Flexible Job Shop Scheduling Problem Research Articles

A dual population collaborative genetic algorithm for solving flexible job shop scheduling problem with AGV

With the increase in labor costs and the development of manufacturing automation technology, automatic guided vehicle (AGV) is widely used in various flexible workshop scenarios. The integrated scheduling of processing machines and AGV is of great significance in real-world workshop production. This article studies the integration problem of flexible job shop scheduling problem (FJSP) and AGV with minimizing the makespan, and proposes a novel mixed integer linear programming (MILP) model and a dual population collaborative genetic algorithm (DCGA). In DCGA, a two-layer encoding strategy based on machine selection and operation sequencing is used. Two decoding methods are designed to determine AGV selection, and each population uses a decoding method. Moreover, a population collaboration operation is designed. The feasibility and effectiveness of the MILP model and DCGA are verified through experimental simulation. Specifically, the DCGA improves 18 current best solutions for benchmarks in the existing studies.

An ensemble of brain storm optimization and Q-learning methods for distributed flexible job shop scheduling problems with distribution operations

Distributed manufacturing scheduling problems have attracted much concern from both industrial and academic areas. Nevertheless, distributed scheduling problems with distribution operations are seldom studied. This work proposes a distributed flexible job shop scheduling problem with distribution operations. A set of jobs is handled at distributed flexible job shops, and then the finished jobs are transported to their corresponding customers following given due dates. First, a mixed integer programming model is established to minimize total tardiness. Second, an ensemble of brain storm optimization and Q-learning methods is developed to solve the formulated model. Six heuristics are hybridized to generate a high-quality initial population. A Q-learning method is devised by fully employing found search information to guide subsequent search processes instead of using fixed parameters as basic brain storm optimization. A variable neighborhood search method combining problem-specific knowledge is designed to further refine the found best individual. At last, the formulated model and method are compared with three state-of-the-art metaheuristics and a mathematical programming solver CPLEX via using a group of problem instances. The results and analysis demonstrate that the developed model and algorithm have more powerful competitiveness in addressing the studied problem.

Dynamic constrained evolutionary optimization based on deep Q-network

Dynamic constrained optimization problems (DCOPs) are common and important optimization problems in real-world, which have great difficulty to solve. Dynamic constrained evolutionary algorithms (DCEAs) are widely used methods for solving DCOPs. However, existing DCEAs often struggle with convergence, particularly for DCOPs with drastic dynamic changes or intricate constraints. To address this issue, this paper proposes a novel DCEA called DCEA-DQN, which leverages the powerful perception and decision-making capabilities of Deep Q-Network (DQN). DCEA-DQN integrates two DQNs to enhance its performance. The first DQN is designed to adaptively respond to dynamic changes, enabling effective handling of DCOPs with various types and degrees of changes. It provides a high-quality re-initialized population for subsequent static optimization, resulting in faster and improved convergence. The second DQN is introduced to guide the mutation direction during offspring generation. It steers the population towards better feasible regions or directs it towards the optimal individual within the current feasible region. Moreover, a penalty mechanism is employed to handle constraints during offspring generation. To evaluate the performance of DCEA-DQN, comprehensive empirical studies are conducted using a new test suite called C-GMPB and a dynamic flexible job-shop scheduling problem. The experimental results, using two commonly used metrics EB and EO in the field of DCOPs, demonstrate that DCEA-DQN outperforms six state-of-the-art DCEAs and achieved optimal performance on 80% and 75% of all 24 test problems, respectively. The source code for DCEA-DQN is available at https://github.com/CIA-SZU/YRT.

