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Journal of Heuristics

, 14:169 | Cite as

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

  • Gregory GutinEmail author
  • Boris Goldengorin
  • Jing Huang
Article

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.

Keywords

Traveling salesman problem Multidimensional assignment problem Greedy heuristics Domination analysis 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Gregory Gutin
    • 1
    • 2
    Email author
  • Boris Goldengorin
    • 3
    • 4
  • Jing Huang
    • 5
    • 6
  1. 1.Department of Computer ScienceRoyal Holloway University of LondonEghamUK
  2. 2.Department of Computer ScienceUniversity of HaifaHaifaIsrael
  3. 3.Department of Econometrics and Operations ResearchUniversity of GroningenGroningenThe Netherlands
  4. 4.Department of Applied MathematicsKhmelnitsky National UniversityKhmelnitskyUkraine
  5. 5.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  6. 6.School of Mathematics and Computer ScienceNanjing Normal UniversityNanjingChina

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