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Traveling salesman problem.

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The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance.

Traveling-salesman problem. --- TSP (Traveling salesman problem) --- Combinatorial optimization --- Graph theory --- Vehicle routing problem --- Computer modelling & simulation

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"What is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics--and it has defied solution to this day. In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it. Cook examines the origins and history of the salesman problem and explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets. He looks at how computers stack up against the traveling salesman problem on a grand scale, and discusses how humans, unaided by computers, go about trying to solve the puzzle. Cook traces the salesman problem to the realms of neuroscience, psychology, and art, and he also challenges readers to tackle the problem themselves. The traveling salesman problem is--literally--a $1 million question. That's the prize the Clay Mathematics Institute is offering to anyone who can solve the problem or prove that it can't be done. In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem"--

Traveling salesman problem. --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- TSP (Traveling salesman problem) --- Combinatorial optimization --- Graph theory --- Vehicle routing problem

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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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This book constitutes the refereed post-conference proceedings of the 6th International Conference on Variable Neighborhood Search, ICVNS 2018, held in Sithonia, Greece, in October 2018. ICVNS 2018 received 49 submissions of which 23 full papers were carefully reviewed and selected. VNS is a metaheuristic based on systematic changes in the neighborhood structure within a search for solving optimization problems and related tasks. The main goal of ICVNS 2018 was to provide a stimulating environment in which researchers coming from various scientific fields could share and discuss their knowledge, expertise, and ideas related to the VNS metaheuristic and its applications.

Electronic data processing. --- Computational complexity. --- Computer software. --- Data structures (Computer scienc. --- Mathematical optimization. --- Numeric Computing. --- Discrete Mathematics in Computer Science. --- Algorithm Analysis and Problem Complexity. --- Data Structures. --- Optimization. --- Data structures (Computer science) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Software, Computer --- Computer systems --- Complexity, Computational --- Electronic data processing --- Machine theory --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Automation --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science) --- Traveling salesman problem --- TSP (Traveling salesman problem) --- Combinatorial optimization --- Graph theory --- Vehicle routing problem --- Numerical analysis. --- Computer science—Mathematics. --- Algorithms. --- Data structures (Computer science). --- Algorism --- Algebra --- Arithmetic --- Foundations --- Discrete mathematics. --- Artificial intelligence—Data processing. --- Numerical Analysis. --- Data Science. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Computer science --- Artificial intelligence --- Mathematics. --- Data processing.