Energy-efficient distributed heterogeneous welding flow shop scheduling problem using a modified MOEA/D

Abstract In this study, a multi-objective evolutionary algorithm based on decomposition (MOEA/D) is proposed for energy-efficient scheduling of distributed heterogeneous welding flow shop (DHWFSP). This problem is extended from distributed flow shop with different amounts of machines in different factories. In addition, it is allowed that multiple machines could operate one job simultaneously. Considering energy efficiency and productivity, this problem could be treated as three sub-problems: job assignment among factories, job scheduling within each factory and deciding the amount of multi-machines upon each job. A multi-objective mathematical model and modified MOEA/D are proposed to minimize the total energy consumption and makespan simultaneously. In modified MOEA/D, various genetic operators and problem-specific local search strategies are designed for multi-level optimization. The comparison experiment with some well-known algorithms shows the effectiveness of the proposed MOEA/D in optimizing and balancing two contradictory objectives.