Solving energy-efficient distributed job shop scheduling via multi-objective evolutionary algorithm with decomposition

The energy-efficient distributed job shop scheduling problem (EEDJSP) is studied in this paper with the criteria of minimizing both makespan and energy consumption. A mathematical model is presented and an effective modified multi-objective evolutionary algorithm with decomposition (MMOEA/D) is proposed. First, the encoding scheme and decoding scheme are designed based on the characteristics of the EEDJSP. Second, several initialization rules are fused together to produce a diverse population with certain diversity. Third, a collaborative search is proposed to exchange the information between individuals for exploring good solutions. Fourth, three problem-specific local intensification heuristics are designed. Moreover, an adaptive selection strategy is proposed to adjust the utilization of local search operators dynamically. Besides, an energy adjustment strategy is designed for further improvement. We carry out extensive numerical tests with the benchmarking instances. The effectiveness of local intensification as well as energy adjustment strategy is verified via the statistical comparisons. It also shows that the MMOEA/D outperforms other algorithms.