Search Results (34)

Distributed hybrid flow-shop scheduling problems (DHFSPs) are widely encountered in manufacturing systems. Their complexity increases significantly when multiple overhead cranes are used for material handling. This paper investigates a distributed hybrid flow-shop scheduling problem with multiple overhead crane transportation (DHFSP-MCT), aiming to simultaneously minimize makespan and total energy consumption (including machining and transport). A hierarchical reinforcement learning-based bi-population collaborative metaheuristic algorithm (HRL-BCMA) is proposed. In HRL-BCMA, an iterated greedy strategy is first adopted to generate an initial population. Then, a two-level reinforcement learning framework is designed: a high-level agent decides when to release jobs to the shop floor, while a low-level agent based on a graph isomorphism network selects improvement operators. Furthermore, a bi-population co-evolutionary framework and a knowledge-informed strategy are introduced to enhance solution quality and diversity. Experimental evaluations on both randomly generated instances and a real-world-inspired aluminum manufacturing case show that HRL-BCMA reduces makespan by 8.6% and total energy consumption by 12.3% on average compared to the best existing algorithm (CBMA) while achieving superior Pareto front coverage. These results demonstrate the effectiveness of the proposed method for green scheduling problems with crane transport constraints. Full article

The Energy-Efficient Hybrid Flow Shop Scheduling Problem poses a significant multi-objective optimization challenge, necessitating the simultaneous minimization of conflicting objectives: Total Tardiness, Total Energy Cost, and Carbon Trading Cost. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is a classic algorithm in the field of multi-objective optimization. However, this algorithm frequently lacks the adaptive capability required to navigate high-dimensional solution spaces, often trapping the search in local optima, particularly when constrained by practical energy states of heterogeneous machines. To address these complexities, this study proposes a hybrid algorithm, named QGN, integrating Q-learning, the Grey Wolf Optimizer (GWO), and the NSGA-II. Specifically, QGN algorithm integrates NSGA-II for robust diversity maintenance with GWO for high-precision intensification. Unlike static hybrid methods, QGN employs a Q-learning agent as an adaptive controller to dynamically balance global exploration and local refinement, providing a theoretically grounded response to the rugged search landscape created by machine heterogeneity. Comprehensive experimental validation across diverse production scenarios confirms that QGN significantly outperforms baselines, including NSGA-II, Jaya, and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), as well as the state-of-the-art Q-learning- and GVNS-driven NSGA-II (QVNS) algorithm, in terms of both convergence and diversity. The results indicate that the proposed algorithm yields superior solution dominance, generates a substantially larger set of non-dominated solutions, and maintains a more uniform distribution along the Pareto front. Full article

Distributed manufacturing introduces new challenges to traditional production shop scheduling, and the combination of machine learning and metaheuristic algorithms offers new approaches to solve these problems. To address the distributed hybrid flow shop scheduling problem with missing operations (MDHFSP), a shuffled frog leaping algorithm with Q-learning (QSFLA) is proposed to minimize the maximum completion time. A dual-string encoding method is proposed to represent factory assignment and job sequencing, with heuristic methods utilized during decoding to determine machine assignments. The state set is constructed based on changes in the minimum and average objective values of solutions in the population, while the action set is built from different optimized solutions and learned solutions during the memeplex search process. Symmetry-driven Q-learning is employed to dynamically adjust the optimization objects based on the state of the population. Testing on 140 benchmarks and a real-life example shows that symmetry-driven Q-learning plays a positive role within QSFLA, and QSFLA effectively solves the MDHFSP. Full article

In this paper, a Multiple-Objective Memetic Algorithm (MOMA) is proposed to address the Energy-Efficient Distributed Assembly Permutation Flow-Shop Scheduling Problem (EEDAPFSP) by explicitly exploiting the structural and objective symmetries inherent in the scheduling process, with the dual objectives of minimizing the maximum completion time (makespan) and total energy consumption (TEC). The EEDAPFSP is a complex NP-hard optimization problem in modern sustainable manufacturing that balances production efficiency and environmental sustainability. During the global search phase, a symmetry-preserving dual-search framework is constructed, in which diverse and potential regions in the solution space are explored by symmetrically generating time-dominant product sub-sequences (TDPSs) and energy-dominant product sub-sequences (EDPSs) in the individuals of each iteration, enabling complementary exploration from time- and energy-oriented perspectives. This is accomplished through the incorporation of a variable-weight metric technique and a first product fixed strategy into an estimation distributed algorithm-based hyper-heuristic (EDAHH), so as to maintain a balanced and symmetric probabilistic modeling of decision patterns with respect to the makespan and energy consumption. In the local search phase, two problem-specific designed neighborhood structures are proposed to refine the job sequences corresponding to the TDPS and EDPS in the superior sub-population, effectively reducing both the makespan and TEC. A box-level $\epsilon$ dominance technique based on the crowding distance is proposed for Pareto archive updating. Additionally, an energy-saving strategy is embedded throughout the algorithm, incorporating three mechanisms—job processing delay, machine shutdown and restart control, and speed regulation—to further optimize TEC during both the global and local search phases. Finally, extensive computational experiments are carried out, and the results demonstrate that the MOMA achieves significantly better performance in terms of the inverted generational distance ($IGD$) and the quality metric $\rho$ compared with state-of-the-art algorithms. The resulting Pareto front of non-dominated solutions provides a comprehensive set of trade-offs between energy consumption and the makespan, offering decision makers flexible and efficient scheduling options. Full article

