An improved MOEA/D for multi-objective flexible job shop scheduling by considering efficiency and cost

To achieve cost reduction and efficiency improvement in the production process of the aerospace industry, this study establishes a mathematical model for the multi-objective flexible job shop scheduling problem (MOFJSP). The model comprehensively considers four optimisation objectives: completion time, tool number, machine load, and machine energy consumption. For solving the MOFJSP, an improved MOEA/D (IMOEA/D) algorithm is proposed. To improve the quality of solutions, the algorithm introduces another global update strategy in addition to the original substitution operation. The population is initialised using four allocation rules, and the neighbourhood is dynamically updated based on the degree of population evolution. The simulation results on a single instance indicate that the simulation time of IMOEA/D has decreased by 10.5% and machine energy consumption has reduced by 9.5%. Moreover, when compared to various classic multi-objective algorithms on 25 benchmark instances, the IMOEA/D algorithm achieved optimal results in 19 instances for inverted generational distance comparisons, 15 instances for hypervolume comparisons and nearly all instances for set coverage comparisons. The results reveal that the proposed IMOEA/D is effective and competitive in solving MOFJSP.