Energy-efficient scheduling for a permutation flow shop with variable transportation time using an improved discrete whale swarm optimization

As environmental issues become more serious, energy-efficient scheduling has emerged as a research hotspot. Although permutation flow shop scheduling has attracted substantial research attention, practical cases that consider conveyor speed control energy-saving strategies have rarely been studied. Motivated by this gap, this paper addresses a permutation flow shop scheduling problem with sequencedependent setup time considering a novel conveyor speed control energy-saving strategy. The aim is to find the optimal processing sequence of jobs and conveyor belt speed setting scheme between any two nodes (i.e., machine or warehouse). A mixed-integer linear programming model is established to minimize both the makespan and total energy consumption. To solve such a bi-objective model, an improved discrete whale swarm optimization (IDWSO) is designed that combines differential evolution, augmented search and job-swapped mutation to enhance performance. Numerical experiments are carried out to compare the performance of the IDWSO with existing algorithms, including the nondominated sorting genetic algorithm-II (NSGA-II) and the multiobjective evolutionary algorithm based on decomposition (MOEA/D). Sensitivity analyses on energy-saving strategies under different scale problems/alternative conveyor speeds are carried out to verify the effectiveness of the model and algorithm.