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27 pages, 737 KB  
Article
A Q-Learning-Based Adaptive NSGA-II for Fuzzy Distributed Assembly Hybrid Flow Shop Scheduling Problem
by Rui Wu, Qiang Li, Bin Cheng, Yanming Chen and Xixing Li
Processes 2026, 14(3), 500; https://doi.org/10.3390/pr14030500 (registering DOI) - 31 Jan 2026
Abstract
With the growing emphasis on holistic management throughout the entire product lifecycle, multi-stage production models that integrate distributed manufacturing, transportation, and assembly processes have gradually attracted research attention. However, studies in this area remain relatively scarce. This paper addresses the fuzzy distributed assembly [...] Read more.
With the growing emphasis on holistic management throughout the entire product lifecycle, multi-stage production models that integrate distributed manufacturing, transportation, and assembly processes have gradually attracted research attention. However, studies in this area remain relatively scarce. This paper addresses the fuzzy distributed assembly hybrid flow shop scheduling problem (FDAHFSP), comprehensively considering the entire production flow from manufacturing and transportation to final assembly. A mathematical model is first established with the objectives of minimizing the fuzzy total weighted earliness/tardiness and the fuzzy total energy consumption. To effectively solve this problem, a Q-learning-based adaptive NSGA-II (Q-ANSGA) is proposed. The algorithm incorporates a hybrid strategy combining multiple rules to enhance the quality of the initial population. Additionally, a Q-learning-based adaptive parameter adjustment mechanism is designed to dynamically optimize genetic algorithm parameters, thereby improving the algorithm’s search efficiency and convergence performance. Furthermore, eight neighborhood search operators are developed, and an iterative greedy strategy is integrated to guide the local search process. Finally, comprehensive experiments on 45 test instances are conducted to evaluate the effectiveness of each improvement component and the overall performance of Q-ANSGA. Experimental results demonstrate that the proposed algorithm achieves superior performance in solving the FDAHFSP due to its systematic enhancements. Full article
(This article belongs to the Section AI-Enabled Process Engineering)
33 pages, 4474 KB  
Article
An Improved Multi-Objective Memetic Algorithm with Q-Learning for Distributed Hybrid Flow Shop Considering Sequence-Dependent Setup Times
by Yong Shen, Yibo Liu, Hongwei Kang, Xingping Sun and Qingyi Chen
Symmetry 2026, 18(1), 135; https://doi.org/10.3390/sym18010135 - 9 Jan 2026
Viewed by 207
Abstract
Most multi-objective studies on distributed hybrid flow shops that include tardiness-related objectives focus solely on optimizing makespan alongside a single tardiness objective. However, in real-world scenarios with strict contractual deadlines or high penalty costs for delays, minimizing both total tardiness and the number [...] Read more.
Most multi-objective studies on distributed hybrid flow shops that include tardiness-related objectives focus solely on optimizing makespan alongside a single tardiness objective. However, in real-world scenarios with strict contractual deadlines or high penalty costs for delays, minimizing both total tardiness and the number of tardy jobs becomes critically important. This paper addresses this gap by prioritizing tardiness-related objectives while simultaneously optimizing makespan, total tardiness, and the number of tardy jobs. It investigates a distributed hybrid flow shop scheduling problem (DHFSP), which has some symmetries on machines. We propose an improved multi-objective memetic algorithm incorporating Q-learning (IMOMA-QL) to solve this problem, featuring (1) a hybrid initialization method that generates high-quality, diverse solutions by balancing all three objectives; (2) a multi-factory SB2OX crossover operator preserving high-performance job sequences across factories; (3) six problem-specific neighborhood structures for efficient solution space exploration; and (4) a Q-learning-guided variable neighborhood search that adaptively selects neighborhood structures. Based on extensive numerical experiments across 100 generated instances and a comprehensive comparison with four comparative algorithms, the proposed IMOMA demonstrates its effectiveness and proves to be a competitive method for solving the DHFSP. Full article
(This article belongs to the Section Computer)
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29 pages, 1016 KB  
Review
Towards Sustainable Factories: A Systematic Review of Energy-Conscious Job-Shop Scheduling Models and Algorithms
by Motlokoa Makhoabenyane, Shunsheng Guo and Ely Leburu
Sustainability 2025, 17(24), 11330; https://doi.org/10.3390/su172411330 - 17 Dec 2025
Viewed by 763
Abstract
Job-shop scheduling plays a pivotal role in sustainable manufacturing because scheduling decisions strongly influence energy consumption, machine utilization, and environmental performance. Traditional job-shop scheduling research has mainly optimized makespan, throughput, and tardiness; however, growing sustainability pressures and Industry 4.0 technologies have shifted attention [...] Read more.
