Symmetry-Driven Two-Population Collaborative Differential Evolution for Parallel Machine Scheduling in Lace Dyeing with Probabilistic Re-Dyeing Operations

In lace textile manufacturing, the dyeing process in parallel machine environments faces challenges from sequence-dependent setup times due to color family transitions, machine eligibility constraints based on weight capacities, and probabilistic re-dyeing operations arising from quality inspection failures, which often lead to increased tardiness. To tackle this multi-constrained problem, a stochastic integer programming model is formulated to minimize total estimated tardiness. A novel symmetry-driven two-population collaborative differential evolution (TCDE) algorithm is then proposed. It features two symmetrically complementary subpopulations that achieve a balance between global exploration and local exploitation. One subpopulation employs chaotic parameter adaptation through a logistic map for symmetrically enhanced exploration, while the other adjusts parameters based on population diversity and convergence speed to facilitate symmetry-aware exploitation. Moreover, it also incorporates a symmetrical collaborative mechanism that includes the periodic migration of top individuals between subpopulations, along with elite-set guidance, to enhance both population diversity and convergence efficiency. Extensive computational experiments were conducted on 21 small-scale (optimally validated via CVX) and 15 large-scale synthetic datasets, as well as 21 small-scale (similarly validated) and 20 large-scale industrial datasets. These experiments demonstrate that TCDE significantly outperforms state-of-the-art comparative methods. Ablation studies also further verify the critical role of its symmetry-based components, with computational results confirming its superiority in solving the considered problem.