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Multi-start Methods

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Handbook of Heuristics

Abstract

Multi-start procedures were originally conceived as a way to exploit a local or neighborhood search procedure, by simply applying it from multiple random initial solutions. Modern multi-start methods usually incorporate a powerful form of diversification in the generation of solutions to help overcome local optimality. Different metaheuristics, such as GRASP or tabu search, have been applied to this end. This survey briefly sketches historical developments that have motivated the field and then focuses on modern contributions that define the current state of the art. Two classical categories of multi-start methods are considered according to their domain of application: global optimization and combinatorial optimization. Additionally, several methods are reviewed to estimate the number of local optima in combinatorial problems. The estimation of this number can help to establish the complexity of a given instance, and also to choose the most convenient neighborhood, which is especially interesting in the context of multi-start methods. Experiments on three well-known combinatorial optimization problems are included to illustrate the local optima estimation techniques.

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Acknowledgements

This work has been partially supported by the Spanish Ministerio de Economía y Competitividad (codes TIN2016-78365-R, TIN2015-65460, and TIN2013-41272P), the Basque Government (IT-609-13 program), and Generalitat Valenciana (project Prometeo 2013/049).

Author information

Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Facultad de Matematicas, Universidad de Valencia, Dr. Moliner 50, 46100, Burjassot (Valencia), Spain

    Rafael Martí

  2. Intelligent Systems Group, Department of Computer Science and Artificial Intelligence, University of the Basque Country, Manuel de Lardizabal 1, 20018, Donostia, Gipuzkoa, Spain

    Jose A. Lozano

  3. Intelligent Systems Group, Department of Computer Architecture and Technology, University of the Basque Country, Manuel de Lardizabal 1, 20018, Donostia, Gipuzkoa, Spain

    Alexander Mendiburu

  4. Intelligent Systems Group, Department of Computer Science and Artificial Intelligence, University of the Basque Country, Manuel de Lardizabal 1, 20018, Donostia, Gipuzkoa, Spain

    Leticia Hernando

Authors
  1. Rafael Martí
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  2. Jose A. Lozano
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  3. Alexander Mendiburu
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  4. Leticia Hernando
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Corresponding author

Correspondence to Rafael Martí .

Editor information

Editors and Affiliations

  1. Department of Statistics and Operations, University of Valencia, Valencia, Spain

    Rafael Martí

  2. University of Florida Industrial and Systems Engineering, Gainesville, Florida, USA

    Pardalos Panos

  3. AT & T Labs Research, Florham Park, New Jersey, USA

    Mauricio G.C. Resende

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Martí, R., Lozano, J.A., Mendiburu, A., Hernando, L. (2015). Multi-start Methods. In: Martí, R., Panos, P., Resende, M. (eds) Handbook of Heuristics. Springer, Cham. https://doi.org/10.1007/978-3-319-07153-4_1-1

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  • DOI: https://doi.org/10.1007/978-3-319-07153-4_1-1

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  • Publisher Name: Springer, Cham

  • Online ISBN: 978-3-319-07153-4

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