On the Impact of Multiobjective Scalarizing Functions

Bilel Derbel^1,2, Dimo Brockhoff¹, Arnaud Liefooghe^1,2, and Sébastien Verel³

¹Inria Lille - Nord Europe, DOLPHIN project-team, France

²Université Lille 1, LIFL, UMR CNRS 8022, France

³Université du Littoral Côte d’Opale, LISIC, France

Abstract. Recently, there has been a renewed interest in decomposition-based approaches for evolutionary multiobjective optimization. However, the impact of the choice of the underlying scalarizing function(s) is still far from being well understood. In this paper, we investigate the behavior of different scalarizing functions and their parameters. We thereby abstract firstly from any specific algorithm and only consider the difficulty of the single scalarized problems in terms of the search ability of a (1 + )-EA on biobjective NK-landscapes. Secondly, combining the outcomes of independent single-objective runs allows for more general statements on set-based performance measures. Finally, we investigate the correlation between the opening angle of the scalarizing function’s underlying contour lines and the position of the final solution in the objective space. Our analysis is of fundamental nature and sheds more light on the key characteristics of multiobjective scalarizing functions.

LNCS 8672, p. 548 ff.

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