Study on flexible job shop scheduling problem considering energy saving

The Flexible Job Shop Scheduling Problem (FJSP) is an extension of the classical Job Shop Scheduling Problem (JSP). The research objective of the traditional FJSP mainly considers the completion time, but ignores the energy consumption of the manufacturing system. In this paper, a mathematical model of the energy-efficient flexible job shop scheduling problem is constructed. The optimization objectives are completion time, delay time, and total equipment energy consumption. To solve the model, an improved non-dominated sorting genetic algorithm (CT-NSGA-II) is proposed to obtain the optimal scheduling solution. First, the heuristic rules of GLR were used to generate the initial population with good quality and diversity. Second, different crossover and variation operators are designed for the process sequencing and equipment selection parts to enhance the diversity of the evolutionary population. The sparsity theory is introduced to find sparse solutions and three neighborhood structures are designed to perform local search on sparse solutions to improve the uniformity of the optimal solution set distribution. Finally, a competitive selection strategy based on the bidding mechanism is proposed for the Pareto optimal solution set to obtain a better scheduling scheme. The experimental results show that the proposed improved algorithm is feasible and effective in the FJSP problem considering energy consumption, and the algorithm has some application value in improving the efficiency of smart shop operation.

Flexible job-shop scheduling problem with parallel batch machines based on an enhanced multi-population genetic algorithm

AbstractThe flexible job-shop scheduling problem (FJSP) with parallel batch processing machine (PBM) is one of those long-standing issues that needs cutting-edge approaches. It is a recent extension of standard flexible job shop scheduling problems. Despite their wide application and prevalence in practical production, it seems that current research on these types of combinatorial optimization problems remains limited and uninvestigated. More specifically, existing research mainly concentrates on the flow shop scenarios in parallel batch machines for job shop scheduling but few literature emphasis on the flexible job shop integration in these contexts. To directly address the above mentioned problems, this paper establishes an optimization model considering parallel batch processing machines, aiming to minimize the maximum completion time in operating and production environments. The proposed solution merges variable neighborhood search with multi-population genetic algorithms, conducting a neighborhood search on the elite population to reduce the likelihood of falling into local optima. Subsequently, its applicability was evaluated in computational experiments using real production scenarios from a partnering enterprise and extended datasets. The findings from the analyses indicate that the enhanced algorithm can decrease the objective value by as much as 15% compared to other standard algorithms. Importantly, the proposed approach effectively resolves flexible job shop scheduling problems involving parallel batch processing machines. The contribution of the research is providing substantial theoretical support for enterprise production scheduling.

Flexible Job Shop Scheduling via Dual Attention Network-Based Reinforcement Learning.

Flexible manufacturing has given rise to complex scheduling problems such as the flexible job shop scheduling problem (FJSP). In FJSP, operations can be processed on multiple machines, leading to intricate relationships between operations and machines. Recent works have employed deep reinforcement learning (DRL) to learn priority dispatching rules (PDRs) for solving FJSP. However, the quality of solutions still has room for improvement relative to that by the exact methods such as OR-Tools. To address this issue, this article presents a novel end-to-end learning framework that weds the merits of self-attention models for deep feature extraction and DRL for scalable decision-making. The complex relationships between operations and machines are represented precisely and concisely, for which a dual-attention network (DAN) comprising several interconnected operation message attention blocks and machine message attention blocks is proposed. The DAN exploits the complicated relationships to construct production-adaptive operation and machine features to support high-quality decision-making. Experimental results using synthetic data as well as public benchmarks corroborate that the proposed approach outperforms both traditional PDRs and the state-of-the-art DRL method. Moreover, it achieves results comparable to exact methods in certain cases and demonstrates favorable generalization ability to large-scale and real-world unseen FJSP tasks.

A self-learning multi-population evolutionary algorithm for flexible job shop scheduling under time-of-use pricing

Due to the energy crisis and environmental downgrade, manufacturing companies face rising costs. The pressure on manufacturers to reduce costs and increase efficiency is increasing. The flexible job shop scheduling problem considering time-of-use pricing (FJSPTOUP) is studied to minimize the maximum completion time and total electricity cost. A new self-learning multi-population evolutionary algorithm (SLMPEA) is proposed to address the static scheduling problem. A self-learning module is designed to acquire knowledge from elite individuals in subpopulations. The knowledge discovered can guide the evolution of subpopulations. To improve the convergence of the algorithm and maintain the diversity of the population, we present an elite retention and enhancement strategy. Two enhancement operators are developed to elevate the quality of elite individuals, and a selection strategy is designed for the enhancement operators. A time-of-use-based adjustment strategy is proposed to reduce the total electricity costs without increasing the maximum completion time. Experimental results show that the proposed SLMPEA outperforms the comparative algorithms in solving FJSPTOUP.

