R2-BEAN: R2 indicator based evolutionary algorithm for noisy multiobjective optimization

This paper proposes and evaluates an indicator-based and noise-aware dominance operator for evolutionary algorithms to solve the multiobjective optimization problems (MOPs) that contain noise in their objective functions. The proposed operator, U_R2-dominance operator is designed with (1) a quality indicator, called R2 indicator, which quantifies the goodness of a given solution candidate (individual) and (2) a non-parametric (i.e., distribution-free) statistical significance test called the Mann-Whitney U-test. The U_R2-dominance operator takes samples of given two individuals in the objective space, calculates the R2 indicator value for each sample, estimates the impacts of noise on the R2 values with a U-test, and determines which individual is statistically superior/inferior. Experimental results show that it operates reliably in noisy MOPs and outperforms existing noise-aware dominance operators particularly when many outliers exist under asymmetric noise distributions.