Combinatorial And Global Optimization

Author : Panos M Pardalos,Athanasios Migdalas,Rainer E Burkard
Publisher : World Scientific
Page : 372 pages
File Size : 55,6 Mb
Release : 2002-04-05
Category : Mathematics
ISBN : 9789814489652

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Combinatorial and Global Optimization by Panos M Pardalos,Athanasios Migdalas,Rainer E Burkard Pdf

Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated Goemans–Williamson relaxation of the maximum cut problem, and the Du–Hwang solution of the Gilbert–Pollak conjecture. Since integer constraints are equivalent to nonconvex constraints, the fundamental difference between classes of optimization problems is not between discrete and continuous problems but between convex and nonconvex optimization problems. This volume is a selection of refereed papers based on talks presented at a conference on “Combinatorial and Global Optimization” held at Crete, Greece. Contents:A Forest Exterior Point Algorithm for Assignment Problems (H Achatz et al.)Location/Allocation of Queuing Facilities in Continuous Space Using Minsum and Minimax Criteria (J Brimberg et al.)Algorithms for the Consistency Analysis in Scenario Projects (R Feldmann et al.)Solving Quadratic Knapsack Problems by Reformulation and Tabu Search. Single Constraint Case (F Glover et al.)Global Optimization Using Dynamic Search Trajectories (A A Groenwold & J A Snyman)On Pareto Efficiency. A General Constructive Existence Principle (G Isac)Piecewise Linear Network Flow Problems (D Kim & P M Pardalos)Semidefinite Programming Approaches for MAX-2-SAT and MAX-3-SAT: Computational Perspectives (E de Klerk & J P Warners)Heuristic Solutions of Vehicle Routing Problems in Supply Chain Management (Y Marinakis & A Migdalas)A New Finite Cone Covering Algorithm for Concave Minimization (C Meyer & B Jaumard)Frequency Assignment for Very Large, Sparse Networks (R Murphey)GPS Network Design: An Application of the Simulated Annealing Heuristic Technique (H A Saleh & P J Dare)Normal Branch and Bound Algorithms for General Nonconvex Quadratic Programming (H Tuy)and other papers Readership: Researchers in numerical & computational mathematics, optimization, combinatorics & graph theory, networking and materials engineering. Keywords:Combinatorial Optimization;Global Optimization

Author : Dingzhu Du,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 808 pages
File Size : 45,9 Mb
Release : 1998
Category : Mathematics
ISBN : 0792350189

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Handbook of combinatorial optimization. 1 by Dingzhu Du,Panos M. Pardalos Pdf

The first of a multi-volume set, which deals with several algorithmic approaches for discrete problems as well as many combinatorial problems. It is addressed to researchers in discrete optimization, and to all scientists who use combinatorial optimization methods to model and solve problems.

Author : Ajith Abraham,Aboul-Ella Hassanien,Patrick Siarry,Andries Engelbrecht
Publisher : Springer
Page : 528 pages
File Size : 48,8 Mb
Release : 2009-05-01
Category : Computers
ISBN : 9783642010859

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Foundations of Computational Intelligence Volume 3 by Ajith Abraham,Aboul-Ella Hassanien,Patrick Siarry,Andries Engelbrecht Pdf

Global optimization is a branch of applied mathematics and numerical analysis that deals with the task of finding the absolutely best set of admissible conditions to satisfy certain criteria / objective function(s), formulated in mathematical terms. Global optimization includes nonlinear, stochastic and combinatorial programming, multiobjective programming, control, games, geometry, approximation, algorithms for parallel architectures and so on. Due to its wide usage and applications, it has gained the attention of researchers and practitioners from a plethora of scientific domains. Typical practical examples of global optimization applications include: Traveling salesman problem and electrical circuit design (minimize the path length); safety engineering (building and mechanical structures); mathematical problems (Kepler conjecture); Protein structure prediction (minimize the energy function) etc. Global Optimization algorithms may be categorized into several types: Deterministic (example: branch and bound methods), Stochastic optimization (example: simulated annealing). Heuristics and meta-heuristics (example: evolutionary algorithms) etc. Recently there has been a growing interest in combining global and local search strategies to solve more complicated optimization problems. This edited volume comprises 17 chapters, including several overview Chapters, which provides an up-to-date and state-of-the art research covering the theory and algorithms of global optimization. Besides research articles and expository papers on theory and algorithms of global optimization, papers on numerical experiments and on real world applications were also encouraged. The book is divided into 2 main parts.

Author : Daniel Scholz
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 41,5 Mb
Release : 2011-11-06
Category : Mathematics
ISBN : 9781461419518

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Deterministic Global Optimization by Daniel Scholz Pdf

This monograph deals with a general class of solution approaches in deterministic global optimization, namely the geometric branch-and-bound methods which are popular algorithms, for instance, in Lipschitzian optimization, d.c. programming, and interval analysis.It also introduces a new concept for the rate of convergence and analyzes several bounding operations reported in the literature, from the theoretical as well as from the empirical point of view. Furthermore, extensions of the prototype algorithm for multicriteria global optimization problems as well as mixed combinatorial optimization problems are considered. Numerical examples based on facility location problems support the theory. Applications of geometric branch-and-bound methods, namely the circle detection problem in image processing, the integrated scheduling and location makespan problem, and the median line location problem in the three-dimensional space are also presented. The book is intended for both researchers and students in the areas of mathematics, operations research, engineering, and computer science.

