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Exploiting run time distributions to compare sequential and parallel stochastic local search algorithms

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  • Celso Ribeiro
  • Isabel Rosseti
  • Reinaldo Vallejos

Abstract

Run time distributions or time-to-target plots are very useful tools to characterize the running times of stochastic algorithms for combinatorial optimization. We further explore run time distributions and describe a new tool to compare two algorithms based on stochastic local search. For the case where the running times of both algorithms fit exponential distributions, we derive a closed form index that gives the probability that one of them finds a solution at least as good as a given target value in a smaller computation time than the other. This result is extended to the case of general run time distributions and a numerical iterative procedure is described for the computation of the above probability value. Numerical examples illustrate the application of this tool in the comparison of different sequential and parallel algorithms for a number of distinct problems. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Celso Ribeiro & Isabel Rosseti & Reinaldo Vallejos, 2012. "Exploiting run time distributions to compare sequential and parallel stochastic local search algorithms," Journal of Global Optimization, Springer, vol. 54(2), pages 405-429, October.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:405-429
    DOI: 10.1007/s10898-011-9769-z
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    References listed on IDEAS

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    1. Abilio Lucena & Celso Ribeiro & Andréa Santos, 2010. "A hybrid heuristic for the diameter constrained minimum spanning tree problem," Journal of Global Optimization, Springer, vol. 46(3), pages 363-381, March.
    2. Lawrence J. Osborne & Billy E. Gillett, 1991. "A Comparison of Two Simulated Annealing Algorithms Applied to the Directed Steiner Problem on Networks," INFORMS Journal on Computing, INFORMS, vol. 3(3), pages 213-225, August.
    3. Thomas A. Feo & Mauricio G. C. Resende & Stuart H. Smith, 1994. "A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set," Operations Research, INFORMS, vol. 42(5), pages 860-878, October.
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    Cited by:

    1. Julliany S. Brandão & Thiago F. Noronha & Celso C. Ribeiro, 2016. "A biased random-key genetic algorithm to maximize the number of accepted lightpaths in WDM optical networks," Journal of Global Optimization, Springer, vol. 65(4), pages 813-835, August.
    2. Wang, Yang & Wu, Qinghua & Glover, Fred, 2017. "Effective metaheuristic algorithms for the minimum differential dispersion problem," European Journal of Operational Research, Elsevier, vol. 258(3), pages 829-843.

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