Balanced Adaptive Subspace Collaboration for Mixed Pareto-Lexicographic Multi-Objective Problems with Priority Levels

Multi-objective Optimization Problems (MOPs) where objectives have different levels of importance in decision-making, known as Mixed Pareto-Lexicographic MOPs with Priority Levels (PL-MPL-MOPs), are increasingly prevalent in real-world applications. General-purpose Multi-Objective Evolutionary Algorithms (MOEAs) that treat all objectives equally not only increase the workload of decision-making but also suffer from computational inefficiencies due to the necessity of generating many additional solutions. Conversely, strictly adhering to Priority Levels (PLs) during optimization can easily result in premature convergence within some PLs. To address this issue, we suggest an effective Balanced Adaptive Subspace Collaboration (BASC) method in this paper. Specifically, this method decomposes the search space into sub-fronts based on PLs and utilizes a sampling mechanism that operates exclusively within subspaces formed by sub-fronts at the same PL to generate new solutions, thereby emphasizing the exploitation of individual PLs. Furthermore, a set of parameters is employed to control the strictness of adherence to each PL, with these parameters adaptively adjusted to balance exploration across different PLs. The two mechanisms are then collaboratively integrated into MOEAs. Comprehensive experimental studies on benchmark problems and a set of complex job-shop scheduling problems in semiconductor manufacturing demonstrate the competitiveness of the proposed method over existing methods.