Research on Solving Flexible Job Shop Scheduling Problem Based on Improved GWO Algorithm SS-GWO

As an important branch of production scheduling, the flexible job shop scheduling problem (FJSP) is a typical NP-hard problem. Researchers have adopted many intelligent algorithms to solve the FJSP problem, nonetheless, the task of dynamically adapting its essential parameters during the computational process is a significant challenge, resulting in the solution efficiency and quality failing to meet the production requirements. To this end, this paper proposes an adaptive gray wolf fast optimization algorithm (SS-GWO), which adopts the gray wolf algorithm (GWO) as the basic optimization method, and the algorithm adaptively selects the global search or local search according to the degree of agglomeration of individuals. Firstly, a non-linear convergence factor strategy is employed to control the global exploration and local exploitation capabilities of the algorithm at different stages. This enhances optimization precision and accelerates convergence speed, achieving a dynamic balance between the two. Secondly, the spiral search mechanism of Whale Optimization Algorithm is used in GWO to improve the exploration capability of Gray Wolf Optimization Algorithm. Finally, the effectiveness of SS-GWO model is verified by comparison experiments. The comparison demonstrates the superiority of SS-GWO over the other five state-of-the-art algorithms in solving the 22 classical benchmark test functions. SS-GWO is applied to solve FJSP by means of the standard test function bandimarte calculus. The optimal solution and performance of SS-GWO for solving FJSP are compared with other algorithms. The experimental results show that the SS-GWO algorithm has good optimization performance, and the maximum completion time is reduced by 19% and 37% compared with that of IGWO and GWO, respectively, and the proposed SS-GWO algorithm achieves a better solution effect on flexible job shop scheduling instances, which can satisfy the actual production scheduling needs.

Research on low-carbon flexible job shop scheduling problem based on improved Grey Wolf Algorithm

Research on low-carbon flexible job shop scheduling problem based on improved Grey Wolf Algorithm

Correction: A memetic NSGA‑II for the multi‑objective flexible job shop scheduling problem with real‑time energy tariffs

Correction: A memetic NSGA‑II for the multi‑objective flexible job shop scheduling problem with real‑time energy tariffs

Multi-objective optimization of dual resource integrated scheduling problem of production equipment and RGVs considering conflict-free routing.

In flexible job shop scheduling problem (FJSP), the collision of bidirectional rail guided vehicles (RGVs) directly affects RGVs scheduling, and it is closely coupled with the allocation of production equipment, which directly affects the production efficiency. In this problem, taking minimizing the maximum completion time of RGVs and minimizing the maximum completion time of products as multi-objectives a dual-resource integrated scheduling model of production equipment and RGVs considering conflict-free routing problem (CFRP) is proposed. To solve the model, a multi-objective improved discrete grey wolf optimizer (MOID-GWO) is designed. Further, the performance of popular multi-objective evolutionary algorithms (MOEAs) such as NSGA-Ⅱ, SPEA2 and MOPSO are selected for comparative test. The results show that, among 42 instances of different scales designed, 37, 34 and 28 instances in MOID-GWO are superior to the comparison algorithms in metrics of generational distance (GD), inverted GD (IGD) and Spread, respectively. Moreover, in metric of Convergence and Diversity (CD), the Pareto frontier (PF) obtained by MOID-GWO is closer to the optimal solution. Finally, taking the production process of a construction machinery equipment component as an example, the validity and feasibility of the model and algorithm are verified.