Author : David Gao,Ning Ruan,Wenxun Xing
Publisher : Springer
Page : 522 pages
File Size : 52,5 Mb
Release : 2014-11-11
Category : Mathematics
ISBN : 9783319083773

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Advances in Global Optimization by David Gao,Ning Ruan,Wenxun Xing Pdf

This proceedings volume addresses advances in global optimization—a multidisciplinary research field that deals with the analysis, characterization and computation of global minima and/or maxima of nonlinear, non-convex and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation and complex simulation and supply chain analysis.

Author : Panos M. Pardalos,Judah Ben Rosen
Publisher : Springer
Page : 160 pages
File Size : 48,8 Mb
Release : 1987
Category : Computers
ISBN : UOM:39015015631529

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Constrained Global Optimization by Panos M. Pardalos,Judah Ben Rosen Pdf

Author : Christos H. Papadimitriou,Kenneth Steiglitz
Publisher : Courier Corporation
Page : 528 pages
File Size : 45,7 Mb
Release : 2013-04-26
Category : Mathematics
ISBN : 9780486320137

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Combinatorial Optimization by Christos H. Papadimitriou,Kenneth Steiglitz Pdf

This graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; local search heuristics for NP-complete problems, more. 1982 edition.

Author : Panos M. Pardalos,J. Ben Rosen
Publisher : Springer
Page : 156 pages
File Size : 50,8 Mb
Release : 1987-07-15
Category : Mathematics
ISBN : PURD:32754003363664

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Constrained Global Optimization: Algorithms and Applications by Panos M. Pardalos,J. Ben Rosen Pdf

Global optimization is concerned with the characterization and computation of global minima or maxima of nonlinear functions. Such problems are widespread in mathematical modeling of real world systems for a very broad range of applications. The applications include economies of scale, fixed charges, allocation and location problems, quadratic assignment and a number of other combinatorial optimization problems. More recently it has been shown that certain aspects of VLSI chip design and database problems can be formulated as constrained global optimization problems with a quadratic objective function. Although standard nonlinear programming algorithms will usually obtain a local minimum to the problem , such a local minimum will only be global when certain conditions are satisfied (such as f and K being convex).

Author : Ajith Abraham,Aboul-Ella Hassanien,Patrick Siarry,Andries Engelbrecht
Publisher : Springer
Page : 0 pages
File Size : 51,6 Mb
Release : 2010-10-28
Category : Computers
ISBN : 3642101658

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Foundations of Computational Intelligence Volume 3 by Ajith Abraham,Aboul-Ella Hassanien,Patrick Siarry,Andries Engelbrecht Pdf

Global optimization is a branch of applied mathematics and numerical analysis that deals with the task of finding the absolutely best set of admissible conditions to satisfy certain criteria / objective function(s), formulated in mathematical terms. Global optimization includes nonlinear, stochastic and combinatorial programming, multiobjective programming, control, games, geometry, approximation, algorithms for parallel architectures and so on. Due to its wide usage and applications, it has gained the attention of researchers and practitioners from a plethora of scientific domains. Typical practical examples of global optimization applications include: Traveling salesman problem and electrical circuit design (minimize the path length); safety engineering (building and mechanical structures); mathematical problems (Kepler conjecture); Protein structure prediction (minimize the energy function) etc. Global Optimization algorithms may be categorized into several types: Deterministic (example: branch and bound methods), Stochastic optimization (example: simulated annealing). Heuristics and meta-heuristics (example: evolutionary algorithms) etc. Recently there has been a growing interest in combining global and local search strategies to solve more complicated optimization problems. This edited volume comprises 17 chapters, including several overview Chapters, which provides an up-to-date and state-of-the art research covering the theory and algorithms of global optimization. Besides research articles and expository papers on theory and algorithms of global optimization, papers on numerical experiments and on real world applications were also encouraged. The book is divided into 2 main parts.

Author : Christodoulos A. Floudas,Panos M. Pardalos,Claire Adjiman,William R. Esposito,Zeynep H. Gümüs,Stephen T. Harding,John L. Klepeis,Clifford A. Meyer,Carl A. Schweiger
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 50,6 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9781475730401

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Handbook of Test Problems in Local and Global Optimization by Christodoulos A. Floudas,Panos M. Pardalos,Claire Adjiman,William R. Esposito,Zeynep H. Gümüs,Stephen T. Harding,John L. Klepeis,Clifford A. Meyer,Carl A. Schweiger Pdf

This collection of challenging and well-designed test problems arising in literature studies also contains a wide spectrum of applications, including pooling/blending operations, heat exchanger network synthesis, homogeneous azeotropic separation, and dynamic optimization and optimal control problems.

