be used to solve the inverse pollution source identification problems. PMID:20633952

Ayvaz, M Tamer

2010-09-20

455

Convex polytopes and quantum separability  

SciTech Connect

We advance a perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose a criterium based on the consideration of convex subsets of quantum states. This criterium generalizes a property of product states to convex subsets (of the set of quantum states) that is able to uncover an interesting geometrical property of the separability property.

Holik, F.; Plastino, A. [Departamento de Matematica - Ciclo Basico Comun, Universidad de Buenos Aires - Pabellon III, Ciudad Universitaria, Buenos Aires, Argentina and CONICET (Argentina); National University La Plata and CONICET IFLP-CCT, C.C. 727 - 1900 La Plata (Argentina)

2011-12-15

456

Bayesian Optimization Algorithm for Multi-Objective Solutions: Application to Electric Equipment Configuration Problems in a Power Plant  

E-print Network

Search (Tabu-BOA) to electric equipments configuration problems in a power plant. Tabu-BOA is a hybrid Optimization Algorithm(1) and Tabu Search(2)(3) (Tabu-BOA) in order to solve electric equipments configuration. For example, Khan et al have proposed a variation of BOA for multi-objective optimization problems(4

Coello, Carlos A. Coello

457

A Novel Hybrid Crossover based Artificial Bee Colony Algorithm for Optimization Problem  

NASA Astrophysics Data System (ADS)

Artificial bee colony (ABC) algorithm has proved its importance in solving a number of problems including engineering optimization problems. ABC algorithm is one of the most popular and youngest member of the family of population based nature inspired meta-heuristic swarm intelligence method. ABC has been proved its superiority over some other Nature Inspired Algorithms (NIA) when applied for both benchmark functions and real world problems. The performance of search process of ABC depends on a random value which tries to balance exploration and exploitation phase. In order to increase the performance it is required to balance the exploration of search space and exploitation of optimal solution of the ABC. This paper outlines a new hybrid of ABC algorithm with Genetic Algorithm. The proposed method integrates crossover operation from Genetic Algorithm (GA) with original ABC algorithm. The proposed method is named as Crossover based ABC (CbABC). The CbABC strengthens the exploitation phase of ABC as crossover enhances exploration of search space. The CbABC tested over four standard benchmark functions and a popular continuous optimization problem.

Kumar, Sandeep; Kumar Sharma, Vivek; Kumari, Rajani

2013-11-01

458

Optimization in Fractal and Fractured Landscapes Using Locust Swarms  

Microsoft Academic Search

Locust Swarms are a newly developed multi-optima particle swarm. They were explicitly developed for non-globally convex search\\u000a spaces, and their non-convergent search behaviours can also be useful for problems with fractal and fractured landscapes.\\u000a On the 1000-dimensional “FastFractal” problem used in the 2008 CEC competition on Large Scale Global Optimization, Locust\\u000a Swarms can perform better than all of the methods

Stephen Chen; Vincent Lupien

2009-01-01

459

CALIBRATING NON-CONVEX PENALIZED REGRESSION IN ULTRA-HIGH DIMENSION.  

PubMed

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of non-convex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis. PMID:24948843

Wang, Lan; Kim, Yongdai; Li, Runze

2013-10-01

460

Two combinatorial optimization problems for SNP discovery using base-specific cleavage and mass spectrometry  

PubMed Central

Background The discovery of single-nucleotide polymorphisms (SNPs) has important implications in a variety of genetic studies on human diseases and biological functions. One valuable approach proposed for SNP discovery is based on base-specific cleavage and mass spectrometry. However, it is still very challenging to achieve the full potential of this SNP discovery approach. Results In this study, we formulate two new combinatorial optimization problems. While both problems are aimed at reconstructing the sample sequence that would attain the minimum number of SNPs, they search over different candidate sequence spaces. The first problem, denoted as SNP - MSP, limits its search to sequences whose in silico predicted mass spectra have all their signals contained in the measured mass spectra. In contrast, the second problem, denoted as SNP - MSQ, limits its search to sequences whose in silico predicted mass spectra instead contain all the signals of the measured mass spectra. We present an exact dynamic programming algorithm for solving the SNP - MSP problem and also show that the SNP - MSQ problem is NP-hard by a reduction from a restricted variation of the 3-partition problem. Conclusions We believe that an efficient solution to either problem above could offer a seamless integration of information in four complementary base-specific cleavage reactions, thereby improving the capability of the underlying biotechnology for sensitive and accurate SNP discovery. PMID:23282116

