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Branch and bound algorithms --- Refuse and refuse disposal --- Mathematical Models

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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.

Mathematical optimization. --- Mathematical optimization --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Branch and bound algorithms. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematics. --- Algorithms. --- Computer mathematics. --- Operations research. --- Management science. --- Optimization. --- Operations Research, Management Science. --- Computational Science and Engineering. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algorithms --- Network analysis (Planning) --- Programming (Mathematics) --- Computer science. --- Algorism --- Algebra --- Arithmetic --- Informatics --- Science --- Foundations --- Quantitative business analysis --- Management --- Problem solving --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Computer mathematics --- Electronic data processing --- Mathematics

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There are a variety of combinatorial optimization problems that are relevant to the examination of statistical data. Combinatorial problems arise in the clustering of a collection of objects, the seriation (sequencing or ordering) of objects, and the selection of variables for subsequent multivariate statistical analysis such as regression. The options for choosing a solution strategy in combinatorial data analysis can be overwhelming. Because some problems are too large or intractable for an optimal solution strategy, many researchers develop an over-reliance on heuristic methods to solve all combinatorial problems. However, with increasingly accessible computer power and ever-improving methodologies, optimal solution strategies have gained popularity for their ability to reduce unnecessary uncertainty. In this monograph, optimality is attained for nontrivially sized problems via the branch-and-bound paradigm. For many combinatorial problems, branch-and-bound approaches have been proposed and/or developed. However, until now, there has not been a single resource in statistical data analysis to summarize and illustrate available methods for applying the branch-and-bound process. This monograph provides clear explanatory text, illustrative mathematics and algorithms, demonstrations of the iterative process, psuedocode, and well-developed examples for applications of the branch-and-bound paradigm to important problems in combinatorial data analysis. Supplementary material, such as computer programs, are provided on the world wide web. Dr. Brusco is a Professor of Marketing and Operations Research at Florida State University, an editorial board member for the Journal of Classification, and a member of the Board of Directors for the Classification Society of North America. Stephanie Stahl is an author and researcher with years of experience in writing, editing, and quantitative psychology research.

Combinatorial analysis. --- Branch and bound algorithms. --- Analyse combinatoire --- Algorithmes de séparation et évaluation --- Combinatorial analysis --- Branch and bound algorithms --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematical Statistics --- Combinatorics --- Mathematics. --- Operations research. --- Decision making. --- Management science. --- Discrete mathematics. --- Statistics. --- Discrete Mathematics. --- Statistics and Computing/Statistics Programs. --- Operation Research/Decision Theory. --- Operations Research, Management Science. --- Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law. --- Statistics for Social Science, Behavioral Science, Education, Public Policy, and Law. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Math --- Science --- Decision making --- Algorithms --- Network analysis (Planning) --- Programming (Mathematics) --- Mathematical analysis --- Mathematical statistics. --- Operations Research/Decision Theory. --- Statistics for Social Sciences, Humanities, Law. --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistics . --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis