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Performance Analysis of Cyclical Simulated Annealing Algorithms

Author

Listed:
  • Sheldon H. Jacobson

    (University of Illinois at Urbana-Champaign)

  • Shane N. Hall

    (University of Illinois at Urbana-Champaign)

  • Laura A. McLay

    (University of Illinois at Urbana-Champaign)

  • Jeffrey E. Orosz

    (Ritchie Capital Management)

Abstract

Generalized hill climbing (GHC) algorithms provide a framework for modeling local search algorithms for addressing intractable discrete optimization problems. Measures for assessing the finite-time performance of GHC algorithms have been developed using this framework, including the expected number of iterations to visit a predetermined objective function value level. This paper analyzes how the expected number of iterations to visit a predetermined objective function value level can be estimated for cyclical simulated annealing. Cyclical simulated annealing uses a cooling schedule that cycles through a set of temperature values. Computational results with traveling salesman problem instances taken from TSPLIB show how the expected number of iterations to visit solutions with predetermined objective function levels can be estimated for cyclical simulated annealing.

Suggested Citation

  • Sheldon H. Jacobson & Shane N. Hall & Laura A. McLay & Jeffrey E. Orosz, 2005. "Performance Analysis of Cyclical Simulated Annealing Algorithms," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 183-201, June.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:2:d:10.1007_s11009-005-1482-2
    DOI: 10.1007/s11009-005-1482-2
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    References listed on IDEAS

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    1. Foerster, Hildegard & Wascher, Gerhard, 1998. "Simulated annealing for order spread minimization in sequencing cutting patterns," European Journal of Operational Research, Elsevier, vol. 110(2), pages 272-281, October.
    2. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
    3. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    4. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    5. G. A. Croes, 1958. "A Method for Solving Traveling-Salesman Problems," Operations Research, INFORMS, vol. 6(6), pages 791-812, December.
    6. J.E. Orosz & S.H. Jacobson, 2002. "Analysis of Static Simulated Annealing Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 165-182, October.
    7. Mark Fleischer & Sheldon H. Jacobson, 1999. "Information Theory and the Finite-Time Behavior of the Simulated Annealing Algorithm: Experimental Results," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 35-43, February.
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