On the Impact of Multiobjective Scalarizing Functions

TL;DR

This paper analyzes how different scalarizing functions influence the difficulty and outcomes of multiobjective optimization, providing fundamental insights into their behavior and impact on solution positioning.

Contribution

It offers a theoretical investigation of scalarizing functions' effects on optimization difficulty and solution distribution, independent of specific algorithms.

Findings

Scalarizing functions' parameters significantly affect search difficulty.

The opening angle of scalarizing functions correlates with solution positions.

Set-based performance can be inferred from single-objective runs.

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+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.