A Pareto-based collaborative multi-objective optimization algorithm for energy-efficient scheduling of distributed permutation flow-shop with limited buffers

Energy-efficient scheduling of distributed production systems has become a common practice among large companies with the advancement of economic globalization and green manufacturing. Nevertheless, energy-efficient scheduling of distributed permutation flow-shop problem with limited buffers (DPFSP-LB) does not receive adequate attention in the relevant literature. This paper is therefore the first attempt to study this DPFSP-LB with objectives of minimizing makespan and total energy consumption (TEC). To solve this energy-efficient DPFSP-LB, a Pareto-based collaborative multi-objective optimization algorithm (CMOA) is proposed. In the proposed CMOA, first, the speed scaling strategy based on problem property is designed to reduce TEC. Second, a collaborative initialization strategy is presented to generate a high-quality initial population. Third, three properties of DPFSP-LB are utilized to develop a collaborative search operator and a knowledge-based local search operator. Finally, we verify the effectiveness of each improvement component of CMOA and compare it against other well-known multi-objective optimization algorithms on instances. Experiment results demonstrate the effectiveness of CMOA in solving this energy-efficient DPFSP-LB. Especially, the CMOA is able to obtain excellent results on all problems regarding the comprehensive metric, and is also competitive to its rivals regarding the convergence metric. •A green criterion is considered in the studied problem.•A new constraint of the limited buffers is introduced into this problem.•A multi-objective optimization algorithm is presented to solve this problem.•An effective energy saving strategy is proposed.•An initialization strategy and local search strategy are proposed.