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Parallel Tempering For The Traveling Salesman Problem

Author

Listed:
  • CHIAMING WANG

    (Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90095-1555, USA)

  • JEFFREY D. HYMAN

    (Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90095-1555, USA)

  • ALLON PERCUS

    (Information Sciences Group, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;
    Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90095-1555, USA)

  • RUSSEL CAFLISCH

    (Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90095-1555, USA)

Abstract

We explore the potential of parallel tempering as a combinatorial optimization method, applying it to the traveling salesman problem. We compare simulation results of parallel tempering with a benchmark implementation of simulated annealing, and study how different choices of parameters affect the relative performance of the two methods. We find that a straightforward implementation of parallel tempering can outperform simulated annealing in several crucial respects. When parameters are chosen appropriately, both methods yield close approximation to the actual minimum distance for an instance with 200 nodes. However, parallel tempering yields more consistently accurate results when a series of independent simulations are performed. Our results suggest that parallel tempering might offer a simple but powerful alternative to simulated annealing for combinatorial optimization problems.

Suggested Citation

  • Chiaming Wang & Jeffrey D. Hyman & Allon Percus & Russel Caflisch, 2009. "Parallel Tempering For The Traveling Salesman Problem," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 539-556.
    • Handle: RePEc:wsi:ijmpcx:v:20:y:2009:i:04:n:s0129183109013893
    DOI: 10.1142/S0129183109013893
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