Job-shop scheduling plays a pivotal role in sustainable manufacturing because scheduling decisions strongly influence energy consumption, machine utilization, and environmental performance. Traditional job-shop scheduling research has mainly optimized makespan, throughput, and tardiness; however, growing sustainability pressures and Industry 4.0 technologies have shifted attention toward energy-conscious scheduling. This review systematically analyzes 2083 publications retrieved from SCOPUS, Web of Science, and IEEE Xplore to map the evolution of energy-efficient job-shop scheduling (EEJSS) models, methods, and industrial applications. Compared with prior surveys, this work contributes a sector-specific analysis, an updated classification of energy-aware models, and the first structured mapping of EEJSS research to sustainability and Industry 4.0 capabilities. Further, challenges such as computational complexity, absence of standardized energy benchmarks, limited industrial deployment, and narrow sustainability metrics are addressed. Overall, this review consolidates the state of EEJSS and positions energy-aware scheduling as a foundational enabler of low-carbon, resilient, and intelligent manufacturing systems. Full article
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27 pages, 1221 KB  
Article
Optimization of Continuous Flow-Shop Scheduling Considering Due Dates
by Feifeng Zheng, Chunyao Zhang and Ming Liu
Algorithms 2025, 18(12), 788; https://doi.org/10.3390/a18120788 - 12 Dec 2025
Viewed by 408
Abstract
For a no-wait flow shop with continuous-flow characteristics, this study simultaneously considers machine setup times and rated processing speed constraints, aiming to minimize the sum of the maximum completion time and the maximum tardiness. First, lower bounds for the maximum completion time, the [...] Read more.
For a no-wait flow shop with continuous-flow characteristics, this study simultaneously considers machine setup times and rated processing speed constraints, aiming to minimize the sum of the maximum completion time and the maximum tardiness. First, lower bounds for the maximum completion time, the maximum tardiness, and the total objective function are developed. Second, a mixed-integer programming (MIP) model is formulated for the problem, and nonlinear elements are subsequently linearized via time discretization. Due to the computational complexity of the problem, two algorithms are proposed: a heuristic algorithm with fixed machine links and greedy rules (HAFG) and a genetic algorithm based on altering machine combinations (GAAM) for solving large-scale instances. The Earliest Due Date (EDD) rule is used as baselines for algorithmic comparison. To better understand the behaviors of the two algorithms, we observe the two components of the objective function separately. The results show that, compared with the EDD rule and GAAM, the HAFG algorithm tends to focus more on optimizing the maximum completion time. The performance of both algorithms is evaluated using their relative deviations from the developed lower bounds and is compared against the EDD rule. Numerical experiments demonstrate that both HAFG and GAAM significantly outperform the EDD rule. In large-scale instances, the HAFG algorithm achieves a gap of about 4%, while GAAM reaches a gap of about 3%, which is very close to the lower bound. In contrast, the EDD rule shows a deviation of about 10%. Combined with a sensitivity analysis on the number of machines, the proposed framework provides meaningful managerial insights for continuous-flow production environments. Full article
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13 pages, 642 KB  
Article
Memory-Dependent Derivative Versus Fractional Derivative (III): Difference in Modeling Epidemics
by Jin-Liang Wang and Hui-Feng Li
Fractal Fract. 2025, 9(12), 814; https://doi.org/10.3390/fractalfract9120814 - 12 Dec 2025
Viewed by 281
Abstract
The outbreaks of large-scale epidemics, such as COVID-19 in 2019–2022, challenge modelers. Beside the effect of the incubation period of the virus, the delay property of detection should be also stressed. This kind of memory effect affects the entire change rate, which cannot [...] Read more.
The outbreaks of large-scale epidemics, such as COVID-19 in 2019–2022, challenge modelers. Beside the effect of the incubation period of the virus, the delay property of detection should be also stressed. This kind of memory effect affects the entire change rate, which cannot be reflected by the conventional instantaneous derivative. The fractional derivative (FD) meets this request to some extent. Yet the shortcoming of it limits its usage. Through a strict modeling approach, a new susceptible–infective–removed (SIR) model with the memory-dependent derivative (MDD) has been constructed. The numerical simulations indicate that (1) the neglecting of the incubation period may underestimate the number of susceptible individuals and overestimate the infected ones; (2) the neglecting of the treatment period may badly overestimate the removed individuals; (3) the consequence of tardy detection intervention may be very serious, and the infectious rate may increase rapidly with a postponed peak time; and (4) the SIR model with the FD yields bad estimations, not only in the primary stage but also in the subsequent evolution. Due to the reasonability of the new SIR model with the MDD, it is suggested to epidemic researchers. Full article
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20 pages, 328 KB  
Article
Resource Allocation and Minmax Scheduling Under Group Technology and Different Due-Window Assignments
by Li-Han Zhang and Ji-Bo Wang
Axioms 2025, 14(11), 827; https://doi.org/10.3390/axioms14110827 - 7 Nov 2025
Cited by 1 | Viewed by 312
Abstract
This article investigates single-machine group scheduling integrated with resource allocation under different due-window (DIFDW) assignment. Three distinct scenarios are examined: one with constant processing times, one with a linear resource consumption function, and one with a convex [...] Read more.
This article investigates single-machine group scheduling integrated with resource allocation under different due-window (DIFDW) assignment. Three distinct scenarios are examined: one with constant processing times, one with a linear resource consumption function, and one with a convex resource consumption function. The objective is to minimize the total cost comprising the maximum earliness/tardiness penalties, the due-window starting time cost, the due-window size cost, and the resource consumption cost. For each problem variant, we analyze the structural properties of optimal solutions and develop corresponding solution algorithms: a polynomial-time optimal algorithm for the case with constant processing times, heuristic algorithms for problems involving linear and convex resource allocation, and the branch-and-bound algorithm for obtaining exact solutions. Numerical experiments are conducted to evaluate the performance of the proposed algorithms. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
12 pages, 402 KB  
Article
Pull-Based Output Rate Control of a Flexible Job Shop in a Multi-Shop Production Chain
by Wei Weng, Meimei Zheng and Jiuchun Ren
Mathematics 2025, 13(21), 3543; https://doi.org/10.3390/math13213543 - 5 Nov 2025
Viewed by 447
Abstract
This paper addresses the problem where optimizing a single production shop within a production chain may not improve the overall performance of the entire chain. To overcome this and synchronize the efficiency of each shop, methods are proposed to align the output rate [...] Read more.
This paper addresses the problem where optimizing a single production shop within a production chain may not improve the overall performance of the entire chain. To overcome this and synchronize the efficiency of each shop, methods are proposed to align the output rate of an upstream shop with the limited intake rate of its downstream shop. In the proposed methods, the output rate of the upstream shop is used to guide job scheduling, processing, and resource allocation in the shop. Simulation results from a real-world case study demonstrate that implementing this pull-based system reduces job earliness and tardiness by over 90% in the tested factory, where the upstream shop is a flexible job shop, leading to lower inventory costs, idling costs, and labor costs. Full article
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8 pages, 1030 KB  
Proceeding Paper
An Improved Fruit Fly Optimization Algorithm for Multi-Objective Scheduling in Hybrid Flow Shops
by Ziyi Shang, Yarong Chen and Jabir Mumtaz
Eng. Proc. 2025, 111(1), 37; https://doi.org/10.3390/engproc2025111037 - 4 Nov 2025
Viewed by 336
Abstract
This study proposes an improved Fruit Fly Optimization Algorithm integrated with Simulated Annealing (SA-FOA) for hybrid flow shop scheduling problems with dual objectives of minimizing makespan and total tardiness. The algorithm adopts a three-stage integration strategy to generate high-quality initial populations, surpassing random [...] Read more.
This study proposes an improved Fruit Fly Optimization Algorithm integrated with Simulated Annealing (SA-FOA) for hybrid flow shop scheduling problems with dual objectives of minimizing makespan and total tardiness. The algorithm adopts a three-stage integration strategy to generate high-quality initial populations, surpassing random initialization. During olfactory search, insertion-based neighborhood operations expand search scope, while visual search incorporates simulated annealing acceptance criteria to escape local optima. Validation employs three scalable instances, comparing SA-FOA against basic FOA and classical scheduling rules. Experimental results demonstrate significant superiority in Inverted Generational Distance (IGD), Non-dominant rate (NR), and Convergence Matrix (C-matrix metrics), highlighting enhanced convergence, distribution, and diversity. Notably, performance advantages amplify with problem scale growth. Full article
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9 pages, 571 KB  
Proceeding Paper
A Study on Multi-Objective Unrelated Parallel Machine Scheduling Using an Improved Spider Monkey Optimization Algorithm
by Ziyang Ji, Yarong Chen, Lixuan Pan and Mudassar Rauf
Eng. Proc. 2025, 111(1), 16; https://doi.org/10.3390/engproc2025111016 - 22 Oct 2025
Viewed by 458
Abstract
For the unrelated parallel machine scheduling problem, an improved Spider Monkey Optimization algorithm incorporating a variable neighborhood search (VNS) mechanism (VNS-SMO) is proposed to minimize the makespan, total tardiness, and total energy consumption. The VNS-SMO incorporates six types of neighborhood searches based on [...] Read more.
For the unrelated parallel machine scheduling problem, an improved Spider Monkey Optimization algorithm incorporating a variable neighborhood search (VNS) mechanism (VNS-SMO) is proposed to minimize the makespan, total tardiness, and total energy consumption. The VNS-SMO incorporates six types of neighborhood searches based on the objective characteristics to strengthen the optimization performance of the algorithm. To verify the effectiveness and superiority of VNS-SMO, first, Taguchi experiments were used to determine the algorithm parameters, and then three instances of different scales were solved and compared with the traditional algorithms NSGA-II, PSO, and SMO. The experimental results indicate that VNS-SMO significantly outperforms the comparison algorithms on IGD, NR, and C-matrix metrics, fully demonstrating its comprehensive advantages in convergence, distribution, and diversity. Full article
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23 pages, 2604 KB  
Article
Flexible Job Shop Scheduling Optimization with Multiple Criteria Using a Hybrid Metaheuristic Framework
by Shubhendu Kshitij Fuladi and Chang Soo Kim
Processes 2025, 13(10), 3260; https://doi.org/10.3390/pr13103260 - 13 Oct 2025
Viewed by 1808
Abstract
The flexible job shop scheduling problem (FJSP) becomes significantly more complex when real-world factors such as due dates, sequence-dependent setup times, and processing times are considered as multiple criteria. This study presents a hybrid scheduling approach that combines a genetic algorithm (GA) and [...] Read more.
The flexible job shop scheduling problem (FJSP) becomes significantly more complex when real-world factors such as due dates, sequence-dependent setup times, and processing times are considered as multiple criteria. This study presents a hybrid scheduling approach that combines a genetic algorithm (GA) and variable neighborhood search (VNS), where several dispatching rules are used to create the initial population and improve exploration. The multiple objectives are to minimize makespan, total tardiness, and total setup time while improving overall production efficiency. To test the proposed approach, standard FJSP datasets were extended with due dates and setup times for two different environments. Due dates were generated using the Total Work Content (TWK) method. This study also introduces a dynamic scheduling framework that addresses dynamic events such as machine breakdowns and new job arrivals. A rescheduling strategy was developed to maintain optimal solutions in dynamic situations. Experimental results show that the proposed hybrid framework consistently performs better than other methods in static scheduling and maintains high performance under dynamic conditions. The proposed method achieved 6.5% and 2.59% improvement over the baseline GA in two different environments. The results confirm that the proposed strategies effectively address complex, multi-constraint scheduling problems relevant to Industry 4.0 and smart manufacturing environments. Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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27 pages, 369 KB  
Review
Industrial Scheduling in the Digital Era: Challenges, State-of-the-Art Methods, and Deep Learning Perspectives
by Alina Itu
Appl. Sci. 2025, 15(19), 10823; https://doi.org/10.3390/app151910823 - 9 Oct 2025
Cited by 1 | Viewed by 2579
Abstract
Industrial scheduling plays a central role in Industry 4.0, where efficiency, robustness, and adaptability are essential for competitiveness. This review surveys recent advances in reinforcement learning, digital twins, and hybrid artificial intelligence (AI)–operations research (OR) approaches, which are increasingly used to address the [...] Read more.
