R2 Indicator Based Multiobjective Search

Brockhoff D, Wagner T, Trautmann H

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 R2 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 R2 indicator exist. In this extended version of our previous conference paper, we thus perform a comprehensive investigation of the properties of the R2 indicator in a theoretical and empirical way. The influence of the number and distribution of the weight vectors on the optimal distribution of μ solutions is analyzed. Based on a comparative analysis, specific characteristics and differences of the R2 and HV indicator are presented. Furthermore, the R2 indicator is integrated into an indicator-based steady-state evolutionary multiobjective optimization algorithm (EMOA). It is shown that the so-called R2-EMOA can accurately approximate the optimal distribution of μ solutions regarding R2.