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2011•Wiley Encyclopedia of Operations Research and Management ScienceRequires access

Combinatorial Traveling Salesman Problem Algorithms

Claudia D’Ambrosio, Andrea Lodi, Silvano Martello

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Abstract

Abstract The traveling salesman problem (TSP) is a fundamental and well‐known problem in combinatorial optimization. We start by reviewing some of its ancestors, including the famous Hamiltonian cycle problem of which the TSP is the weighted version. We then introduce the most famous formulations of both the symmetric and the asymmetric TSP, and describe combinatorial approaches for both versions of the problem. We conclude with a brief discussion on the available TSP software.

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What this paper is about

Abstract The traveling salesman problem (TSP) is a fundamental and well‐known problem in combinatorial optimization. We start by reviewing some of its ancestors, including the famous Hamiltonian cycle problem of which the TSP is the weighted version. We then introduce the most famous formulations of both the symmetric and the asymmetric TSP, and describe combinatorial approaches for both versions of the problem. We conclude with a brief discussion on the available TSP software.

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Available abstract

Abstract The traveling salesman problem (TSP) is a fundamental and well‐known problem in combinatorial optimization. We start by reviewing some of its ancestors, including the famous Hamiltonian cycle problem of which the TSP is the weighted version. We then introduce the most famous formulations of both the symmetric and the asymmetric TSP, and describe combinatorial approaches for both versions of the problem. We conclude with a brief discussion on the available TSP software.

Key concepts: Travelling salesman problem, Combinatorial optimization, Hamiltonian path, Combinatorics, Lin–Kernighan heuristic, Mathematics, Computer science, Bottleneck traveling salesman problem

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