2 Indicator-Based Multiobjective Search

Abstract

In multiobjective optimization, set-based performance indicators are commonly used to assess the quality of a Pareto front approximation. Based on the scalarization obtained by these indicators, a performance comparison of multiobjective optimization algorithms becomes possible. The [Formula: see text] and the hypervolume (HV) indicator represent two recommended approaches which have shown a correlated behavior in recent empirical studies. Whereas the HV indicator has been comprehensively analyzed in the last years, almost no studies on the [Formula: see text] indicator exist. In this extended version of our previous conference paper, we thus perform a comprehensive investigation of the properties of the [Formula: see text] indicator in a theoretical and empirical way. The influence of the number and distribution of the weight vectors on the optimal distribution of [Formula: see text] solutions is analyzed. Based on a comparative analysis, specific characteristics and differences of the [Formula: see text] and HV indicator are presented. Furthermore, the [Formula: see text] indicator is integrated into an indicator-based steady-state evolutionary multiobjective optimization algorithm (EMOA). It is shown that the so-called [Formula: see text]-EMOA can accurately approximate the optimal distribution of [Formula: see text] solutions regarding [Formula: see text].