IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v55y2004i7d10.1057_palgrave.jors.2601611.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2601611
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2601611?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Terry Jones, 1995. "Evolutionary Algorithms, Fitness Landscapes and Search," Working Papers 95-05-048, Santa Fe Institute.
    3. C.R. Reeves, 1999. "Landscapes, operators and heuristic search," Annals of Operations Research, Springer, vol. 86(0), pages 473-490, January.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jooken, Jorik & Leyman, Pieter & De Causmaecker, Patrick, 2023. "Features for the 0-1 knapsack problem based on inclusionwise maximal solutions," European Journal of Operational Research, Elsevier, vol. 311(1), pages 36-55.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    2. Dimitris Fouskakis & David Draper, 2002. "Stochastic Optimization: a Review," International Statistical Review, International Statistical Institute, vol. 70(3), pages 315-349, December.
    3. J M Framinan & J N D Gupta & R Leisten, 2004. "A review and classification of heuristics for permutation flow-shop scheduling with makespan objective," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1243-1255, December.
    4. Nowicki, Eugeniusz & Smutnicki, Czeslaw, 2006. "Some aspects of scatter search in the flow-shop problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 654-666, March.
    5. Wilson, Amy D. & King, Russell E. & Wilson, James R., 2004. "Case study on statistically estimating minimum makespan for flow line scheduling problems," European Journal of Operational Research, Elsevier, vol. 155(2), pages 439-454, June.
    6. Christian M. Reidys & Peter F. Stadler, 1998. "Neutrality in Fitness Landscapes," Working Papers 98-10-089, Santa Fe Institute.
    7. Sündüz Dağ, 2013. "An Application On Flowshop Scheduling," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 1(1), pages 47-56, December.
    8. Koen Frenken & Luigi Marengo & Marco Valente, 1999. "Interdependencies, nearly-decomposability and adaption," CEEL Working Papers 9903, Cognitive and Experimental Economics Laboratory, Department of Economics, University of Trento, Italia.
    9. Solimanpur, M. & Vrat, Prem & Shankar, Ravi, 2004. "A heuristic to minimize makespan of cell scheduling problem," International Journal of Production Economics, Elsevier, vol. 88(3), pages 231-241, April.
    10. Ganesan, Viswanath Kumar & Sivakumar, Appa Iyer, 2006. "Scheduling in static jobshops for minimizing mean flowtime subject to minimum total deviation of job completion times," International Journal of Production Economics, Elsevier, vol. 103(2), pages 633-647, October.
    11. Ramalhinho Lourenco, Helena, 1996. "Sevast'yanov's algorithm for the flow-shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 91(1), pages 176-189, May.
    12. Jean-Paul Watson & Laura Barbulescu & L. Darrell Whitley & Adele E. Howe, 2002. "Contrasting Structured and Random Permutation Flow-Shop Scheduling Problems: Search-Space Topology and Algorithm Performance," INFORMS Journal on Computing, INFORMS, vol. 14(2), pages 98-123, May.
    13. Joseph B. Mazzola & Robert H. Schantz, 1997. "Multiple‐facility loading under capacity‐based economies of scope," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(3), pages 229-256, April.
    14. Liu, Jiyin & Reeves, Colin R, 2001. "Constructive and composite heuristic solutions to the P//[summation operator]Ci scheduling problem," European Journal of Operational Research, Elsevier, vol. 132(2), pages 439-452, July.
    15. Adenso-Diaz, Belarmino, 1996. "An SA/TS mixture algorithm for the scheduling tardiness problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 516-524, February.
    16. Ben-Daya, M. & Al-Fawzan, M., 1998. "A tabu search approach for the flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 109(1), pages 88-95, August.
    17. Pagnozzi, Federico & Stützle, Thomas, 2019. "Automatic design of hybrid stochastic local search algorithms for permutation flowshop problems," European Journal of Operational Research, Elsevier, vol. 276(2), pages 409-421.
    18. Peter F. Stadler & Robert Happel, 1995. "Random Field Models for Fitness Landscapes," Working Papers 95-07-069, Santa Fe Institute.
    19. Mansouri, S. Afshin & Aktas, Emel & Besikci, Umut, 2016. "Green scheduling of a two-machine flowshop: Trade-off between makespan and energy consumption," European Journal of Operational Research, Elsevier, vol. 248(3), pages 772-788.
    20. Stutzle, Thomas, 2006. "Iterated local search for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1519-1539, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pal:jorsoc:v:55:y:2004:i:7:d:10.1057_palgrave.jors.2601611. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.