Author : Hassan AbouEisha,Talha Amin,Igor Chikalov,Shahid Hussain,Mikhail Moshkov
Publisher : Springer
Page : 280 pages
File Size : 52,7 Mb
Release : 2018-05-22
Category : Technology & Engineering
ISBN : 9783319918396

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Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining by Hassan AbouEisha,Talha Amin,Igor Chikalov,Shahid Hussain,Mikhail Moshkov Pdf

Dynamic programming is an efficient technique for solving optimization problems. It is based on breaking the initial problem down into simpler ones and solving these sub-problems, beginning with the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. This book develops extensions of dynamic programming, enabling us to (i) describe the set of objects under consideration; (ii) perform a multi-stage optimization of objects relative to different criteria; (iii) count the number of optimal objects; (iv) find the set of Pareto optimal points for bi-criteria optimization problems; and (v) to study relationships between two criteria. It considers various applications, including optimization of decision trees and decision rule systems as algorithms for problem solving, as ways for knowledge representation, and as classifiers; optimization of element partition trees for rectangular meshes, which are used in finite element methods for solving PDEs; and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths. The results presented are useful for researchers in combinatorial optimization, data mining, knowledge discovery, machine learning, and finite element methods, especially those working in rough set theory, test theory, logical analysis of data, and PDE solvers. This book can be used as the basis for graduate courses.

Author : Ding-Zhu Du,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 45,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475730234

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Handbook of Combinatorial Optimization by Ding-Zhu Du,Panos M. Pardalos Pdf

Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air line crew scheduling, corporate planning, computer-aided design and man ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi tion, linear programming relaxations are often the basis for many approxi mation algorithms for solving NP-hard problems (e.g. dual heuristics).

Author : Godfrey C. Onwubolu,Donald Davendra
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 47,5 Mb
Release : 2009-01-13
Category : Computers
ISBN : 9783540921509

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Differential Evolution: A Handbook for Global Permutation-Based Combinatorial Optimization by Godfrey C. Onwubolu,Donald Davendra Pdf

This is the first book devoted entirely to Differential Evolution (DE) for global permutative-based combinatorial optimization. Since its original development, DE has mainly been applied to solving problems characterized by continuous parameters. This means that only a subset of real-world problems could be solved by the original, classical DE algorithm. This book presents in detail the various permutative-based combinatorial DE formulations by their initiators in an easy-to-follow manner, through extensive illustrations and computer code. It is a valuable resource for professionals and students interested in DE in order to have full potentials of DE at their disposal as a proven optimizer. All source programs in C and Mathematica programming languages are downloadable from the website of Springer.

Author : Svetlana Stepanenko
Publisher : Sudwestdeutscher Verlag Fur Hochschulschriften AG
Page : 0 pages
File Size : 44,5 Mb
Release : 2009
Category : Electronic
ISBN : 3838103424

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Global Optimization Methods based on Tabu Search by Svetlana Stepanenko Pdf

Many activities can be formulated as optimization problems. Because of the computational complexity of these problems, exact optimization techniques of operations research like linear programming or dynamic programming are for the most part unfeasible for large-scale problems. Therefore, researchers, engineers, and scientists have used metaheuristic search techniques to find near optimal, good-enough optimal or even the global solutions. This work encompasses three parts. The first part provides a concise review of the most prominent metaheuristic concepts currently available and gives essential preliminaries together with definition of the combinatorial optimization problems. In the second part the new nonlinear global optimization routines based on the TS strategy are described: the Gradient Tabu Search (GTS), the Gradient Only Tabu Search (GOTS), and the Tabu Search with Powell's Algorithm (TSPA). The new algorithms are compared with other approaches using various well-known test functions with varying dimensionality. In the last part of the work the GOTS is applied for global minimum energy conformation.

Author : Michal Mankowski,Mikhail Moshkov
Publisher : Springer Nature
Page : 213 pages
File Size : 48,9 Mb
Release : 2021-02-08
Category : Technology & Engineering
ISBN : 9783030639204

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Dynamic Programming Multi-Objective Combinatorial Optimization by Michal Mankowski,Mikhail Moshkov Pdf

This book introduces a fairly universal approach to the design and analysis of exact optimization algorithms for multi-objective combinatorial optimization problems. It proposes the circuits without repetitions representing the sets of feasible solutions along with the increasing and strictly increasing cost functions as a model for such problems. The book designs the algorithms for multi-stage and bi-criteria optimization and for counting the solutions in the framework of this model. As applications, this book studies eleven known combinatorial optimization problems: matrix chain multiplication, global sequence alignment, optimal paths in directed graphs, binary search trees, convex polygon triangulation, line breaking (text justification), one-dimensional clustering, optimal bitonic tour, segmented least squares, optimization of matchings in trees, and 0/1 knapsack problem. The results presented are useful for researchers in combinatorial optimization. This book is also useful as the basis for graduate courses.