An Improved NSGA-II for Three-Stage Distributed Heterogeneous Hybrid Flowshop Scheduling with Flexible Assembly and Discrete Transportation

This study tackles scheduling challenges in multi-product assembly within distributed manufacturing, where components are produced simultaneously at dedicated factories (single capacity per site) and assembled centrally upon completion. To minimize makespan and maximum tardiness, we design a symmetry-exploiting enhanced Non-dominated Sorting Genetic Algorithm II (NSGA-II) integrated with Q-learning. Our approach systematically explores the solution space using dual symmetric variable neighborhood search (VNS) strategies and two novel crossover operators that enhance solution-space symmetry and genetic diversity. An ε-greedy policy leveraging maximum Q-values guides the symmetry-aware search toward optimality while enabling strategic exploration. We validate an MILP model (Gurobi-implemented) and present our symmetry-refined algorithm against six heuristics. Multi-scale experiments confirm superiority, with Friedman tests demonstrating statistically significant gains over benchmarks, providing actionable insights for efficient distributed manufacturing scheduling.