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Estimating the number of basins of attraction of multi-objective combinatorial problems

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  • Madalina M. Drugan

    (ITLearns.Online)

Abstract

The efficiency of local search is proportional to the number and the distribution of basins of attraction. Often combinatorial optimisation problems have a large number of local optima, uncountable with available computational resources. Approximating the number of basins of attraction and the minimal number of samples for visiting all basins at least once are complex problems for which we assume specific distributions of basins of attraction. We define two types of basins of attraction of multi-objective combinatorial optimisation problems with complementary properties. Acknowledging that each local search run generates a Pareto front of solutions, either each Pareto local solution corresponds to a basin of attraction, or a Pareto basin matches an entire Pareto local front. Simulations compare parametric and non-parametric estimators on bi-objective quadratic assignment problem instances.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:4:d:10.1007_s10878-018-0357-8
    DOI: 10.1007/s10878-018-0357-8
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    References listed on IDEAS

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    1. Zvi Drezner & Peter Hahn & Éeric Taillard, 2005. "Recent Advances for the Quadratic Assignment Problem with Special Emphasis on Instances that are Difficult for Meta-Heuristic Methods," Annals of Operations Research, Springer, vol. 139(1), pages 65-94, October.
    2. 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.
    3. Paquete, Luis & Stutzle, Thomas, 2006. "A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices," European Journal of Operational Research, Elsevier, vol. 169(3), pages 943-959, March.
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    Cited by:

    1. Zhiguo Wang & Lufei Huang & Cici Xiao He, 2021. "A multi-objective and multi-period optimization model for urban healthcare waste’s reverse logistics network design," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 785-812, November.
    2. Zhiguo Wang & Lufei Huang & Cici Xiao He, 0. "A multi-objective and multi-period optimization model for urban healthcare waste’s reverse logistics network design," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-28.
    3. Mihael Baketarić & Marjan Mernik & Tomaž Kosar, 2021. "Attraction Basins in Metaheuristics: A Systematic Mapping Study," Mathematics, MDPI, vol. 9(23), pages 1-25, November.

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