Energy-Efficiency Oriented Distributed Heterogeneous Hybrid Flow Shop Scheduling With Multilevelled Mixed-Model Assembly

This article studies an energy-efficient scheduling problem in a two-stage manufacturing system with distributed heterogeneous hybrid flow shops and mixed-model assembly lines (EDHHFSP-MMAL). A mixed-integer linear programming model is proposed that simultaneously optimizes total tardiness and energy consumption (including operational, idle, and common energy components). To solve this multiobjective problem, a learning competitive swarm optimizer (LCSO) is proposed that integrates two novel mechanisms: 1) environmental-competitive learning through probability models capturing product-task relationships and 2) comprehensive learning utilizing reinforcement learning to guide local search based on nondominated solution states. The hybrid approach balances convergence speed and solution diversity by combining solution-space and policy-space learning perspectives. Experimental results demonstrate LCSO’s superior performance over compared methods, achieving 25% improvement in energy-time tradeoff compared to other state-of-the-art multiobjective optimizers in solving related problems. The proposed method particularly excels in optimizing complex energy-time tradeoffs while maintaining better solution diversity and convergence across different problem scales.