Worst case analysis of max-regret, greedy and other heuristics for multidimensional assignment and traveling salesman problems

Authors:
Gregory Gutin;Boris Goldengorin;Jing Huang
Affiliations:
Department of Computer Science, Royal Holloway University of London, Egham, Surrey, UK;Department of Econometrics and Operations Research, University of Groningen, Groningen, AV, The Netherlands;Department of Mathematics and Statistics, University of Victoria, Canada
Venue:
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Year:
2006

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Abstract

Optimization heuristics are often compared with each other to determine which one performs best by means of worst-case performance ratio reflecting the quality of returned solution in the worst case. The domination number is a complement parameter indicating the quality of the heuristic in hand by determining how many feasible solutions are dominated by the heuristic solution. We prove that the Max-Regret heuristic introduced by Balas and Saltzman finds the unique worst possible solution for some instances of the s-dimensional (s≥3) assignment and asymmetric traveling salesman problems of each possible size. We show that the Triple Interchange heuristic (for s=3) also introduced by Balas and Saltzman and two new heuristics (Part and Recursive Opt Matching) have factorial domination numbers for the s-dimensional (s≥3) assignment problem.