Book Description

Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial--geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space.The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory.Audience: Researchers in network design, applied optimization, and design of algorithms. ... Read more

Book Description

This book should be considered as an introduction to a specialclass of hierarchical systems of optimal control, where subsystems aredescribed by partial differential equations of various types.Optimization is carried out by means of a two-level scheme, where thecenter optimizes coordination for the upper level and subsystems findthe optimal solutions for independent local problems. The mainalgorithm is a method of iterative aggregation. The coordinator solvesthe problem with macrovariables, whose number is less than the numberof initial variables. On the lower level, we have the usual optimalcontrol problems of mathematical physics, which are far simpler thanthe initial statements. Thus, we bridge the gap between twodisciplines: optimization theory of large-scale systems andmathematical physics. The first motivation was a special model ofbranch planning, where the final product obeys a precept assortmentrelation. Audience: The monograph is addressed to specialists inoperations research, optimization, optimal control, and mathematicalphysics. ... Read more

Book Description

This monograph is devoted to transportation problems withminimax criteria. The cost function of the classical transportationproblem contains tariff coefficients. It is a common situation thatthe decision-maker does not know their values. In other situations,they do not have any meaning at all, and neither do nonlinear tariffobjective functions. Instead of the classical cost function, a minimax cost function isintroduced. In other words, a matrix with the minimal largest elementis sought in the class of matrices with non-negative elements andgiven sums of row and column elements. The problem may also beinterpreted as follows: suppose that the shipment time is proportionalto the amount to be shipped. Then, the minimax gives the minimal timerequired to complete all shipments. An algorithm for finding theminimax and the corresponding matrix is developed. An extension tointeger matrices is presented. Alternative minimax criteria are alsoconsidered. The solutions obtained are important for the theory oftransportation polyhedrons. They determine the vertices of convexhulls of the sets of basis vector pairs and the corresponding matricesof solutions. Audience: The monograph is addressed to specialists inoperations research, optimization, and transportation problems. ... Read more

Book Description

The book presents and discusses theoretical and practical developments in the field of optimization. All papers contain new results and the emphasis has been put on the accessibility of each paper for researchers working in optimization. The topics covered in this volume include: - Mathematical programming. - Nonsmooth analysis. - Equilibrium and fixed point theory. - Stochastic programming. - Optimal control. - Global optimization. - Multicriteria optimization. ... Read more

Book Description

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the `G. Stampacchia' School of Mathematics of the `E. Majorana' Centre for Scientific Culture, June 23--July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of nonlinear optimization, and of related topics such as convex optimization, nonsmooth optimization, variational inequalities and complementarity problems. ... Read more

Book Description

This book provides tools for making decisions in an environmentof uncertainty. In Chapter 1 the author explains the most importantaspects of the concept of relation. From this start arise the otherthree concepts that cover practically all processes from whichdecisions stem. These three concepts are: attribution from which theconcept of assignment arises; and grouping, which includes the conceptof an original function. The techniques presented, as well as themodels and algorithms developed, constitute an invaluable aid forthose who must make decisions. Audience: Researchers and graduate students interested inmathematics applied to economics and management. ... Read more

Book Description

The first objective of this book is to provide an up-to-date exposition of the techniques that are available for optimizing complex systems and to do so in a way that unifies the theory of nondifferentiable and two-level mathematical programming. The second objective is to highlight the most effective algorithms developed for solving a particular instance of the two-level problem known as a static Stackelberg game. In approaching these objectives, close attention is paid to two ideas: (i) the integration of material on differentiable and nondifferentiable mathematical programming, and (ii) the treatment of various two-level mathematical programming problems in a unified manner.This book is intended for the use of researchers, graduate students and practitioners specializing in systems optimization and its applications. In particular, operations researchers, system designers, management scientists, control engineers and mathematicians who work on either applied or theoretical aspects of optimization will find the book useful and beneficial. ... Read more

Book Description

Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimizations comprises a carefully refereed selection of extended versions of the best papers presented at the Second Meta-Heuristics Conference (MIC 97). The selected articles describe the most recent developments in theory and applications of meta-heuristics, heuristics for specific problems, and comparative case studies. The book is divided into six parts, grouped mainly by the techniques considered. The extensive first part with twelve papers covers tabu search and its application to a great variety of well-known combinatorial optimization problems (including the resource-constrained project scheduling problem and vehicle routing problems). In the second part we find one paper where tabu search and simulated annealing are investigated comparatively and two papers which consider hybrid methods combining tabu search with genetic algorithms. The third part has four papers on genetic and evolutionary algorithms. Part four arrives at a new paradigm within meta-heuristics. The fifth part studies the behavior of parallel local search algorithms mainly from a tabu search perspective. The final part examines a great variety of additional meta-heuristics topics, including neural networks and variable neighbourhood search as well as guided local search. Furthermore, the integration of meta-heuristics with the branch-and-bound paradigm is investigated. ... Read more

Reviews (2)

