R2-IBEA: R2 Indicator Based Evolutionary Algorithm for Multiobjective Optimization

This paper proposes and evaluates an evolutionary multiobjective optimization algorithm (EMOA) that eliminates dominance ranking in selection and performs indicator-based selection with the R2 indicator. Although it is known that the R2 indicator possesses desirable properties to quantify the goodness of a solution or a solution set, few attempts have been made until recently to investigate indicator-based EMOAs with the R2 indicator. The proposed EMOA, called R2-IBEA, is designed to obtain a diverse set of Pareto-approximated solutions by correcting an inherent bias in the R2 indicator. (The R2 indicator has a stronger bias to the center of the Pareto front than to its edges.) Experimental results demonstrate that R2-IBEA outperforms existing indicator-based, decomposition-based and dominance ranking based EMOAs in the optimality and diversity of solutions. R2-IBEA successfully produces diverse individuals that are distributed well in the objective space. It is also empirically verified that R2-IBEA scales well from two-dimensional to five-dimensional problems.