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, UK TW20 0EX and Department of Computer Science, University of Haifa, Haifa, Israel;Department of Econometrics and Operations Research, University of Groningen, Groningen, The Netherlands 9700 and Department of Applied Mathematics, Khmelnitsky National University, Khmelnitsky, Uk ...;Department of Mathematics and Statistics, University of Victoria, Victoria, Canada V8W 3P4 and School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, China
Venue:
Journal of Heuristics
Year:
2008

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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 (Oper. Res. 39:150---161, 1991) finds the unique worst possible solution for some instances of the s-dimensional (s驴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驴3) assignment problem.