A Novel Hybrid Differential Evolutionary Algorithm for Solving Multi-objective Distributed Permutation Flow-Shop Scheduling Problem

The Distributed Permutation Flow-Shop Scheduling Problem (DPFSP) is a classic issue in distributed scheduling that involves job allocation and processing order within a factory, and it is known to be NP-hard. Numerous researchers have proposed various intelligent optimization algorithms to address the DPFSP; however, there are fewer studies related to the multi-objective DPFSP problem, and the algorithms for solving this problem also suffer from poor solution quality and tend to fall into local optimization and so on. To tackle the multi-objective DPFSP, this paper proposes a novel hybrid differential evolutionary algorithm aimed at minimizing both the maximum completion time and total delay time. In this algorithm, Bernoulli chaotic mapping is applied during the population initialization process to enhance the diversity of the initial population. Additionally, an adaptive mutation factor and crossover rate are designed to balance the global and local search capabilities of the algorithm. Furthermore, a novel selection strategy is constructed based on the NEH algorithm, specular reflection learning, and Pareto dominance relation to improve the quality of the solution set when solving instances of varying sizes. This strategy enhances the algorithm's optimization ability and helps it escape local optima. The effectiveness and superiority of the proposed algorithm are verified through 24 instances of different sizes. The results demonstrate that the proposed algorithm outperforms other improved algorithms in terms of convergence, and the uniformity and diversity of the solution set, making it an effective solution for the multi-objective distributed permutation flow-shop scheduling problem.