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Convergence in Probability of Compressed Annealing

Author

Listed:
  • Jeffrey W. Ohlmann

    () (Department of Management Sciences, University of Iowa, 108 John Pappajohn Business Building, Iowa City, Iowa 52242-1000)

  • James C. Bean

    () (Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, Michigan 48109-2117)

  • Shane G. Henderson

    () (School of Operations Research and Industrial Engineering, Cornell University, 230 Rhodes Hall, Ithaca, New York 14853)

Abstract

We consider combinatorial optimization problems for which the formation of a neighborhood structure of feasible solutions is impeded by a set of constraints. Neighborhoods are recovered by relaxing the complicating constraints into the objective function within a penalty term. We examine a heuristic called compressed annealing that integrates a variable penalty multiplier approach within the framework of simulated annealing. We refer to the value of the penalty multiplier as “pressure.” We analyze the behavior of compressed annealing by exploring the interaction between temperature (which controls the ability of compressed annealing to climb hills) and pressure (which controls the height of the hills). We develop a necessary and sufficient condition on the joint cooling and compression schedules for compressed annealing to converge in probability to the set of global minima. Our work generalizes the results of Hajek (1988) in the sense that when there are no relaxed constraints, our results reduce to his.

Suggested Citation

  • Jeffrey W. Ohlmann & James C. Bean & Shane G. Henderson, 2004. "Convergence in Probability of Compressed Annealing," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 837-860, November.
  • Handle: RePEc:inm:ormoor:v:29:y:2004:i:4:p:837-860
    DOI: 10.1287/moor.1040.0095
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    File URL: http://dx.doi.org/10.1287/moor.1040.0095
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    References listed on IDEAS

    as
    1. Yao, J., 2000. "On constrained simulation and optimization by Metropolis chains," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 187-193, January.
    2. Atidel Ben Hadj-Alouane & James C. Bean, 1997. "A Genetic Algorithm for the Multiple-Choice Integer Program," Operations Research, INFORMS, vol. 45(1), pages 92-101, February.
    3. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
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    Cited by:

    1. Graeme J. Doole & David J. Pannell & Clinton K. Revell, 2009. "Economic contribution of French serradella (Ornithopus sativus Brot.) pasture to integrated weed management in Western Australian mixed-farming systems: an application of compressed annealing ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 53(2), pages 193-212, April.
    2. Graeme J. Doole & David J. Pannell, 2008. "Optimisation of a Large, Constrained Simulation Model using Compressed Annealing," Journal of Agricultural Economics, Wiley Blackwell, vol. 59(1), pages 188-206, February.
    3. Jeffrey W. Ohlmann & Barrett W. Thomas, 2007. "A Compressed-Annealing Heuristic for the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 80-90, February.
    4. F. Mendivil & R. Shonkwiler, 2010. "Annealing a Genetic Algorithm for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 395-410, November.

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