Exact Algorithms for the Equitable Traveling Salesman Problem

19 Pages Posted: 29 Apr 2016

See all articles by Joris Kinable

Joris Kinable

Carnegie Mellon University, David A. Tepper School of Business, Students

Bart Smeulders

KU Leuven

Eline Delcour

KU Leuven

Frits Spieksma

Catholic University of Leuven (KUL)

Date Written: March 31, 2016

Abstract

Given a weighted graph G = (V, E), the Equitable Traveling Salesman Problem (ETSP) asks for two perfect matchings in G such that (1) the two matchings together form a Hamiltonian cycle in G and (2) the absolute difference in costs between the two matchings is minimized. The problem is shown to be NP-Hard, even when the graph G is complete. We present two integer programming models to solve the ETSP problem. One model is solved through branch-and-bound-and-cut, whereas the other model is solved through a branch-and-price-and-cut framework. A simple local search heuristic is also implemented. We conduct computational experiments on different types of instances, often derived from the TSPLib. It turns out that the behavior of the different approaches varies with the type of instances; however, the branch-and-bound-and-cut approach implemented in Cplex seems to work best overall.

Suggested Citation

Kinable, Joris and Smeulders, Bart and Delcour, Eline and Spieksma, Frits, Exact Algorithms for the Equitable Traveling Salesman Problem (March 31, 2016). Available at SSRN: https://ssrn.com/abstract=2770542 or http://dx.doi.org/10.2139/ssrn.2770542

Joris Kinable (Contact Author)

Carnegie Mellon University, David A. Tepper School of Business, Students ( email )

Pittsburgh, PA
United States

Bart Smeulders

KU Leuven ( email )

Oude Markt 13
Leuven, Vlaams-Brabant 3000
Belgium

Eline Delcour

KU Leuven ( email )

Oude Markt 13
Leuven, Vlaams-Brabant 3000
Belgium

Frits Spieksma

Catholic University of Leuven (KUL) ( email )

Leuven, B-3000
Belgium

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