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Statistical analysis of local search landscapes

Author

Listed:
  • C R Reeves

    (Coventry University)

  • A V Eremeev

    (Sobolev Institute of Mathematics)

Abstract

This paper discusses the application of some statistical estimation tools in trying to understand the nature of the combinatorial landscapes induced by local search methods. One interesting property of a landscape is the number of optima that are present. In this paper we show that it is possible to compute a confidence interval on the number of independent local searches needed to find all optima. By extension, this also expresses the confidence that the global optimum has been found. In many cases, this confidence may be too low to be acceptable, but it is also possible to estimate the number of optima that exist. Theoretical analysis and empirical studies are discussed, which show that it may be possible to obtain a fairly accurate picture of this property of a combinatorial landscape. The approach is illustrated by analysis of an instance of the flowshop scheduling problem.

Suggested Citation

  • C R Reeves & A V Eremeev, 2004. "Statistical analysis of local search landscapes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(7), pages 687-693, July.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:7:d:10.1057_palgrave.jors.2601611
    DOI: 10.1057/palgrave.jors.2601611
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    References listed on IDEAS

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    1. Terry Jones, 1995. "Evolutionary Algorithms, Fitness Landscapes and Search," Working Papers 95-05-048, Santa Fe Institute.
    2. C.R. Reeves, 1999. "Landscapes, operators and heuristic search," Annals of Operations Research, Springer, vol. 86(0), pages 473-490, January.
    3. Los, Marc & Lardinois, Christian, 1982. "Combinatorial programming, statistical optimization and the optimal transportation network problem," Transportation Research Part B: Methodological, Elsevier, vol. 16(2), pages 89-124, April.
    4. Taillard, E., 1990. "Some efficient heuristic methods for the flow shop sequencing problem," European Journal of Operational Research, Elsevier, vol. 47(1), pages 65-74, July.
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    Cited by:

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    2. Madalina M. Drugan, 2019. "Estimating the number of basins of attraction of multi-objective combinatorial problems," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1367-1407, May.

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