Tolerance based algorithms for the ATSP

Authors:
Boris Goldengorin;Gerard Sierksma;Marcel Turkensteen
Affiliations:
Faculty of Economic Sciences, University of Groningen, Groningen, The Netherlands;Faculty of Economic Sciences, University of Groningen, Groningen, The Netherlands;Faculty of Economic Sciences, University of Groningen, Groningen, The Netherlands
Venue:
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2004

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Abstract

In this paper we use arc tolerances, instead of arc costs, to improve Branch-and-Bound type algorithms for the Asymmetric Traveling Salesman Problem (ATSP). We derive new tighter lower bounds based on exact and approximate bottleneck upper tolerance values of the Assignment Problem (AP). It is shown that branching by tolerances provides a more rational branching process than branching by costs. Among others, we show that branching on an arc with the bottleneck upper tolerance value is the best choice, while such an arc appears quite often in a shortest cycle of the current AP relaxation. This fact shows why branching on shortest cycles was always found as a best choice. Computational experiments confirm our theoretical results.