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Worst case analysis of Max-Regret, Greedy and other heuristics for Multidimensional Assignment and Traveling Salesman Problems

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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≥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.

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Authors and Affiliations

  1. Department of Computer Science, Royal Holloway University of London, Egham, Surrey, TW20 0EX, UK

    Gregory Gutin

  2. Department of Computer Science, University of Haifa, Haifa, Israel

    Gregory Gutin

  3. Department of Econometrics and Operations Research, University of Groningen, P.O. Box 800, 9700, AV, Groningen, The Netherlands

    Boris Goldengorin

  4. Department of Applied Mathematics, Khmelnitsky National University, Khmelnitsky, Ukraine

    Boris Goldengorin

  5. Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, Canada, V8W 3P4

    Jing Huang

  6. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, China

    Jing Huang

Authors
  1. Gregory Gutin
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  2. Boris Goldengorin
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  3. Jing Huang
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Correspondence to Gregory Gutin.

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Gutin, G., Goldengorin, B. & Huang, J. Worst case analysis of Max-Regret, Greedy and other heuristics for Multidimensional Assignment and Traveling Salesman Problems. J Heuristics 14, 169–181 (2008). https://doi.org/10.1007/s10732-007-9033-3

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  • DOI: https://doi.org/10.1007/s10732-007-9033-3

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