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The quadratic binary optimization problem (QUBO) is a versatile combinatorial optimization model with a variety of applications and rich theoretical properties. Application areas of the model include finance, cluster analysis, traffic management, machine scheduling, VLSI physical design, physics, quantum computing, engineering, and medicine. In addition, various mathematical optimization models can be reformulated as a QUBO, including the resource constrained assignment problem, set partitioning problem, maximum cut problem, quadratic assignment problem, the bipartite unconstrained binary optimization problem, among others. This book presents a systematic development of theory, algorithms, and applications of QUBO. It offers a comprehensive treatment of QUBO from various viewpoints, including a historical introduction along with an in-depth discussion of applications modelling, complexity and polynomially solvable special cases, exact and heuristic algorithms, analysis of approximation algorithms, metaheuristics, polyhedral structure, probabilistic analysis, persistencies, and related topics. Available software for solving QUBO is also introduced, including public domain, commercial, as well as quantum computing based codes.
Numerical methods of optimisation --- Operational research. Game theory --- Discrete mathematics --- Mathematical statistics --- Planning (firm) --- Business management --- Computer science --- Computer. Automation --- quantumcomputers --- discrete wiskunde --- management --- mathematische modellen --- econometrie --- wiskunde --- algoritmen --- operationeel onderzoek --- Mathematical optimization. --- Quadratic programming. --- Binary system (Mathematics)
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This volume, which contains chapters written by reputable researchers, provides the state of the art in theory and algorithms for the traveling salesman problem (TSP). The book covers all important areas of study on TSP, including polyhedral theory for symmetric and asymmetric TSP, branch and bound, and branch and cut algorithms, probabilistic aspects of TSP, thorough computational analysis of heuristic and metaheuristic algorithms, theoretical analysis of approximation algorithms, including the emerging area of domination analysis of algorithms, discussion of TSP software and variations of TSP such as bottleneck TSP, generalized TSP, prize collecting TSP, maximizing TSP, orienteering problem, etc. Audience This book is intended for researchers, practitioners, and academicians in mathematics, computer science, and operations research. It is appropriate as a reference work or as a main or supplemental textbook in graduate and senior undergraduate courses and projects.
Combinatorial optimization. --- Traveling-salesman problem. --- Traveling-salesman problem --- Combinatorial optimization --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Computer Science --- Algebra --- Optimization, Combinatorial --- TSP (Traveling salesman problem) --- Computer science. --- Operations research. --- Decision making. --- Computer science --- Algorithms. --- Mathematical optimization. --- Computer Science. --- Discrete Mathematics in Computer Science. --- Optimization. --- Operation Research/Decision Theory. --- Mathematics. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algorism --- Arithmetic --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Informatics --- Science --- Foundations --- Decision making --- Computer science—Mathematics. --- Operations Research/Decision Theory. --- Traveling salesman problem. --- Combinatorial analysis --- Mathematical optimization --- Graph theory --- Vehicle routing problem
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Mathematical optimization. --- Quadratic programming. --- Binary system (Mathematics) --- Base two numeration --- Binary-quaternary system --- Binary scale --- Numeration, Base two --- Pair system --- Computer arithmetic --- Mathematics --- Numeration --- Nonlinear programming --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis
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