2012-01-01

461

Sequential RBF surrogate-based efficient optimization method for engineering design problems with expensive black-box functions  

NASA Astrophysics Data System (ADS)

As a promising technique, surrogate-based design and optimization(SBDO) has been widely used in modern engineering design optimizations. Currently, static surrogate-based optimization methods have been successfully applied to expensive optimization problems. However, due to the low efficiency and poor flexibility, static surrogate-based optimization methods are difficult to efficiently solve practical engineering cases. At the aim of enhancing efficiency, a novel surrogate-based efficient optimization method is developed by using sequential radial basis function(SEO-SRBF). Moreover, augmented Lagrangian multiplier method is adopted to solve the problems involving expensive constraints. In order to study the performance of SEO-SRBF, several numerical benchmark functions and engineering problems are solved by SEO-SRBF and other well-known surrogate-based optimization methods including EGO, MPS, and IARSM. The optimal solutions, number of function evaluations, and algorithm execution time are recorded for comparison. The comparison results demonstrate that SEO-SRBF shows satisfactory performance in both optimization efficiency and global convergence capability. The CPU time required for running SEO-SRBF is dramatically less than that of other algorithms. In the torque arm optimization case using FEA simulation, SEO-SRBF further reduces 21% of the material volume compared with the solution from static-RBF subject to the stress constraint. This study provides the efficient strategy to solve expensive constrained optimization problems.

Peng, Lei; Liu, Li; Long, Teng; Guo, Xiaosong

2014-11-01

462

Efficient implementation and application of the artificial bee colony algorithm to low-dimensional optimization problems  

NASA Astrophysics Data System (ADS)

We adapt a swarm-intelligence-based optimization method (the artificial bee colony algorithm, ABC) to enhance its parallel scaling properties and to improve the escaping behavior from deep local minima. Specifically, we apply the approach to the geometry optimization of Lennard-Jones clusters. We illustrate the performance and the scaling properties of the parallelization scheme for several system sizes (5-20 particles). Our main findings are specific recommendations for ranges of the parameters of the ABC algorithm which yield maximal performance for Lennard-Jones clusters and Morse clusters. The suggested parameter ranges for these different interaction potentials turn out to be very similar; thus, we believe that our reported values are fairly general for the ABC algorithm applied to chemical optimization problems.

von Rudorff, Guido Falk; Wehmeyer, Christoph; Sebastiani, Daniel

2014-06-01

463

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

NASA Astrophysics Data System (ADS)

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

Takasaki, Koichi

464

Robust Optimization Model and Algorithm for Railway Freight Center Location Problem in Uncertain Environment  

PubMed Central

Railway freight center location problem is an important issue in railway freight transport programming. This paper focuses on the railway freight center location problem in uncertain environment. Seeing that the expected value model ignores the negative influence of disadvantageous scenarios, a robust optimization model was proposed. The robust optimization model takes expected cost and deviation value of the scenarios as the objective. A cloud adaptive clonal selection algorithm (C-ACSA) was presented. It combines adaptive clonal selection algorithm with Cloud Model which can improve the convergence rate. Design of the code and progress of the algorithm were proposed. Result of the example demonstrates the model and algorithm are effective. Compared with the expected value cases, the amount of disadvantageous scenarios in robust model reduces from 163 to 21, which prove the result of robust model is more reliable. PMID:25435867

He, Shi-wei; Song, Rui; Sun, Yang; Li, Hao-dong

2014-01-01

465

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem  

NASA Technical Reports Server (NTRS)

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Gibson, J. S.; Rosen, I. G.

1986-01-01

466

A global optimization method for the solution of a magnetic field synthesis problem  

SciTech Connect

The determination of the current system which produces a given magnetic field in a region of finite extent, is considered. The magnetic field synthesis problem arisen from this, is solved by means of a global optimization method. The method is based on search trajectories. This technique utilizes the expression of the gradient of the cost functional and allows to save calculation time when the expression of it is known. The algorithm for the solution of the problem is developed for an axisymmetric electromagnetic configuration. Two applications for the determination of the poloidal current system in toroidal devices for thermonuclear fusion experiments, are considered.

Borghi, C.A.; Fabbri, M. [Univ. of Bologna (Italy). Dept. of Electrical Engineering] [Univ. of Bologna (Italy). Dept. of Electrical Engineering

1996-05-01

467

A General Optimality Conditions for Stochastic Control Problems of Jump Diffusions  

SciTech Connect

We consider a stochastic control problem where the system is governed by a non linear stochastic differential equation with jumps. The control is allowed to enter into both diffusion and jump terms. By only using the first order expansion and the associated adjoint equation, we establish necessary as well as sufficient optimality conditions of controls for relaxed controls, who are a measure-valued processes.

Bahlali, Seid; Chala, Adel, E-mail: adelchala@yahoo.fr [University Med Khider, Laboratory of Applied Mathematics (Algeria)

2012-02-15

468

Optimization of the heating surface shape in the contact melting problem  

NASA Technical Reports Server (NTRS)

The theoretical analysis of contact melting by the migrating heat source with an arbitrary shaped isothermal heating surface is presented. After the substantiated simplification, the governing equations are transformed to the convenient equations for engineering calculations relationships. Analytical solutions are used for numerical prediction of optimal shape of the heating surface. The problem is investigated for the constant and for temperature dependent physical properties of the melt.

Fomin, Sergei A.; Cheng, Shangmo

1991-01-01

469

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

NASA Technical Reports Server (NTRS)

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

Miura, H.

1984-01-01

470

A bilevel fuzzy principal-agent model for optimal nonlinear taxation problems  

Microsoft Academic Search

This paper presents a bilevel fuzzy principal-agent model for optimal nonlinear taxation problems with asymmetric information,\\u000a in which the government and the monopolist are the principals, the consumer is their agent. Since the assessment of the government\\u000a and the monopolist about the consumer’s taste is subjective, therefore, it is reasonable to characterize this assessment as\\u000a a fuzzy variable. What’s more,

Yanfei Lan; Ruiqing Zhao; Wansheng Tang

2011-01-01

471

POD a-posteriori error estimates for linear-quadratic optimal control problems  

Microsoft Academic Search

The main focus of this paper is on an a-posteriori analysis for the method of proper orthogonal decomposition (POD) applied\\u000a to optimal control problems governed by parabolic and elliptic PDEs. Based on a perturbation method it is deduced how far\\u000a the suboptimal control, computed on the basis of the POD model, is from the (unknown) exact one. Numerical examples illustrate

F. Tröltzsch; S. Volkwein

2009-01-01

472

A Discrete Particle Swarm Optimization Algorithm for the Permutation Flowshop Sequencing Problem with Makespan Criterion  

Microsoft Academic Search

\\u000a In this paper, a discrete particle swarm optimization (DPSO) algorithm is presented to solve the permutation flowshop sequencing problem with the makespan criterion. A new crossover\\u000a operator, here we call it the PTL crossover operator, is presented. In addition, the DPSO algorithm is hybridized with a simple local search algorithm based on an insert neighborhood to further improve the solution

Quan-Ke Pan; M. Fatih Tasgetiren; Yun-Chia Liang

2007-01-01

473

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem  

NASA Technical Reports Server (NTRS)

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, K.; Teglas, R.

1984-01-01

474

Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints  

NASA Technical Reports Server (NTRS)

Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

Juang, J.-N.; Turner, J. D.; Chun, H. M.

1984-01-01

475

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem  

NASA Technical Reports Server (NTRS)

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, Kazufumi; Teglas, Russell

1987-01-01

476

6.893 Approximability of Optimization Problems September 20, 1999 Lecturer: Madhu Sudan Scribe: Adam Smith  

E-print Network

6.893 Approximability of Optimization Problems September 20, 1999 Lecture 4 Lecturer: Madhu Sudan boolean variables x 1 ; : : : ; xn and m clauses C 1 ; : : : ; Cm . The goal is to determine the maximum for all i, 2. 0 Ÿ Z j Ÿ 1 for all j and, 3. for each clause C j of the form x i 1 â?? ¯ x i 2 â?? \\Delta

