Multi-objective Scheduling Optimization for Distributed Flexible Job Shop with Multiple Factories

Aiming at the multi-factory distributed flexible job shop scheduling problem, this paper proposes an improved NSGA-II algorithm incorporating Variable Neighborhood Search (VNS) to simultaneously optimize three objectives: maximum completion time, total energy consumption, and machine load balancing. In terms of modeling, a dynamic transportation time model based on job complexity, processing time, and process route is designed, and a three-layer encoding mechanism is adopted to represent factory assignment, machine selection, and operation sequencing. In terms of algorithm, multiple variable neighborhood search structures are embedded into the NSGA-II framework to enhance local search capability. Comparative experiments with the standard NSGA-II, MOEA/D, RVEA and Memetic Algorithm on 20 instances show that the NSGA-II-VNS outperforms the other algorithms in at least two objectives. The Wilcoxon signed-rank test indicates that the proposed algorithm is significantly superior to other representative algorithms in most cases.