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The hypervolume based directed search method for multi-objective optimization problems

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Abstract

We present a new hybrid evolutionary algorithm for the effective hypervolume approximation of the Pareto front of a given differentiable multi-objective optimization problem. Starting point for the local search (LS) mechanism is a new division of the decision space as we will argue that in each of these regions a different LS strategy seems to be most promising. For the LS in two out of the three regions we will utilize and adapt the Directed Search method which is capable of steering the search into any direction given in objective space and which is thus well suited for the problem at hand. We further on integrate the resulting LS mechanism into SMS-EMOA, a state-of-the-art evolutionary algorithm for hypervolume approximations. Finally, we will present some numerical results on several benchmark problems with two and three objectives indicating the strength and competitiveness of the novel hybrid.

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Notes

  1. An overview about recent results on the complexity of HV computation is provided in http://simco.gforge.inria.fr/doku.php?id=openproblems.

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Acknowledgments

Victor Adrian Sosa Hernández acknowledges support by the Consejo Nacional de Ciencia y Tecnología (CONACYT). Heike Trautmann acknowledges support by the European Center of Information Systems (ERCIS). All authors acknowledge support from CONACYT Project no. 174443 and DFG Project no. TR 891/5-1

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Authors and Affiliations

  1. Computer Science Department, CINVESTAV-IPN, Av. IPN 2508, Col. San Pedro Zacatenco, Mexico, C. P. 07360, Mexico

    Oliver Schütze & Víctor Adrián Sosa Hernández

  2. Department of Information Systems, University of Münster, Leonardo-Campus 3, 48149, Münster, Germany

    Heike Trautmann

  3. Fakultät für Informatik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Günter Rudolph

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  1. Oliver Schütze
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  2. Víctor Adrián Sosa Hernández
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  3. Heike Trautmann
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  4. Günter Rudolph
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Correspondence to Oliver Schütze.

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Schütze, O., Hernández, V.A.S., Trautmann, H. et al. The hypervolume based directed search method for multi-objective optimization problems. J Heuristics 22, 273–300 (2016). https://doi.org/10.1007/s10732-016-9310-0

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