A dual-population-based evolutionary algorithm for multi-objective optimization problems with irregular Pareto fronts

When solving multi-objective optimization problems (MOPs) with irregular Pareto fronts (e.g., disconnected, degenerated, inverted) via evolutionary algorithms, a critical issue is how to obtain a set of well-distributed Pareto optimal solutions. To remedy this issue, we propose a dual-population-based evolutionary algorithm with individual exploitation and weight vector adaptation, named DPEA-IEAW. Specifically, the two populations, termed globPop and locPop, individually evolve by decomposition-based and Pareto dominance-based methods, responsible for global evolution and local evolution, respectively. These two populations collaborate through substantial information exchange, thereby facilitating each other's evolution. Firstly, the distribution of the two populations is analyzed and an individual exploitation operation is designed for locPop to exploit some promising areas that are undeveloped in globPop. Then, the guide-position is devised for globPop to indicate the optimal point for a subproblem on the Pareto front (PF). By using the guide-position, a strategy for generating uniform weight vectors is proposed to improve the population diversity. Finally, comprehensive experiments on 37 widely used test functions and 2 real-world problems demonstrate that the proposed DPEA-IEAW outperforms comparison algorithms in solving MOPs with various PFs.