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Reports (Research Report) Year : 2014

On the Impact of Scalarizing Functions on Evolutionary Multiobjective Optimization

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 more carefully the effect of different scalarizing functions (weighted Tchebycheff, weighted sum, and combinations thereof) and their parameters on the search performance. 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+ λ)-EA on biobjective NK-landscapes. Secondly, combining the outcomes of independent single-objective runs allows for more general statements on the impact of the scalarizing function parameters on set-based performance measures such as hypervolume and ε-indicator. Finally, we investigate the correlation between the opening angle of the scalarizing function's underlying contour lines and the position of the final solution found by the (1+λ)-EA in the objective space. Our analysis is of fundamental nature and sheds more light on the optimization of scalarizing functions within decomposition-based algorithms and also on how these algorithms might be improved.
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Dates and versions

hal-00968145 , version 1 (31-03-2014)

Identifiers

  • HAL Id : hal-00968145 , version 1

Cite

Bilel Derbel, Dimo Brockhoff, Arnaud Liefooghe, Sébastien Verel. On the Impact of Scalarizing Functions on Evolutionary Multiobjective Optimization. [Research Report] RR-8512, 2014. ⟨hal-00968145⟩
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