Industrial scheduling plays a central role in Industry 4.0, where efficiency, robustness, and adaptability are essential for competitiveness. This review surveys recent advances in reinforcement learning, digital twins, and hybrid artificial intelligence (AI)–operations research (OR) approaches, which are increasingly used to address the complexity of flexible job-shop and distributed scheduling problems. We focus on how these methods compare in terms of scalability, robustness under uncertainty, and integration with industrial IT systems. To move beyond an enumerative survey, the paper introduces a structured analysis in three domains: comparative strengths and limitations of different approaches, ready-made tools and integration capabilities, and representative industrial case studies. These cases, drawn from recent literature, quantify improvements such as reductions in makespan, tardiness, and cycle time variability, or increases in throughput and schedule stability. The review also discusses critical challenges, including data scarcity, computational cost, interoperability with Enterprise Resource Planning (ERP)/Manufacturing Execution System (MES) platforms, and the need for explainable and human-in-the-loop frameworks. By synthesizing methodological advances with industrial impact, the paper highlights both the potential and the limitations of current approaches and outlines key directions for future research in resilient, data-driven production scheduling. Full article
(This article belongs to the Special Issue Advances in AI and Optimization for Scheduling Problems in Industry)
55 pages, 29751 KB  
Article
Multi-Objective Combinatorial Optimization for Dynamic Inspection Scheduling and Skill-Based Team Formation in Distributed Solar Energy Infrastructure
by Mazin Alahmadi
Systems 2025, 13(9), 822; https://doi.org/10.3390/systems13090822 - 19 Sep 2025
Viewed by 1355
Abstract
Maintaining operational efficiency in distributed solar energy systems requires intelligent coordination of inspection tasks and workforce resources to handle diverse fault conditions. This study presents a bi-level multi-objective optimization framework that addresses two tightly coupled problems: dynamic job scheduling and skill-based team formation. [...] Read more.
Maintaining operational efficiency in distributed solar energy systems requires intelligent coordination of inspection tasks and workforce resources to handle diverse fault conditions. This study presents a bi-level multi-objective optimization framework that addresses two tightly coupled problems: dynamic job scheduling and skill-based team formation. The job scheduling component assigns geographically dispersed inspection tasks to mobile teams while minimizing multiple conflicting objectives, including travel distance, tardiness, and workload imbalance. Concurrently, the team formation component ensures that each team satisfies fault-specific skill requirements by optimizing team cohesion and compactness. To solve the bi-objective team formation problem, we propose HMOO-AOS, a hybrid algorithm integrating six metaheuristic operators under an NSGA-II framework with an Upper Confidence Bound-based Adaptive Operator Selection. Experiments on datasets of up to seven instances demonstrate statistically significant improvements (p<0.05) in solution quality, skill coverage, and computational efficiency compared to NSGA-II, NSGA-III, and MOEA/D variants, with computational complexity OG·N·(M+logN) (time complexity), O(N·L) (space complexity). A cloud-integrated system architecture is also proposed to contextualize the framework within real-world solar inspection operations, supporting real-time data integration, dynamic rescheduling, and mobile workforce coordination. These contributions provide scalable, practical tools for solar operators, maintenance planners, and energy system managers, establishing a robust and adaptive approach to intelligent inspection planning in renewable energy operations. Full article
(This article belongs to the Special Issue Advances in Operations and Production Management Systems)
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12 pages, 1344 KB  
Proceeding Paper
Decision Support System for Assessing Teacher Performance Using the Simple Additive Weighting (SAW) Method at SMK XYZ
by Anggun Fergina, Asep Sukandar, Rahma Nisa Salsabila and Ayuni Indah Wulandari
Eng. Proc. 2025, 107(1), 75; https://doi.org/10.3390/engproc2025107075 - 9 Sep 2025
Viewed by 893
Abstract
SMK XYZ is a private school under Yayasan Pembina Pendidikan Doa Bangsa (YPPDB) which was established in 2011. The school has several expertise programs, including Software Engineering, Institutional Accounting and Finance, and Motorcycle Business Engineering. Assessing the success of a school is an [...] Read more.
