Soft Computing

, Volume 17, Issue 1, pp 49–62 | Cite as

Designing effective improvement methods for scatter search: an experimental study on global optimization

  • Lars Magnus Hvattum
  • Abraham Duarte
  • Fred Glover
  • Rafael Martí
Original Paper


Scatter search (SS) is a metaheuristic framework that explores solution spaces by evolving a set of reference points. These points (solutions) are initially generated with a diversification method and the evolution of these reference points is induced by the application of four methods: subset generation, combination, improvement and update. In this paper, we consider the application of the SS algorithm to the unconstrained global optimization problem and study its performance when coupled with different improvement methods. Specifically, we design and implement new procedures that result by combining SS with eight different improvement methods. We also propose an SS procedure (on the space of parameters) to determine the values of the key search parameters used to create the combined methods. We finally study whether improvement methods of different quality have a direct effect on the performance of the SS procedure, and whether this effect varies depending on attributes of the function that is minimized. Our experimental study reveals that the improvement method is a key element in an effective SS method for global optimization, and finds that the best improvement methods for high-dimensional functions are the coordinate method and two versions of scatter search itself. More significantly, extensive computational tests conducted with 12 leading methods from the literature show that our resulting method outperforms competing methods in the quality of both average solutions and best solutions obtained.


Global optimization Scatter search Evolutionary methods 



This research has been partially supported by the Ministerio de Ciencia e Innovación of Spain (TIN2009-07516 and TIN2012-35632). The authors thank the anonymous referees for suggestions and comments that improved on the first version of this paper.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Lars Magnus Hvattum
    • 1
  • Abraham Duarte
    • 2
  • Fred Glover
    • 3
  • Rafael Martí
    • 4
  1. 1.Department of Industrial Economics and Technology ManagementThe Norwegian University of Science and TechnologyTrondheimNorway
  2. 2.Departamento de Ciencias de la ComputaciónUniversidad Rey Juan CarlosMadridSpain
  3. 3.OptTek Systems, Inc.BoulderUSA
  4. 4.Departamento de Estadística e Investigación OperativaUniversidad de ValenciaValenciaSpain

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