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

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

Production scheduling that involves distributed factories, machine maintenance, and resource constraints plays a crucial role in manufacturing. However, these realistic constraints have rarely been considered simultaneously in the hybrid flow shop (HFS). To address this issue, a distributed resource-constrained hybrid flow shop scheduling problem with machine breakdowns (DRCHFSP-MB) is studied. There are two optimization objectives, i.e., makespan and total energy consumption (TEC). To solve the strongly NP-hard problem, a mathematical model is established and a block–neighborhood-based multi-objective evolutionary algorithm (BNMOEA) is developed. In the proposed algorithm, an efficient hybrid initialization method is adopted to obtain high-quality individuals to participate in the evolutionary process of the population. Next, to enhance the search capability of the BNMOEA, three well-designed crossover operators are used in the global search. Then, the convergence of the proposed algorithm is improved by utilizing eight critical factory-based local search operators combined with block–neighborhood. Finally, the BNMOEA is compared with several of the most advanced multi-objective algorithms; the results indicate that the BNMOEA has an outstanding performance in solving DRCHFSP-MB. Full article

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

The Distributed No-Wait Flow Shop Scheduling Problem (DNWFSP) arises in various manufacturing contexts, such as chemical production and electronic assembly, where strict no-wait constraints and multi-factory coordination are required. Solving the DNWFSP involves determining the allocation of jobs to factories and the no-wait processing sequences within each factory, making it a highly complex combinatorial problem. To address the limitations of existing methods—including poor initial solution quality, limited neighborhood exploration, and a tendency to converge prematurely—this paper proposes a Multi-Neighborhood Adaptive Tabu Search Algorithm (MNATS). The MNATS integrates a balance–lookahead NEH initializer (BL-NEH), an adaptive neighborhood local search (ANLS) strategy, and an Adaptive Tabu-Guided Perturbation (ATP) strategy. Experimental results on multiple benchmark instances demonstrate that MNATS algorithm significantly outperforms several state-of-the-art algorithms in terms of solution quality and robustness. Full article

In order to address the Distributed Displacement Flow Shop Scheduling Problem (DPFSP) with uncertain processing times in real production environments, Plant Simulation is employed to construct a simulation model for the MSRDPFSP. The model conducts quantitative analyses of workshop layout, assembly line design, worker status, operating status of robotic arms and AGV vehicles, and production system failure rates. A hybrid NEH-DDQN algorithm is integrated into the simulation model via a COM interface and DLL, where the NEH algorithm ensures the model maintains optimal performance during the early training phase. Four scheduling strategies are designed for workpiece allocation across different workshops. A deep neural network replaces the traditional Q-table for greedy selection among these four scheduling strategies, using each workshop’s completion time as a simplified state variable. This approach reduces algorithm training complexity by abstracting away intricate workpiece allocation details. Experimental comparisons show that for the data of 500 workpieces, the NEH algorithm in 3 s demonstrates equivalent quality to that produced by the GA algorithm in 300 s. After 2000 iterations, the DDQN algorithm achieves a 15% reduction in makespan with only a 2.5% increase in computational time compared to random search, this joint simulation system offers an efficient and stable solution for the modeling and optimization of the MSRDPFSP issue. Full article

The Mixed No-Idle Permutation Flow Shop Scheduling Problem (MNPFSSP) represents a specific case within regular flow scheduling problems. In this problem, some machines allow idle times between consecutive jobs or operations while other machines do not. Traditionally, the MNPFSSP has been addressed using the metaheuristics and exact methods. This work proposes an Evolutionary Strategy Based on the Generalized Mallows Model (ES-GMM) to solve the issue. Additionally, its advanced version, ES-GMMc, is developed, incorporating operating conditions to improve execution times without compromising solution quality. The proposed approaches are compared with algorithms previously used for the problem under study. Statistical tests of the experimental results show that the ES-GMMc achieved reductions in execution time, especially standing out in large instances, where the shortest computing times were obtained in 23 of 30 instances, without affecting the quality of the solutions. Full article

