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On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives

Sébastien Verel 1, 2 Arnaud Liefooghe 2, 3 Laetitia Jourdan 2 Clarisse Dhaenens 2, 3
1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Groupe SCOBI
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
2 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
Inria Lille - Nord Europe, LIFL - Laboratoire d'Informatique Fondamentale de Lille
Abstract : The structure of the search space explains the behavior of multiobjective search algorithms, and helps to design well-performing approaches. In this work, we analyze the properties of multiobjective combinatorial search spaces, and we pay a particular attention to the correlation between the objective functions. To do so, we extend the multiobjective NK-landscapes in order to take the objective correlation into account. We study the co-influence of the problem dimension, the degree of non-linearity, the number of objectives, and the objective correlation on the structure of the Pareto optimal set, in terms of cardinality and number of supported solutions, as well as on the number of Pareto local optima. This work concludes with guidelines for the design of multiobjective local search algorithms, based on the main fitness landscape features.
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https://hal.archives-ouvertes.fr/hal-00760097
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Submitted on : Thursday, September 9, 2021 - 11:23:55 AM
Last modification on : Tuesday, May 3, 2022 - 3:20:22 AM
Long-term archiving on: : Saturday, December 11, 2021 - 7:19:51 AM

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Sébastien Verel, Arnaud Liefooghe, Laetitia Jourdan, Clarisse Dhaenens. On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives. European Journal of Operational Research, Elsevier, 2013, 227 (2), pp.331-342. ⟨10.1016/j.ejor.2012.12.019⟩. ⟨hal-00760097⟩

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