Energy-Efficient Shop Scheduling Using Space-Cooperation Multi-Objective Optimization

Since Industry 5.0 emphasizes that manufacturing enterprises should raise awareness of social contribution to achieve sustainable development, more and more meta-heuristic algorithms are investigated to save energy in manufacturing systems. Although non-dominated sorting-based meta-heuristics have been recognized as promising multi-objective optimization methods for solving the energy-efficient flexible job shop scheduling problem (EFJSP), it is hard to guarantee the quality of the Pareto front (e.g., total energy consumption, makespan) due to the lack of population diversity. This is mainly because an improper individual comparison inevitably reduces population diversity, thus limiting exploration and exploitation abilities during population updates. To achieve efficient population evolution, this paper introduces a novel space-cooperation multi-objective optimization (SCMO) method that can effectively solve EFJSP to obtain scheduling schemes with better trade-offs. By cooperatively evaluating the similarity among individuals in both the decision space and objective space, we propose a space-cooperation population update method based on a three-vector representation that can accurately eliminate repetitive individuals to derive higher-quality Pareto solutions. To further improve search efficiency, we propose a difference-driven local search, which selectively changes the positions of operations with higher differences to search for neighbors effectively. Based on the Taguchi method, we conduct experiments to obtain a suitable parameter combination of SCMO. Comprehensive experimental results show that, compared to state-of-the-art methods, our SCMO method achieves the highest HV and NR and the lowest IGD, with an average of 0.990, 0.952, and 0.001, respectively. Meanwhile, compared to traditional local search approaches, our difference-driven local search obtains twice the HV on instance Mk12 and reduces the solving time from 1521 s to 475 s.