R2 Indicator and Objective Space Partition Based Evolutionary Algorithm for Many-objective Optimization

Evolutionary multi-objective optimization algorithms based on the R2 indicator have achieved better convergence and well-diversified Pareto front for solving traditional multi-objective optimization problems, which contains two or three objectives. Recently there are some new developments to explore the relationship between the R2 indicator based selection strategy and the decomposition based selection methods to address many-objective optimization problems. This paper proposes the R2 indicator and objective space partition based evolutionary algorithm to address many-objective optimization. A set of weight vectors gives the possible relationship between two selection methods. In the proposed algorithm, the original R2 indicator was modified by adopting the penalty-based boundary intersection scalarizing method to balance the convergence and the diversity in high-dimensional space. Then, a new selection strategy, which combined the R2 indicator with the objective space partition together, is proposed. Finally, the adaptive penalty parameter is updated adaptively to guarantee the elitist population along a set of weight vectors. Our proposed algorithm has been tested on some benchmark test problems. The performance of the proposed algorithm performs better or at par with recent R2 indicator based evolutionary algorithms and the decomposition based evolutionary algorithms for solving many-objective optimization.