Improving the Convergence and Diversity of Evolutionary Algorithms in Biobjective Optimization Problems

Multiobjective optimization problems require algorithms capable of efficiently approximating the Pareto optimal front while ensuring good convergence and diversity. In this paper, we introduce and analyze two approaches designed to refine the search process in the later stages of evolutionary multiobjective optimization algorithms. Our proposal takes an approximation of the Pareto optimal front for a multiobjective optimization problem. Then, it defines different subregions, reference points, and weight vectors, to better converge to the true Pareto optimal front. We propose two approaches: (1) defining subregions based on objective space partitioning and (2) dynamically adapting weight vectors distributions based on the front's geometry. These strategies allow for a more precise approximation of the Pareto optimal front while maintaining a well-distributed set of solutions.