Clustering-based genetic offspring generation for solving multi-objective optimization problems with intricate Pareto sets

In contrast to traditional benchmarks, multiobjective optimization problems (MOPs) encountered in practical applications often exhibit intricate variable interdependencies, giving rise to complex Pareto sets (PSs) characterized by rotated or nonlinear shapes. Simulated binary crossover (SBX), a widely used genetic operator for solving MOPs, experiences significant performance degradation when applied to MOPs with intricate PSs. The rotation-based SBX (RSBX) incorporates the rotational property into SBX to handle MOPs with linear but rotated PSs. Nevertheless, RSBX may encounter difficulties in solving MOPs with nonlinear PSs. In order to tackle this challenge, we propose a clustering-based mating restriction strategy to address MOPs with intricate PSs, and the proposed approach has been integrated with RSBX to formulate an algorithm named CRSBX. The clustering-based mating restriction strategy involves partitioning the parent population into approximately linearly distributed clusters, then RSBX is applied to each cluster for effective offspring generation. We empirically investigate the impact of the clustering algorithm and its associated parameters on CRSBX. Ablation studies are also conducted to examine the efficacy of the clustering-based mating restriction strategy. Additionally, we compare CRSBX with other representative algorithms on benchmark problems and real-world applications with intricate PSs. Comparison results highlight the promising performance of CRSBX in effectively addressing MOPs with intricate PSs.