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Article

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

by
Jing Wang
1,2,
Jingsheng Lian
2,
Youpeng Deng
2,
Lang Pan
2,
Huan Xue
2,
Yanming Chen
3,
Debiao Li
4,
Xixing Li
2 and
Deming Lei
5,*
1
Hubei Yangtze River Shipping Development Research Center, Wuhan 430014, China
2
Hubei Key Laboratory of Modern Manufacturing and Quality Engineering, School of Mechanical Engineering, Hubei University of Technology, Wuhan 430068, China
3
Hubei Standardization and Quality Institute, Wuhan 430000, China
4
School of Economics and Management, Fuzhou University, Fuzhou 350108, China
5
School of Automation, Wuhan University of Technology, Wuhan 430070, China
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(8), 1243; https://doi.org/10.3390/sym17081243
Submission received: 4 June 2025 / Revised: 12 July 2025 / Accepted: 17 July 2025 / Published: 5 August 2025
(This article belongs to the Special Issue Meta-Heuristics for Manufacturing Systems Optimization, 3rd Edition)
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Abstract

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.
Keywords: lace dyeing; parallel machine scheduling; probabilistic re-dyeing operations; symmetry-driven differential evolution; collaborative mechanism lace dyeing; parallel machine scheduling; probabilistic re-dyeing operations; symmetry-driven differential evolution; collaborative mechanism

Share and Cite

MDPI and ACS Style

Wang, J.; Lian, J.; Deng, Y.; Pan, L.; Xue, H.; Chen, Y.; Li, D.; Li, X.; Lei, D. Symmetry-Driven Two-Population Collaborative Differential Evolution for Parallel Machine Scheduling in Lace Dyeing with Probabilistic Re-Dyeing Operations. Symmetry 2025, 17, 1243. https://doi.org/10.3390/sym17081243

AMA Style

Wang J, Lian J, Deng Y, Pan L, Xue H, Chen Y, Li D, Li X, Lei D. Symmetry-Driven Two-Population Collaborative Differential Evolution for Parallel Machine Scheduling in Lace Dyeing with Probabilistic Re-Dyeing Operations. Symmetry. 2025; 17(8):1243. https://doi.org/10.3390/sym17081243

Chicago/Turabian Style

Wang, Jing, Jingsheng Lian, Youpeng Deng, Lang Pan, Huan Xue, Yanming Chen, Debiao Li, Xixing Li, and Deming Lei. 2025. "Symmetry-Driven Two-Population Collaborative Differential Evolution for Parallel Machine Scheduling in Lace Dyeing with Probabilistic Re-Dyeing Operations" Symmetry 17, no. 8: 1243. https://doi.org/10.3390/sym17081243

APA Style

Wang, J., Lian, J., Deng, Y., Pan, L., Xue, H., Chen, Y., Li, D., Li, X., & Lei, D. (2025). Symmetry-Driven Two-Population Collaborative Differential Evolution for Parallel Machine Scheduling in Lace Dyeing with Probabilistic Re-Dyeing Operations. Symmetry, 17(8), 1243. https://doi.org/10.3390/sym17081243

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