A Cooperative Fruit Fly Optimization Algorithm for Energy-Efficient Scheduling of Distributed Permutation Flow-Shop with Limited Buffers

The scheduling problem of distributed permutation flow shop with limited buffer aiming at production efficiency measures has attracted widespread attention due to its closer alignment with real manufacturing environments. However, the energy efficiency metric is often ignored. The Energy-Efficient scheduling of Distributed Permutation Flow Shop Problem with Limited Buffer (EEDPFSP-LB) with the objectives of Makespan ( $C_{max}$) and Total Energy Consumption (TEC) is studied, and a Cooperative Fruit fly Optimization Algorithm (CFOA) is proposed in this paper. First, the critical path of EEDPFSP-LB is identified, and energy-efficient operation is applied to non-critical paths to reduce the system’s energy consumption. Second, five acceptance criteria for multi-objective optimization are introduced to enhance the diversity of the population. Third, to select a superior next-generation population, a new congestion calculation method is introduced to resolve the issue of indeterminate positional relationships among non-dominated solutions with identical crowding distances at the same dominance level. Finally, CFOA is extensively tested and compared with state-of-the-art algorithms across 360 instances, demonstrating CFOA’s strong competitiveness in solving EEDPFSP-LB.