Improved NSGA-II for the energy-efficient distributed blocking flow shop scheduling problem

In the context of the national carbon peak and carbon neutrality strategies, the green advancement of the manufacturing industry has become a key issue of concern for manufacturing enterprises. This paper takes into account the energy consumption (EC) problem in the Distributed Blocking Flow Shop Scheduling Problem (DBFSP). For the energy-efficient Distributed Blocking Flow Shop Scheduling Problem (EEDBFSP) with the optimization objectives of makespan ( C _max ) and total energy consumption (TEC), an improved NSGA-II algorithm (INSGA-II) is presented. The algorithm employs a dual-mode initialization strategy that synergistically combines the improved distributed NEH (IDNEH) heuristic with randomized solution generation, strategically balancing solution quality and population diversity. To strengthen the algorithm's exploration-convergence balance, we design a local search strategy. In addition, by defining the critical path and non-critical path, we accelerate operations on the critical path to optimize the makespan while decelerating those on the non-critical path, which reduces EC without extending the makespan. This paper systematically explores the impact of algorithm parameter settings on the optimization effect and performs extensive comparative experiments with others algorithms. The results of extensive benchmark tests and statistical analyses confirm that INSGA-II, as an optimizer for solving the EEDBFSP, is significantly effective, and its performance is notably better than that of other comparative algorithms.