Decision Support
Once one has read the articles in this book it becomes clear that meta-heuristics are intelligently designed methods to provide decision makers with tools for decision support. Each chapter is self-contained and provides different insights into specific methods (especially genetic algorithms, neural networks, tabu search, simulated annealing). These methods are well explored and explained by means of theoretical as well as practical results, e.g., for vehicle routing or mail delivery or generalized assignment. Ideas on how to implement the methods are also provided. Most papers are easy to read with only some preliminaries in mathematics (or combinatorial optimization). The chapters are carefully collected and could have been accepted for high-quality journals as well. Well done.

this book must be good@
i have no idea what it is avbout, but it looks really cool from the name and totally confusing nature of it. ... Read more

Book Description

The topology of global optimization is treated in detail (Morse Theory, Karush--Kuhn--Tucker points, Chebyshev Approximation). Moreover, three further basic subjects in nonlinear optimization are treated: Stability and sensitivity, gradient- and Newton's differential equations and, finally, parametric aspects.

Audience: Researchers and graduate students working in optimization and operations research. ... Read more

Book Description

The book consists of research papers based on results presentedat a conference held in Sweden to celebrate Hoang Tuy's achievementsin Optimization. The collection is dedicated to Professor Tuy on theoccasion of his 70th birthday. The papers appear in alphabetical order by first author and cover awide range of recent results in Mathematical Programming. The work ofHoang Tuy, in particular in Global Optimization, has provideddirections for new algorithmic developments in the field. Audience: Faculty, graduate students, and researchers inmathematical programming, computer science and engineering. ... Read more

Book Description

Evolutionary Algorithms, such as Evolution Strategies, Genetic Algorithms, or Evolutionary Programming, have found broad acceptance in the last ten years. In contrast to the broad propagation and the resulting practical prosperity in different scientific fields, the theory has not progressed as much. This monograph provides the framework and the first steps toward the theoretical analysis of Evolution Strategies (ES). The main emphasis is on understanding the functioning of these probabilistic optimization algorithms in real-valued search spaces by investigating the dynamical properties of some well-established ES algorithms on simple objective functions. The book introduces the basic concepts of such an analysis, such as the progress rate, the quality gain, and the self-adaptation response, and shows how to calculate these quantities. Based on this analysis, functioning principles are derived, aiming at a qualitative understanding of why and how ES algorithms do work. ... Read more

Reviews (1)

The first of its kind
This is the first book that I am aware of that addresses the foundations of evolutionary and genetic algorithms, evolution strategies, and evolutionary programming from a rigorous mathematical point of view. The book is designed for an audience of mathematicians and computer scientists who are curious about evolutionary strategies and need a formal treatment of its foundations. Readers currently involved in designing and writing genetic programs will find this book helpful in the optimizing of their algorithms, even though at times they might find the presentation a little heavy-handed.

Evolutionary strategies are thought of as dynamical systems in the book, but these are not in general deterministic, but probabilistic in nature. The state space of the dynamical system consists of the direct product of an object parameter space, an endogenous strategy parameter set, and a collection of fitness functions. Evolution takes place in this state space via the "genetic operators", i.e. the selection, mutation, reproduction, and recombination operators. The goal of course is to find an optimum solution to the problem, and so a consideration of the convergence of the evolution strategy to this optimum must be addressed.

These issues and others, such as the differentiation between evolutionary strategies and ordinary Monte Carlo methods, are discussed in great detail in the book. The author emphasizes that the mechanism of evolutionary strategies lies in the local properties of state space, the evolutionary process being obtained by small steps in this space. He also suggests three prerequisites for the working of evolutionary algorithms, namely the evolutionary progress principle, the genetic repair hypothesis, and mutation-induced operation by recombination. The first is the statement that each change of the individuals in the state space can result in fitness gain as well as fitness loss. The second is a device employed for statistical estimation, and attempts to answer why recombinant evolution strategies are better than nonrecombinant strategies. The third is the statement that dominant recombination causes cohesion of a population and is represented by a local operator which transforms the mutations by a random sampling process.

The author makes use of differential geometry in the book to establish a theoretical framework to predict the local performance of evolution strategies. The hypersurface model is constructed as a fitness model for the calculation of progress measures, and for an elementary model of evolution dynamics. Tensor calculus is employed to study deformations of the sphere model, with the goal of obtaining useful formulae for the progress rate. A mean radius of this deformation is calculated, to serve as a substitute radius in the progress rate formulae for the sphere model.

For the case of (1+1)-selection, i.e. one parent and one offspring, where both parents and offspring are contained in the selection pool, the author derives exact integral representations for the progress rate. The quality gain for one parent and any member of offspring is also considered, and the author derives an integral expression for it using an approximation of the distribution function of the mutation-induced fitness distribution. He argues that the progress rate and the quality gain are progress measures that describe totally different aspects of the performance of evolution strategies.

The general problem of an evolution strategy with arbitrary numbers of parents and offspring is also considered. Since the distribution of parents in the parameter space is unknow, and since it changes in successive generations, this makes the analysis of the progress rate extremely difficult. The author does however derive the relations for this model in terms of a formal expression for the progress rate which is given as an integral over the distribution of a single descendant, which is generation-dependent and unknown. This distribution is approximated using Hermite polynomials and the determination of this function is then reduced to the finding of a collection of coefficients. These coefficients are functions of moments of the offspring and are estimated by the random selection process of the evolution strategy.