Goldwasser, Shafi

477

6.893 Approximability of Optimization Problems November 22, 1999 Lecturer: Madhu Sudan Scribe: John Dunagan  

E-print Network

6.893 Approximability of Optimization Problems November 22, 1999 Lecture 20 Lecturer: Madhu Sudan of length Ÿ n and 1. computes Ÿ p probes and a circuit C of size O(p \\Delta a(n)) using Ÿ r(n) random bits 2 of length Ÿ a(n) 4. decides whether to accept or not based on whether the responses from \\Pi satisfies C Let

Goldwasser, Shafi

478

6.893 Approximability of Optimization Problems September 13, 1999 Lecturer: Madhu Sudan Scribe: Alantha Newman  

E-print Network

6.893 Approximability of Optimization Problems September 13, 1999 Lecture 2 Lecturer: Madhu Sudan) Goal: Find C ` V such that 8(u; v) 2 E, either u or v is in C. Objective: Minimize jCj First we note that if M is a maximal matching for G, then jM j Ÿ OPT V C . Take any maximal matching; for each edge

Goldwasser, Shafi

479

Multi-objective optimization algorithms for flow shop scheduling problem: a review and prospects  

Microsoft Academic Search

Since multi-objective flow shop scheduling problem (MFSP) plays a key role in practical scheduling, there has been an increasing\\u000a interest in MFSP according to the literature. However, there still have been wide gaps between theories and practical applications,\\u000a and the review research of multi-objective optimization algorithms in MFSP (objectives > 2) field is relatively scarce. In\\u000a view of this, this

Yi Sun; Chaoyong Zhang; Liang Gao; Xiaojuan Wang

2011-01-01

480

An efficient ant colony optimization system for the manufacturing cells formation problem  

Microsoft Academic Search

An ant colony optimization (ACO) scheme for the manufacturing cells design problem is proposed, which uses a tight eigenvalue-based\\u000a bound to guide and accelerate the search. This feature is combined with a good initialization procedure and with ideas from\\u000a successful ACO implementations in other areas, to achieve efficiency and reliability with the minimum structure and set of\\u000a parameters. The resulting

K. Spiliopoulos; S. Sofianopoulou

2008-01-01

481

A Comparison of Heuristics for the Discrete Cost Multicommodity Network Optimization Problem  

Microsoft Academic Search

Abstract In this paper, approximate solutions algorithms for discrete cost multicommodity,network optimization problems are presented and compared. Firstly, extensions of classical greedy heuristics, based on link-rerouting and ?ow-rerouting heuristics, are presented in details. Secondly, a new approximate solution algorithm, which basically con- sists in a heuristic implementation of the exact Benders-type cutting plane generation method, is proposed. All these algorihms

Virginie Gabrel; Arnaud Knippel; Michel Minoux

2003-01-01

482

Multi-criteria human resource allocation for solving multistage combinatorial optimization problems using multiobjective hybrid genetic algorithm  

Microsoft Academic Search

Multi-criteria human resource allocation involves deciding how to divide human resource of limited availability among multiple demands in a way that optimizes current objectives. In this paper, we focus on multi-criteria human resource allocation for solving multistage combinatorial optimization problem. Hence we tackle this problem via a multistage decision-making model. A multistage decision-making model is similar to a complex problem

Chi-ming Lin; Mitsuo Gen

2008-01-01

483

The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities  

NASA Astrophysics Data System (ADS)

The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

Cain, George L., Jr.; González, Luis

2008-02-01

484

Weak Convergence and Fluid Limits in Optimal Time-to-Empty Queueing Control Problems  

SciTech Connect

We consider a class of controlled queue length processes, in which the control allocates each server's effort among the several classes of customers requiring its service. Served customers are routed through the network according to (prescribed) routing probabilities. In the fluid rescaling, X{sup n}(t) = 1/nX(nt) , we consider the optimal control problem of minimizing the integral of an undiscounted positive running cost until the first time that X{sup n}=0. Our main result uses weak convergence ideas to show that the optimal value functions V{sup n} of the stochastic control problems for X{sup n}(t) converge (as n{yields}{infinity}) to the optimal value V of a control problem for the limiting fluid process. This requires certain equicontinuity and boundedness hypotheses on (V{sup n}). We observe that these are essentially the same hypotheses that would be needed for the Barles-Perthame approach in terms of semicontinuous viscosity solutions. Sufficient conditions for these equicontinuity and boundedness properties are briefly discussed.

