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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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The Vehicle Routing Problem (VRP) dates back to the end of the fifties of the last century when Dantzig and Ramser set the mathematical programming formulation and algorithmic approach to solve the problem of delivering gasoline to service stations. Since then the interest in VRP evolved from a small group of mathematicians to a broad range of researchers and practitioners from different disciplines who are involved in this field today. Nine chapters of this book present recent improvements, innovative ideas and concepts regarding the vehicle routing problem. It will be of interest to students, researchers and practitioners with knowledge of the main methods for the solution of the combinatorial optimization problems.

Traveling salesman problem. --- Vehicle routing problem. --- VRP (Vehicle routing problem) --- Combinatorial optimization --- Traveling salesman problem --- TSP (Traveling salesman problem) --- Graph theory --- Vehicle routing problem --- Operational research

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This book presents novel and original metaheuristics developed to solve the cost-balanced traveling salesman problem. This problem was taken into account for the Metaheuristics Competition proposed in MESS 2018, Metaheuristics Summer School, and the top 4 methodologies ranked are included in the book, together with a brief introduction to the traveling salesman problem and all its variants. The book is aimed particularly at all researchers in metaheuristics and combinatorial optimization areas. Key uses are metaheuristics; complex problem solving; combinatorial optimization; traveling salesman problem.

Metaheuristics. --- Heuristic algorithms --- Combinatorial optimization. --- Traveling salesman problem, --- TSP (Traveling salesman problem) --- Combinatorial optimization --- Graph theory --- Vehicle routing problem --- Optimization, Combinatorial --- Combinatorial analysis --- Mathematical optimization

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"In Pursuit of the Traveling Salesman covers the history, applications, theory, and computation of the traveling salesman problem right up to state-of-the-art solution machinery"--Provided by publisher. "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"--Provided by publisher.

Traveling salesman problem --- Computational complexity --- Complexité de calcul (Informatique) --- Computational Complexity --- 519.6 --- 519.8 --- Computational mathematics. Numerical analysis. Computer programming --- Operational research --- Computational complexity. --- Traveling salesman problem. --- 519.8 Operational research --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Complexité de calcul (Informatique) --- TSP (Traveling salesman problem) --- Combinatorial optimization --- Graph theory --- Vehicle routing problem --- Complexity, Computational --- Electronic data processing --- Machine theory

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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