An approach for the local exploration of discrete many objective optimization problems

Oliver Cuate (1) , Bilel Derbel (2) , Arnaud Liefooghe (2) , El-Ghazali Talbi (2) , Oliver Schütze (1)

1 CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional
2 DOLPHIN - Parallel Cooperative Multi-criteria Optimization

Multi-objective optimization problems with more than three objectives, which are also termed as many objective optimization problems , play an important role in the decision making process. For such problems, it is computationally expensive or even intractable to approximate the entire set of optimal solutions. An alternative is to compute a subset of optimal solutions based on the preferences of the decision maker. Commonly, interactive methods from the literature consider the user preferences at every iteration by means of weight vectors or reference points. Besides the fact that mathematical programming techniques only produce one solution at each iteration, they generally require first or second derivative information, that limits its applicability to certain problems. The approach proposed in this paper allows to steer the search into any direction in the objective space for optimization problems of discrete nature. This provides a more intuitive way to set the preferences, which represents a useful tool to explore the regions of interest of the decision maker. Numerical results on multi-objective multi-dimensional knapsack problem instances show the interest of the proposed approach.

Mots clés: Many objective optimization; Multi-Criteria Decision Making; Discrete Optimization; Knapsack; Evolutionary Computation

Domaines: Recherche opérationnelle [math.OC]; Optimisation et contrôle [math.OC]

Oliver Cuate, Bilel Derbel, Arnaud Liefooghe, El-Ghazali Talbi, Oliver Schütze. An approach for the local exploration of discrete many objective optimization problems. 9th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2017), Mar 2017, Münster, Germany. pp.135-150, ⟨10.1109/TSMCB.2008.926329⟩. ⟨hal-01581433⟩