Day, Martin V., E-mail: day@math.vt.edu [Virginia Tech, Department of Mathematics (United States)

2011-12-15

485

A linear decomposition method for large optimization problems. Blueprint for development  

NASA Technical Reports Server (NTRS)

A method is proposed for decomposing large optimization problems encountered in the design of engineering systems such as an aircraft into a number of smaller subproblems. The decomposition is achieved by organizing the problem and the subordinated subproblems in a tree hierarchy and optimizing each subsystem separately. Coupling of the subproblems is accounted for by subsequent optimization of the entire system based on sensitivities of the suboptimization problem solutions at each level of the tree to variables of the next higher level. A formalization of the procedure suitable for computer implementation is developed and the state of readiness of the implementation building blocks is reviewed showing that the ingredients for the development are on the shelf. The decomposition method is also shown to be compatible with the natural human organization of the design process of engineering systems. The method is also examined with respect to the trends in computer hardware and software progress to point out that its efficiency can be amplified by network computing using parallel processors.

Sobieszczanski-Sobieski, J.

1982-01-01

486

Intersection of convex objects in two and three dimensions  

Microsoft Academic Search

One of the basic geometric operations involves determining whether a pair of convex objects intersect. This problem is well understood in a model of computation in which the objects are given as input and their intersection is returned as output. For many applications, however, it may be assumed that the objects already exist within the computer and that the only

Bernard Chazelle; David P. Dobkin

1987-01-01

487

Rebalancing an Investment Portfolio in the Presence of Convex ...  

E-print Network

sible to reduce the measure of risk by discarding assets, which is not an .... by this method given in §4; this method leads to a model which can be cast as a quadratic. 3 ...... If the transaction cost function is continuous and has convex level sets then problem .... Journal of Economic Dynamics and Control, 26:889–

2004-12-17

488

A Coordinate Gradient Descent Method for l1-regularized Convex ...  

E-print Network

Apr 16, 2008 ... l1-regularized logistic regression problems for feature selection in data ... supported in part by NUS Academic Research Grant ... sarily strictly convex, ? is a given nonnegative weight vector, and |x| ... the theoretical convergence properties have not been analyzed. .... The identity matrix is denoted by I.

2008-04-23

489

Gyroscopic Forces and Collision Avoidance with Convex Obstacles  

E-print Network

Gyroscopic Forces and Collision Avoidance with Convex Obstacles Dong Eui Chang1 and Jerrold E, CA 91125; marsden@cds.caltech.edu Summary. This paper introduces gyroscopic forces as an tool- ular gyroscopic control forces--in the problem of collision and obstacle avoid- ance. We are also

Marsden, Jerrold

490

Deciding Under Uncertainty vs. Reducing Uncertainty by Observations: the Optimal Observation Problem  

NASA Astrophysics Data System (ADS)

In order to manage a system, a decision maker (DM) solves a problem of stochastic optimal control, that is: trying to make the best decision under uncertainty, having partial knowledge on the effects of his/her decision. Additionally, uncertainty can be reduced by getting more information by new observations. Of the many possible observations, each one leads to a different uncertainty reduction. Deciding what to observe is a problem, complementary to the control problem, that the DM has to face. A second question is whether it is worth to observe more or not. At some point, the cost of the next observation is larger than its marginal value. In that case it is better to take a decision, accepting the present uncertainty, rather than trying to reduce it further. The method we present offers a solution to the questions on what and how much to observe by setting up an Optimal Observation Problem (OOP). OOP selects the observation with the highest (expected) net value. The net value of an observation is the difference between the gross value of the information carried by that observation, less the cost to obtain the observation itself. The gross value of information is the expected added value of a better decision thanks to uncertainty reduction. If information is used rationally, this value is always non-negative and specific to the system objective, which is defined by the optimal control problem. A first application of the OOP is shown on the River Cart, in Scotland, where the DM has to choose between giving a flood warning or not, and the uncertainty on the rating curve can be reduced by extra gaugings.

Weijs, S. V.; Raso, L.; Werner, M.

2012-12-01

491

Non-convex entropies for conservation laws with involutions.  

