Improved Metaheuristic Based on the R2 Indicator for Many-Objective Optimization

In recent years, performance indicators were introduced as a selection mechanism in multi-objective evolutionary algorithms (MOEAs). A very attractive option is the R2 indicator due to its low computational cost and weak-Pareto compatibility. This indicator requires a set of utility functions, which map each objective to a single value. However, not all the utility functions available in the literature scale properly for more than four objectives and the diversity of the approximation sets is sensitive to the choice of the reference points during normalization. In this paper, we present an improved version of a MOEA based on the $R2$ indicator, which takes into account these two key aspects, using the achievement scalarizing function and statistical information about the population's proximity to the true Pareto optimal front. Moreover, we present a comparative study with respect to some other emerging approaches, such as NSGA-III (based on Pareto dominance), Δp-DDE (based on the Δp indicator) and some other MOEAs based on the R2 indicator, using the DTLZ and WFG test problems. Experimental results indicate that our approach outperforms the original algorithm as well as the other MOEAs in the majority of the test instances, making it a suitable alternative for solving many-objective optimization problems.