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Attraction probabilities in variable neighborhood search

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Abstract

Empirical evidence demonstrates that when the same local search operator is used, variable neighborhood search consistently outperforms random multistart local search on all types of combinatorial and global optimization problems tested. In this paper we suggest that this superiority in performance may be explained by the distribution of the attraction basins around a current solution as a function of the distance from the solution. We illustrate with a well-known instance of the multisource Weber problem that the “attraction probabilities” for finding better solutions can be orders of magnitude larger in neighborhoods that are close to the current solution. The paper also discusses the global convergence properties of both general methods in the context of attraction probabilities.

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References

  • Boese KD, Kahng AB, Muddu S (1994) A new adaptive multi-start technique for combinatorial global optimizations. Oper Res Lett 16: 101–113

    Article  Google Scholar 

  • Brimberg J, Hansen P, Mladenović N, Taillard É (2000) Improvements and comparison of heuristics for solving the multisource Weber problem. Oper Res 48(3): 444–460

    Article  Google Scholar 

  • Cooper L (1964) Heuristic methods for location–allocation problems. SIAM Rev 6: 37–53

    Article  Google Scholar 

  • Eilon S, Watson-Gandy CDT, Christofides N (1971) Distibution management. Hafner, New York

    Google Scholar 

  • Garnier J, Kallel L (2000) Efficiency of local search with multiple local optima. SIAM J Discr Math 15: 122–141

    Article  Google Scholar 

  • Glover F, Hanafi S (2002) Tabu search and finite convergence. Discrete Appl Math 119: 3–36

    Article  Google Scholar 

  • Hanafi S (2001) On the convergence of Tabu search. J Heuristics 7: 47–58

    Article  Google Scholar 

  • Hansen P, Mladenović N (1997) Variable neighborhood search for the p-median. Locat Sci 5: 207–226

    Article  Google Scholar 

  • Hansen P, Mladenović N (2001a) Variable neihborhood search: principles and applications. Eur J Oper Res 130: 449–467

    Article  Google Scholar 

  • Hansen P, Mladenović N (2001b) Developments of variable neighborhood search. In: Ribeiro C, Hansen P (eds) Essays and surveys in metaheuristics. Kluwer, Boston, pp 415–440

    Google Scholar 

  • Hansen P, Mladenović N, Moreno-Perez JA (2008) Variable neighborhood search: methods and applications. 4OR 6: 319–360

    Article  Google Scholar 

  • Hansen P, Mladenović N, Taillard É (1998) Heuristic solution of the multisource Weber problem as a p-median problem. Oper Res Lett 22: 55–62

    Article  Google Scholar 

  • Jacobson S (2001) Analyzing the performance of local search algorithms using generalized hill climbing algorithms. In: Ribeiro C, Hansen P (eds) Essays and surveys in metaheuristics. Kluwer, Boston, pp 441–467

    Google Scholar 

  • Jonson AW, Jacobsen SH (2002) On the convergence of generalized hill climbing algorithms. Discrete Appl Math 119: 37–57

    Article  Google Scholar 

  • Kuenne RE, Soland RM (1972) Exact and approximate solutions to the multisource Weber problem. Math Program 3: 193–209

    Article  Google Scholar 

  • Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24: 1097–1100

    Article  Google Scholar 

  • Mulenbein H, Zimmermann J (2002) Size of neighborhood more important than temperature for stochastic local search, Technical report, GMD Laboratory, Germany

  • Reinelt G (1991) TSLIB—A traveling salesman library. ORSA J Comput 3: 376–384

    Google Scholar 

  • Whitaker R (1983) A fast algorithm for the greedy interchange for large-scale clustering and median location problems. INFOR 21: 95–108

    Google Scholar 

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Correspondence to Nenad Mladenovic.

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Brimberg, J., Hansen, P. & Mladenovic, N. Attraction probabilities in variable neighborhood search. 4OR-Q J Oper Res 8, 181–194 (2010). https://doi.org/10.1007/s10288-009-0108-x

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  • DOI: https://doi.org/10.1007/s10288-009-0108-x

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