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Optimized annealing of traveling salesman problem from the nth-nearest-neighbor distribution

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  • Chen, Yong
  • Zhang, Pan

Abstract

We report a new statistical general property in traveling salesman problem, that the nth-nearest-neighbor distribution of optimal tours verifies with very high accuracy an exponential decay as a function of the order of neighbor n. Defining the energy function as deviation λ from this exponential decay, which is different to the tour length d in normal annealing processes, we propose a distinct highly optimized annealing scheme which is performed in λ-space and d-space by turns. The simulation results of some standard traveling salesman problems in TSPLIB95 are presented. It is shown that our annealing recipe is superior to the canonical simulated annealing.

Suggested Citation

  • Chen, Yong & Zhang, Pan, 2006. "Optimized annealing of traveling salesman problem from the nth-nearest-neighbor distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 627-632.
    • Handle: RePEc:eee:phsmap:v:371:y:2006:i:2:p:627-632
    DOI: 10.1016/j.physa.2006.04.052
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    Cited by:

    1. Huang, Zhendong & Xiao, Renbin, 2013. "An emergent computation approach to the problem of polygon layout with performance constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5074-5088.
    2. A. S. Santos & A. M. Madureira & M. L. R. Varela, 2018. "The Influence of Problem Specific Neighborhood Structures in Metaheuristics Performance," Journal of Mathematics, Hindawi, vol. 2018, pages 1-14, July.

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