Competitive and Cooperative-Based Strength Pareto Evolutionary Algorithm for Green Distributed Heterogeneous Flow Shop Scheduling

This work aims to resolve the distributed heterogeneous permu-tation flow shop scheduling problem (DHPFSP) with minimizing makespan and total energy consumption (TEC). To solve this NP-hard problem, this work proposed a competitive and cooperative-based strength Pareto evo-lutionary algorithm (CCSPEA) which contains the following features: 1) An initialization based on three heuristic rules is developed to generate a population with great diversity and convergence. 2) A comprehensive metric combining convergence and diversity metrics is used to better represent the heuristic information of a solution. 3) A competitive selection is designed which divides the population into a winner and a loser swarms based on the comprehensive metric. 4) A cooperative evolutionary schema is proposed for winner and loser swarms to accelerate the convergence of global search. 5) Five local search strategies based on problem knowledge are designed to improve convergence. 6) A problem-based energy-saving strategy is presented to reduce TEC. Finally, to evaluate the performance of CCSPEA, it is compared to four state-of-art and run on 22 instances based on the Taillard benchmark. The numerical experiment results demonstrate that 1) the proposed comprehensive metric can efficiently represent the heuristic information of each solution to help the later step divide the population. 2) The global search based on the competitive and cooperative schema can accelerate loser solutions convergence and further improve the winner's exploration. 3) The problem -based initialization, local search, and energy-saving strategies can efficiently reduce the makespan and TEC. 4) The proposed CCSPEA is superior to the state-of-art for solving DHPFSP.