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Hypervolume-based multi-objective local search

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Abstract

This paper presents a multi-objective local search, where the selection is realized according to the hypervolume contribution of solutions. The HBMOLS algorithm proposed is inspired from the IBEA algorithm, an indicator-based multi-objective evolutionary algorithm proposed by Zitzler and Künzli in 2004, where the optimization goal is defined in terms of a binary indicator defining the selection operator. In this paper, we use the indicator optimization principle, and we apply it to an iterated local search algorithm, using hypervolume contribution indicator as selection mechanism. The methodology proposed here has been defined in order to be easily adaptable and to be as parameter-independent as possible. We carry out a range of experiments on the multi-objective flow shop problem and the multi-objective quadratic assignment problem, using the hypervolume contribution selection as well as two different binary indicators which were initially proposed in the IBEA algorithm. Experimental results indicate that the HBMOLS algorithm is highly effective in comparison with the algorithms based on binary indicators.

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Notes

  1. We assume throughout the paper that all the objective functions are normalized.

  2. If a neighbor does not exist, its objective value is replaced by the objective value of the reference point Z ref.

  3. http://www.tik.ee.ethz.ch/pisa/assessment.html.

  4. http://www.seas.upenn.edu/qaplib/inst.html.

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Acknowledgments

We are grateful to the referees for their comments and questions which helped us to improve the paper. The work is partially supported by the “Pays de la Loire” Region (France) within the RaDaPop (2009–2013) and LigeRO (2010–2013) projects.

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Authors and Affiliations

  1. Department of Computer Science, University of Angers, 2, Boulevard Lavoisier, 49045, Angers Cedex 01, France

    Matthieu Basseur, Rong-Qiang Zeng & Jin-Kao Hao

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  1. Matthieu Basseur
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  2. Rong-Qiang Zeng
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  3. Jin-Kao Hao
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Correspondence to Rong-Qiang Zeng.

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Basseur, M., Zeng, RQ. & Hao, JK. Hypervolume-based multi-objective local search. Neural Comput & Applic 21, 1917–1929 (2012). https://doi.org/10.1007/s00521-011-0588-4

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