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.