PubMed

The paper discusses systems of conservation laws endowed with involutions and contingent entropies. Under the assumption that the contingent entropy function is convex merely in the direction of a cone in state space, associated with the involution, it is shown that the Cauchy problem is locally well posed in the class of classical solutions, and that classical solutions are unique and stable even within the broader class of weak solutions that satisfy an entropy inequality. This is on a par with the classical theory of solutions to hyperbolic systems of conservation laws endowed with a convex entropy. The equations of elastodynamics provide the prototypical example for the above setting. PMID:24249772

Dafermos, Constantine M

2013-12-28

492

On the taxonomy of optimization problems under estimation of distribution algorithms.  

PubMed

Understanding the relationship between a search algorithm and the space of problems is a fundamental issue in the optimization field. In this paper, we lay the foundations to elaborate taxonomies of problems under estimation of distribution algorithms (EDAs). By using an infinite population model and assuming that the selection operator is based on the rank of the solutions, we group optimization problems according to the behavior of the EDA. Throughout the definition of an equivalence relation between functions it is possible to partition the space of problems in equivalence classes in which the algorithm has the same behavior. We show that only the probabilistic model is able to generate different partitions of the set of possible problems and hence, it predetermines the number of different behaviors that the algorithm can exhibit. As a natural consequence of our definitions, all the objective functions are in the same equivalence class when the algorithm does not impose restrictions to the probabilistic model. The taxonomy of problems, which is also valid for finite populations, is studied in depth for a simple EDA that considers independence among the variables of the problem. We provide the sufficient and necessary condition to decide the equivalence between functions and then we develop the operators to describe and count the members of a class. In addition, we show the intrinsic relation between univariate EDAs and the neighborhood system induced by the Hamming distance by proving that all the functions in the same class have the same number of local optima and that they are in the same ranking positions. Finally, we carry out numerical simulations in order to analyze the different behaviors that the algorithm can exhibit for the functions defined over the search space [Formula: see text]. PMID:23136917

Echegoyen, Carlos; Mendiburu, Alexander; Santana, Roberto; Lozano, Jose A

2013-01-01

493

[Type text] Convex Optimization + DEA Courses  

E-print Network

://vpnreg.ucs.ed.ac.uk/ease/selfreg.cgi. Note that this page is EASE protected so you cannot set a wifi password until you have first registered To use the computing labs and (eduroam) wifi, you will be given a temporary University of Edinburgh. The initial password for all of these accounts is natcor. What to do first: When you first log

Hall, Julian

494

Tensor Principal Component Analysis via Convex Optimization  

E-print Network

Dec 9, 2012 ... data, such as images, video, range data and medical data such as CT and ... Note that a variety of eigenvalues and eigenvectors of a real symmetric tensor .... some a ? Rn. Moreover, the CP rank of F is defined as follows.

2012-12-09

495

Conditional Gradient Sliding for Convex Optimization  

E-print Network

Oct 17, 2014 ... †Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611. (email: ... Our main goal in this paper is to show that, although the number of calls to the LO oracle cannot ...... Kluwer Academic.

2014-10-17

496

Modeling and optimization of the multiobjective stochastic joint replenishment and delivery problem under supply chain environment.  

PubMed

As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD) decision. In this paper, a new multiobjective stochastic JRD (MSJRD) of the one-warehouse and n-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonable replenishment interval, safety stock factor, and traveling routing. Secondly, two approaches are designed to handle this complex multi-objective optimization problem. Linear programming (LP) approach converts the multi-objective to single objective, while a multi-objective evolution algorithm (MOEA) solves a multi-objective problem directly. Thirdly, three intelligent optimization algorithms, differential evolution algorithm (DE), hybrid DE (HDE), and genetic algorithm (GA), are utilized in LP-based and MOEA-based approaches. Results of the MSJRD with LP-based and MOEA-based approaches are compared by a contrastive numerical example. To analyses the nondominated solution of MOEA, a metric is also used to measure the distribution of the last generation solution. Results show that HDE outperforms DE and GA whenever LP or MOEA is adopted. PMID:24302880

Wang, Lin; Qu, Hui; Liu, Shan; Dun, Cai-xia

2013-01-01

497

Modeling and Optimization of the Multiobjective Stochastic Joint Replenishment and Delivery Problem under Supply Chain Environment  

