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MIRHA: multi-start biased randomization of heuristics with adaptive local search for solving non-smooth routing problems

TOP volume 21, pages 109–132 (2013)Cite this article

Abstract

This paper discusses the use of probabilistic or randomized algorithms for solving vehicle routing problems with non-smooth objective functions. Our approach employs non-uniform probability distributions to add a biased random behavior to the well-known savings heuristic. By doing so, a large set of alternative good solutions can be quickly obtained in a natural way and without complex configuration processes. Since the solution-generation process is based on the criterion of maximizing the savings, it does not need to assume any particular property of the objective function. Therefore, the procedure can be especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods—both of exact and approximate nature—may fail to reach their full potential. The results obtained so far are promising enough to suggest that the idea of using biased probability distributions to randomize classical heuristics is a powerful one that can be successfully applied in a variety of cases.

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Acknowledgements

This work has been partially supported by the Spanish Ministry of Science and Innovation (grants MTM2008-06695-C03-03, TRA2010-21644-C03 and ECO2009-11307), by the Working Community of the Pyrenees (grants IIQ13172.R11-CTP09-R2 and CTP09-00007), by the CYTED-IN3-HAROSA network (http://dpcs.uoc.edu) and by the Jerónimo de Ayanz network (Government of Navarre, Spain).

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Authors and Affiliations

  1. Computer Science Dept., Open University of Catalonia, Barcelona, Spain

    Angel A. Juan

  2. Statistics and Operations Research Dept., Public University of Navarre, Pamplona, Spain

    Javier Faulin

  3. Applied Mathematics 1 Dept., Technical University of Catalonia, Barcelona, Spain

    Albert Ferrer

  4. Economics and Business Dept., Universitat Pompeu Fabra, Barcelona, Spain

    Helena R. Lourenço

  5. Industrial Engineering and Management Science Dept., Northwestern University, Evanston, IL, USA

    Barry Barrios

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  1. Angel A. Juan
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  4. Helena R. Lourenço
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Correspondence to Javier Faulin.

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Juan, A.A., Faulin, J., Ferrer, A. et al. MIRHA: multi-start biased randomization of heuristics with adaptive local search for solving non-smooth routing problems. TOP 21, 109–132 (2013). https://doi.org/10.1007/s11750-011-0245-1

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