Worst Case Analysis of Max-Regret, Greedy and Other Heuristics for Multidimensional Assignment and Traveling Salesman Problems
G. Gutin, B. Goldengorin and J. Huang
In: 4th Workshop on Approximation and Online Algorithms, 13 Sept - 15 Sept, 2006, Zurich, Switzerland.

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 (1991) finds the unique worst possible solution for some instances of the $s$-dimensional ($s\ge 3$) 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 ($s\ge 3$) assignment problem.

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