A Bi-Population Cooperative Discrete Differential Evolution for Multiobjective Energy-Efficient Distributed Blocking Flow Shop Scheduling Problem

Peak carbon emissions and carbon neutrality have become important initiatives for the country to solve outstanding problems of resource and environmental constraints and promote green and low-energy development, and have attracted widespread attention from the industry. The distributed flow shop scheduling problem (DPFSP) is a typical problem that mainly works by consuming energy. However, DPFSP rarely considers energy efficiency and blocking constraints. In this study, an excellent bi-population cooperative discrete differential evolution (BCDDE) is proposed, aiming to address the energy-efficient distributed blocking flow shop scheduling problem (EEDBFSP) with total energy consumption (TEC) and total tardiness (TTD) as two objectives. A bi-population cooperative strategy is constructed to enhance the diversity of BCDDE, while utilizing it to initialize the population to enhance the quality of the initial solution. An adaptive local search operator strategy is developed to improve the BCDDE convergence. Critical and noncritical paths are devised to further optimize TEC and TTD objectives. The efficiency of each strategy related to BCDDE is verified and compared with state-of-the-art algorithms in the benchmark suite. Numerical results show that BCDDE becomes an efficient optimizer for the EEDBFSP, significantly outperforming the state-of-the-art algorithms at the 95% confidence interval.