A decomposition-based evolutionary algorithm with clustering and hierarchical estimation for multi-objective fuzzy flexible jobshop scheduling

As an effective approximation algorithm for multi-objective jobshop scheduling, multi-objective evolutionary algorithms (MOEAs) have received extensive attention. However, maintaining a balance between the diversity and convergence of non-dominated solutions while ensuring overall convergence is an open problem in the context of solving Multi-objective Fuzzy Flexible Jobshop Scheduling Problems (MFFJSPs). To address it, we propose a new MOEA named MOEA/DCH by introducing a hierarchical estimation method, a clustering-based adaptive decomposition strategy, and a heuristic-based initialization method into a basic MOEA based on decomposition. Specifically, a hierarchical estimation method balances the convergence and diversity of non-dominant solutions by integrating Pareto dominance and scalarization function information. A clustering-based adaptive decomposition strategy is constructed to enhance the population's ability to approximate a complex Pareto front. A heuristic-based initialization method is developed to provide high-quality initial solutions. The performance of MOEA/DCH is verified and compared with five competitive MOEAs on widely-tested benchmark datasets. Empirical results demonstrate the effectiveness of MOEA/DCH in balancing the diversity and convergence of non-dominated solutions while ensuring overall convergence.