A cooperative whale optimization algorithm for energy-efficient scheduling of the distributed blocking flow-shop with sequence-dependent setup time

The distributed blocking flow-shop sequence-dependent scheduling problem (DBFSDSP) with the production efficiency measures has been extensively concerned as its wide industrial applications. Whereas, energy efficiency indicators are often ignored in the literature. The DBFSDSP considered makespan, total tardiness, and total energy consumption is investigated in this paper. A cooperative whale optimization algorithm (CWOA) is proposed to solve the DBFSDSP as the complexity of the distributed and multi-objective optimization. First, the critical path of DBFSDSP is defined. An energy-saving operation for the non-critical path is designed to reduce the energy consumption of the system. Second, an accelerated operation for the critical path is designed to reduce the makespan and total tardiness. Third, three acceptance criteria for multi-objective optimization are proposed to improve the diversity of the population. The statistical and computational experimentation in an extensive benchmark testified that the CWOA outperforms the state-of-the-art algorithms regarding efficiency and significance in solving DBFSDSP. •The critical path of DBFSDSP is defined.•An energy-saving operation for the non-critical path is designed.•An accelerated operation for the critical path is presented.•An insertion operation for the critical factory is introduced.•Three acceptance criteria for multi-objective optimization are proposed.