An improved multi-objective evolutionary algorithm based on decomposition for energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time

With the increasing attention on environment issues, green scheduling in manufacturing industry has been a hot research topic. As a typical scheduling problem, permutation flow shop scheduling has gained deep research, but the practical case that considers both setup and transportation times still has rare research. This paper addresses the energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time to minimise both makespan as economic objective and energy consumption as green objective. The mathematical model of the problem is formulated. To solve such a bi-objective problem effectively, an improved multi-objective evolutionary algorithm based on decomposition is proposed. With decomposition strategy, the problem is decomposed into several sub-problems. In each generation, a dynamic strategy is designed to mate the solutions corresponding to the sub-problems. After analysing the properties of the problem, two heuristics to generate new solutions with smaller total setup times are proposed for designing local intensification to improve exploitation ability. Computational tests are carried out by using the instances both from a real-world manufacturing enterprise and generated randomly with larger sizes. The comparisons show that dynamic mating strategy and local intensification are effective in improving performances and the proposed algorithm is more effective than the existing algorithms.