SMK XYZ is a private school under Yayasan Pembina Pendidikan Doa Bangsa (YPPDB) which was established in 2011. The school has several expertise programs, including Software Engineering, Institutional Accounting and Finance, and Motorcycle Business Engineering. Assessing the success of a school is an important thing that greatly affects the development of students in the learning process to achieve their goals. Assessment of teachers’ work should be performed using appropriate and efficient methods. To improve teacher performance, the development of an agenda monitoring and assessment system based on the Simple Additive Weighting (SAW) method can be an effective alternative. This system is designed to assist school management in monitoring teacher activities objectively and measurably, as well as providing clear assessments based on certain criteria such as attendance, tardiness, student evaluation results, and innovation in learning. The SAW method is used to calculate the final score of teacher performance by summing up the weighted values of each normalized criterion. In this case study, the system helps decision makers to recognize the strengths and weaknesses of each teacher, so that related recommendations for competency development can be given. The implementation of this system demonstrates increased responsibility in appraisal and motivates teachers to improve their performance according to set standards. Full article
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23 pages, 994 KB  
Article
A Random Forest-Enhanced Genetic Algorithm for Order Acceptance Scheduling with Past-Sequence-Dependent Setup Times
by Yu-Yan Zhang, Shih-Hsin Chen, Yen-Wen Wang, Chia-Hsuan Liao and Chen-Hsiang Yu
Mathematics 2025, 13(16), 2672; https://doi.org/10.3390/math13162672 - 19 Aug 2025
Viewed by 1047
Abstract
This study developed a simple genetic algorithm (SGA) enhanced by a random forest (RF) surrogate model, namely SGARF, to solve the permutation flow-shop scheduling problem with order acceptance under the conditions of limited capacity, weighted-tardiness, and past-sequence-dependent (PSD) [...] Read more.
This study developed a simple genetic algorithm (SGA) enhanced by a random forest (RF) surrogate model, namely SGARF, to solve the permutation flow-shop scheduling problem with order acceptance under the conditions of limited capacity, weighted-tardiness, and past-sequence-dependent (PSD) setup times (PFSS-OAWT with PSD). To the best of our knowledge, this is the first study to investigate this problem. Our proposed algorithm increases the setup time for each successive job by a constant proportion of the cumulative processing time of preceding jobs to capture the progressive slowdown that often occurs on real production lines. In the developed algorithm with maximum 105 fitness evaluations, the RF surrogate model predicts objective function values and guides crossover and mutation. On the PFSS-OAWT with PSD benchmark (up to 500 orders and 20 machines, 160 instances), SGARF represents improvements of 0.9% over SGA, 0.8% over SGALS, and 5.6% over SABPO. Although the surrogate incurs additional runtime, the gains in both profit and order-acceptance rates justify its use for high-margin, offline planning. Overall, the results of this study suggest that integrating evolutionary search into data-driven prediction is an effective strategy for solving complex capacity-constrained scheduling problems. Full article
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29 pages, 5522 KB  
Article
An Improved NSGA-II for Three-Stage Distributed Heterogeneous Hybrid Flowshop Scheduling with Flexible Assembly and Discrete Transportation
by Zhiyuan Shi, Haojie Chen, Fuqian Yan, Xutao Deng, Haiqiang Hao, Jialei Zhang and Qingwen Yin
Symmetry 2025, 17(8), 1306; https://doi.org/10.3390/sym17081306 - 12 Aug 2025
Cited by 2 | Viewed by 1209
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Engineering and Materials)
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