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Traveling Salesman Problem

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Encyclopedia of Operations Research and Management Science

Introduction

The traveling salesman problem (TSP) has commanded much attention from mathematicians and computer scientists specifically because it is so easy to describe and so difficult to solve. The problem can simply be stated as: if a traveling salesman wishes to visit exactly once each of a list of m cities (where the cost of traveling from city i to city j is c ij ) and then return to the home city, what is the least costly route the traveling salesman can take? A complete historical development of this and related problems can be found in Hoffman and Wolfe (1985), Applegate et al. (2006), and Cook (2011).

The importance of the TSP is that it is representative of a larger class of problems known as combinatorial optimization problems. The TSP problem belongs in the class of such problems known as NP-complete. Specifically, if one can find an efficient (i.e., polynomial-time) algorithm for the traveling salesman problem, then efficient algorithms could be found for all other...

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Author information

Authors and Affiliations

  1. George Mason University, Fairfax, VA, USA

    Karla L. Hoffman

  2. New York University, New York, NY, USA

    Manfred Padberg

  3. CNR – Istituto di Analisi dei Sistemi ed Informatica (IASI), Viale Manzoni 30, 00185, Rome, Italy

    Giovanni Rinaldi

Authors
  1. Karla L. Hoffman
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  2. Manfred Padberg
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  3. Giovanni Rinaldi
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Corresponding author

Correspondence to Karla L. Hoffman .

Editor information

Editors and Affiliations

  1. Robert H. Smith School of Business, University of Maryland, College Park, MD, USA

    Saul I. Gass

  2. Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, MD, USA

    Michael C. Fu

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Hoffman, K.L., Padberg, M., Rinaldi, G. (2013). Traveling Salesman Problem. In: Gass, S.I., Fu, M.C. (eds) Encyclopedia of Operations Research and Management Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1153-7_1068

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  • DOI: https://doi.org/10.1007/978-1-4419-1153-7_1068

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