PubMed Central

As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD) decision. In this paper, a new multiobjective stochastic JRD (MSJRD) of the one-warehouse and n-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonable replenishment interval, safety stock factor, and traveling routing. Secondly, two approaches are designed to handle this complex multi-objective optimization problem. Linear programming (LP) approach converts the multi-objective to single objective, while a multi-objective evolution algorithm (MOEA) solves a multi-objective problem directly. Thirdly, three intelligent optimization algorithms, differential evolution algorithm (DE), hybrid DE (HDE), and genetic algorithm (GA), are utilized in LP-based and MOEA-based approaches. Results of the MSJRD with LP-based and MOEA-based approaches are compared by a contrastive numerical example. To analyses the nondominated solution of MOEA, a metric is also used to measure the distribution of the last generation solution. Results show that HDE outperforms DE and GA whenever LP or MOEA is adopted. PMID:24302880

Dun, Cai-xia

2013-01-01

498

Primal and dual formulations of sequential gradient-restoration algorithms for trajectory optimization problems  

NASA Technical Reports Server (NTRS)

One of the most effective first-order algorithms for solving trajectory optimization problems is the sequential gradient-restoration algorithm (SGRA). Originally developed in the primal formulation, this algorithm is extended to incorporate a dual formulation. Both the primal formulation and the dual formulation involve a sequence of two-phase cycles, each cycle including a gradient phase and a restoration phase. In turn, each iteration of the gradient phase and the restoration phase requires the solution of an auxiliary minimization problem (AMP). In the primal formulation, the AMP is solved with respect to the variations of the state, the control, and the parameter. In the dual formulation, the AMP is solved with respect to the Lagrange multipliers. A characteristic of the dual formulation is that the AMPs associated with the gradient phase and the restoration phase of SGRA can be reduced to mathematical programming problems involving a finite number of parameters as unknowns. A comparison of the primal formulation and the dual formulation is presented. The comparison is done in terms of several trajectory optimization problems having current aerospace interest.

Miele, A.; Wang, T.; Basapur, V. K.

1986-01-01

499

Fuzzy Random ?-Mean SAD Portfolio Selection Problem: An Ant Colony Optimization Approach  

NASA Astrophysics Data System (ADS)

To reach the investment goal, one has to select a combination of securities among different portfolios containing large number of securities. Only the past records of each security do not guarantee the future return. As there are many uncertain factors which directly or indirectly influence the stock market and there are also some newer stock markets which do not have enough historical data, experts' expectation and experience must be combined with the past records to generate an effective portfolio selection model. In this paper the return of security is assumed to be Fuzzy Random Variable Set (FRVS), where returns are set of random numbers which are in turn fuzzy numbers. A new ?-Mean Semi Absolute Deviation (?-MSAD) portfolio selection model is developed. The subjective opinions of the investors to the rate of returns of each security are taken into consideration by introducing a pessimistic-optimistic parameter vector ?. ?-Mean Semi Absolute Deviation (?-MSAD) model is preferred as it follows absolute deviation of the rate of returns of a portfolio instead of the variance as the measure of the risk. As this model can be reduced to Linear Programming Problem (LPP) it can be solved much faster than quadratic programming problems. Ant Colony Optimization (ACO) is used for solving the portfolio selection problem. ACO is a paradigm for designing meta-heuristic algorithms for combinatorial optimization problem. Data from BSE is used for illustration.

Thakur, Gour Sundar Mitra; Bhattacharyya, Rupak; Mitra, Swapan Kumar

2010-10-01

500

Bayesian Optimization Algorithm for the Non-unique Oligonucleotide Probe Selection Problem  

NASA Astrophysics Data System (ADS)

DNA microarrays are used in order to recognize the presence or absence of different biological components (targets) in a sample. Therefore, the design of the microarrays which includes selecting short Oligonucleotide sequences (probes) to be affixed on the surface of the microarray becomes a major issue. This paper focuses on the problem of computing the minimal set of probes which is able to identify each target of a sample, referred to as Non-unique Oligonucleotide Probe Selection. We present the application of an Estimation of Distribution Algorithm (EDA) named Bayesian Optimization Algorithm (BOA) to this problem, for the first time. The presented approach considers integration of BOA and state-of-the-art heuristics introduced for the non-unique probe selection problem. This approach provides results that compare favorably with the state-of-the-art methods. It is also able to provide biologists with more information about the dependencies between the probe sequences of each dataset.

Soltan Ghoraie, Laleh; Gras, Robin; Wang, Lili; Ngom, Alioune