Recombinative evolution strategies are also studied by the author, and two special recombination types considered, namely the intermediate and dominant cases. Intermediate recombination is shown to lead to higher performance compared to nonrecombinativie strategies. The dominant case is shown to lead to mutation-induced speciation by recombination.

The author also analyzes the dynamic adaptation of the mutation strength to the local topology of the fitness landscape. Self-adaptation, which is the method for applying evolution to the adjustment of optimal strategy parameter values, is given detailed treatment for the case of one parent in terms of mean value dynamics. ... Read more

Book Description

Randomization techniques have been employed to solve numerousproblems of computing both sequentially and in parallel. Examples ofrandomized algorithms that are asymptotically better than theirdeterministic counterparts in solving various fundamental problemsabound. Randomized algorithms have the advantages of simplicity andbetter performance both in theory and often in practice. Thistwo-volume handbook is a collection of articles written by renownedexperts and cover a wide spectrum of issues in Randomization. Thehandbook will be a valuable reference for all the important areas ofalgorithm design, including those essential to its applications incomputer science and engineering.Audience: The handbook is addressed to faculty, graduatestudents, and researchers in all areas of computer sciences,mathematics, operations research, and engineering. ... Read more

Book Description

The numerous advances in mathematical programming have openedup new insights about sensitivity analysis. The paradigm `What if...?'question is no longer the only question of interest. Often, we want toknow `Why...?' and `Why not...?' Such questions were not analyzed inthe early years of mathematical programming to the same extent thatthey are now, and we have not only expanded our thinking about`post-optimal analysis', but also about `solution analysis', even ifthe solution obtained is not optimal. Therefore, it is now time to examine all the recent advances onsensitivity analysis and parametric programming. This book combinesthe origins of sensitivity analysis with the state of the art. Itcovers much of the traditional approaches with a modern perspective,and shows recent results using the optimal partition approach,stemming from interior methods, for both linear and quadraticprogramming. It examines the special case of network models. Itpresents a neglected topic, qualitative sensitivity analysis, as wellas elements of mixed integer programming and gives a modernperspective of nonlinear programming. It provides recent advances inmulti-criteria mathematical programming and also describes thestate-of-the-art in stochastic programming. It covers recent advancesin understanding redundancy in quadratic programs, considers anapproach to diagnosing infeasibility in linear and nonlinear programs,and gives an overview of sensitivity analysis for fuzzy mathematicalprogramming. ... Read more

Book Description

This Handbook is intended for use by researchers and students working in the fields of engineering, economics, and management science. ... Read more

Book Description

Performance analysis of modern communication systems has lead to a revision and sharpening of nonlinear stability analysis techniques developed over the last century. Applicability of such techniques involves a number of areas, including: process control systems, active queue management in data networks, and other branches of engineering.This monograph presents some recent performance analysis results within a unified stability analysis framework. Several interesting counterexamples to the existing nonlinear stability theory are given. Additionally, several cutting-edge case studies from air traffic control systems and data networks are presented to further illustrate the applications of the theory. The main theoretical results build upon the well-established multiplier theory, which has received much interest because of recent advances in software packages such as the linear matrix inequality (LMI) toolbox.The exposition demonstrates the existence of monotone nonlinearites in problems of interest and gives an exhaustive stability analysis treatment of systems containing such nonlinearities.Key features: * broad range of topics: stability analysis, monotone nonlinearities, multiplier theory, service quality in data networks, protocol scalability, air traffic congestion control * recent and original results presented * many examples and case studies illustrate the applicability of the theory * comprehensive glossaries, bibliography, index, and appendices"Qualitative Nonlinear Dynamics of Communication Networks" is a useful reference for graduate students, and practitioners in control, computer, electrical, aerospace, and mechanical engineering. It can be used as a supplementary text for nonlinear stability courses at the graduate level. Prerequisites are a familiarity with elementary control theory, linear systems theory, matrix theory, and functional analysis. ... Read more

Book Description

This volume contains refereed papers presented at the workshop on"Semidefinite Programming and Interior-Point Approaches forCombinatorial Optimization Problems" held at The FieldsInstitute in May 1996. Semidefinite programming (SDP) is ageneralization of linear programming (LP) in that thenonnegativity constraints on the variables are replaced by apositive semidefinite constraint on matrix variables. Many ofthe elegant theoretical properties and powerful solutiontechniques follow through from LP to SDP. In particular, theprimal-dual interior-point methods, which are currently sosuccessful for LP, can be used to efficiently solve SDPproblems.

In addition to the interesting theoretical and algorithmicquestions, SDP has found many important applications incombinatorial optimization, control theory and other areas ofmathematical programming. SDP is currently a very hot area ofresearch. The papers in this volume cover a wide spectrum ofrecent developments in SDP. The volume would be suitable as atextbook for advanced courses in optimization. ... Read more