Improved Large-Step Markov Chain Variants for the Symmetric TSP

  • Authors:
  • Inki Hong;Andrew B. Kahng;Byung-Ro Moon

  • Affiliations:
  • UCLA Computer Science Department Los Angeles, CA 90095-1596 USA. E-mail: {inki, abk}@cs.ucla.edu;UCLA Computer Science Department Los Angeles, CA 90095-1596 USA. E-mail: {inki, abk}@cs.ucla.edu;Design Technology Research Center, LG Semicon Co., Ltd. 16 Woomyon-dong, Seocho-gu, Seoul, Korea. E-mail: moon@lgsemicon.co.kr

  • Venue:
  • Journal of Heuristics
  • Year:
  • 1997

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Abstract

The large-step Markov chain (LSMC) approach is the mosteffective known heuristic for large symmetric TSP instances; cf.recent results of [Martin, Otto and Felten, 1991] and [Johnson,1990]. In this paper, we examine relationships among (i) theunderlying local optimization engine within the LSMC approach, (ii)the “kick move” perturbation that is applied between successivelocal search descents, and (iii) the resulting LSMC solutionquality. We find that the traditional “double-bridge” kick move isnot necessarily optimum: stronger local optimization engines (e.g.,Lin-Kernighan) are best matched with stronger kick moves. We alsopropose use of an adaptive temperature schedule to allow escape fromdeep basins of attraction; the resulting hierarchical LSMCvariant outperforms traditional LSMC implementations that useuniformly zero temperatures. Finally, a population-based LSMCvariant is studied, wherein multiple solution paths can interact toachieve improved solution quality.