Digitalization plays a crucial role in improving the performance of chemical companies. In this context, different modeling, simulation, and optimization techniques such as MILP, discrete-event simulation (DES), and data-driven (DD) models are being used. Due to their heterogeneity, these techniques must be executed individually, and holistic optimization is manual and time-consuming. We propose Benders decomposition to combine these techniques into one rigorous optimization procedure. The main idea is that heterogeneous models can simultaneously be optimized as Benders subproblems. We illustrate this concept with the distributed permutation flow shop scheduling problem (DPFSP) and assume that a MILP, DES, and DD model exist for three flow shops. Our approach can compute bounds and report gap information on the optimal makespan for five medium-sized literature instances. The approach is promising because it enables the optimization of heterogeneous models and makes it possible to build optimization capabilities on an existing model and tool landscape in chemical companies. Full article

Demand fluctuates in actual production. When manufacturers face demand under their maximum capacity, suspension shifts are crucial for cost reduction and on-time delivery. In this case, suspension shifts are needed to minimize idle time and prevent inventory buildup. Thus, it is essential to integrate suspension shifts with scheduling under an uncertain production environment. This paper addresses the two-stage hybrid flow shop scheduling problem (THFSP) with suspension shifts under uncertain processing times, aiming to minimize the weighted sum of earliness and tardiness. We develop a stochastic integer programming model and validate it using the Gurobi solver. Additionally, we propose a dual-space co-evolutionary biased random key genetic algorithm (DCE-BRKGA) with parallel evolution of solutions and scenarios. Considering decision-makers’ risk preferences, we use both average and pessimistic criteria for fitness evaluation, generating two types of solutions and scenario populations. Testing with 28 datasets, we use the value of the stochastic solution (VSS) and the expected value of perfect information (EVPI) to quantify benefits. Compared to the average scenario, the VSS shows that the proposed algorithm achieves additional value gains of 0.9% to 69.9%. Furthermore, the EVPI indicates that after eliminating uncertainty, the algorithm yields potential improvements of 2.4% to 20.3%. These findings indicate that DCE-BRKGA effectively supports varying decision-making risk preferences, providing robust solutions even without known processing time distributions. Full article

Prefabricated cabin modular units (PMCUs) are a widespread type of intermediate products used during ship or offshore platform construction. This paper focuses on the scheduling problem of PMCU assembly flow shops, which is summarized as a multi-objective, fuzzy-blocking hybrid flow-shop-scheduling problem based on learning and fatigue effects (FB-HFSP-LF) to minimize the maximum fuzzy makespan and maximize the average fuzzy due-date agreement index. This paper proposes a multi-objective non-dominated sorting gravitational search algorithm (MONSGSA) to solve it. In the proposed MONSGSA, the ranked-order value is used to convert continuous solutions to discrete solutions. Multi-dimensional Latin hypercube sampling is used to enhance initial population diversity. Setting up an external archive to maintain non-dominated solutions while introducing an adaptive inertia factor and a trap avoidance operator to guide individual positional updates. The results of multiple sets of experiments show that Pareto solutions of MONSGSA have better distribution and convergence compared to other competitors. Finally, the instance of PMCU manufacturer is used for validation, and the results show that MONSGSA has better applicability to practical problems. Full article

The permutation flow-shop scheduling problem is a classical problem in scheduling that aims at identifying the optimal sequence of jobs that should be processed in a number of machines in an effort to minimize makespan or some other performance criterion. The distributed permutation flow-shop scheduling problem adds multiple factories where copies of the machines exist and asks for minimizing the makespan on the longest-running location. In this paper, the problem is approached using Constraint Programming and its specialized scheduling features, such as interval variables and non-overlap constraints, while a novel heuristic is proposed for computing lower bounds. Two constraint programming models are proposed: one that solves the Distributed Permutation Flow-shop Scheduling problem, and another one that drops the constraint of processing jobs under the same order for all machines of each factory. The experiments use an extended public dataset of problem instances to validate the approach’s effectiveness. In the process, optimality is proved for many problem instances known in the literature but has yet to be proven optimal. Moreover, a high speed of reaching optimal solutions is achieved for many problems, even with moderate big sizes (e.g., seven factories, 20 machines, and 20 jobs). The critical role that the number of jobs plays in the complexity of the problem is identified and discussed. In conclusion, this paper demonstrates the great benefits of scheduling problems that stem from using state-of-the-art constraint programming solvers and models that capture the problem tightly. Full article