On the Impact of Multiobjective Scalarizing Functions
This foundational analysis provides insights into key characteristics of scalarizing functions for researchers in evolutionary multiobjective optimization, though it is incremental in nature.
The paper investigates how different scalarizing functions and their parameters affect the difficulty of single scalarized problems in evolutionary multiobjective optimization, using a (1+lambda)-EA on biobjective NK-landscapes, and analyzes correlations with solution positions in objective space.
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+lambda)-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.