An improved MOEA/D for low-carbon many-objective flexible job shop scheduling problem

The low-carbon many-objective flexible job shop scheduling problem (LCMa-FJSP) has developed into a major topic of current research owing to global warming and energy crises. In this study on the LCMa-FJSP, a comprehensive scheduling model with four objectives, such as minimizing the completion time, total delay time, processing load rate of the bottleneck machine and total carbon emissions of the system is built. To solve this complex LCMa-FJSP, a novel multi-objective evolutionary algorithm (MOEA) with three modified strategies, named IMOEA/D-HS, is proposed. First, a novel hybrid initialization strategy combining five heuristic methods is used to obtain a reliable initial population. Second, a new restart strategy that considers limited restarts is applied to reduce carbon emissions while protecting the lifetime of the machine. Third, a local reinforcement strategy is proposed that can efficiently improve the convergence of a part of sub-problems identified by distance and angle-based evaluation indicator (APD). To impartially and comprehensively analyze and evaluate the performance of IMOEA/D-HS, it is compared with four state-of-the-art algorithms, i.e., MOEA/D-DRA, MOEA/DD, NSGA-III and RVEA on 15 numerical tests. The results demonstrate that IMOEA/D-HS outperforms these four algorithms in the terms of convergence and diversity, which proves its ability to solve complex LCMa-FJSPs.

Joint optimization of flexible job shop scheduling and preventive maintenance under high-frequency production switching

To secure a larger market share in the dynamically evolving personalized market demand, enterprises have to adopt a more flexible production mode. In this context, the implementation of parallel production with multiple product types necessitates frequent switching between different products, imposing elevated requirements on machine fault-free operation and stable production. There is a compelling motivation to investigate the joint optimization of the flexible job shop scheduling problem and preventive maintenance (FJSSP-PM). However, existing research has primarily focused on utilizing predetermined maintenance as inputs for optimizing production scheduling, while overlooking the uncertain maintenance requirements of machines during the production process. Therefore, this paper proposes a two-stage joint optimization model to simultaneously address three subproblems: machine assignment, operation sequencing, and maintenance arrangement. Specifically, the first stage involves constructing a mathematical model for the FJSSP to minimize penalties for tardiness and workload balancing. Subsequently, a comprehensive failure rate model is developed to determine maintenance requirements for machines with production-dependent failure behavior, particularly under high-frequency production switching scenarios. Furthermore, a feedback-updated strategy is proposed to achieve synchronous optimization of production and maintenance activities in an economically and operationally efficient manner. Given the complexity of the problem, a hybrid meta-heuristic algorithm is designed to effectively handle large-scale cases. The effectiveness of the proposed model in terms of cost-savings has been verified compared with existing relevant methods.

Multi-resource constrained flexible job shop scheduling problem with fixture-pallet combinatorial optimisation

There is a lack of research on the flexible job shop scheduling problem (FJSP) considering limited fixture-pallet resources in multi-product mixed manufacturing workshops. However, field research in a leading engine manufacturer in China has revealed that fixture-pallet resources are a key factor limiting capacity breakthroughs although they play an auxiliary role in the production process. Thus, in this paper, we propose a methodology for the multi-resource constrained flexible job shop scheduling problem with fixture-pallet combinatorial optimisation. First, a mixed integer programming model with machine-fixture-pallet constraints is constructed aiming to minimize makespan. Then, a novel genetic algorithm integrated with feasibility correction strategy and self-learning variable neighbourhood search (VNS) is proposed to address the complicated scheduling problem, where the feasibility correction strategy is designed to solve potential conflict between machine selection and fixture selection chromosomes and self-learning VNS is executed to further improve the optimisation capability. Moreover, the effectiveness and efficiency of proposed algorithm are demonstrated by computational experiments with real data from cooperated engine manufacturing plant, which would provide convincing support for real production scheduling under complex scenarios.

Integrated Genetic Algorithm with Dispatching Rules to solve the Flexible Job Shop Scheduling Problem under Multi-AMR Transportation Constraints

The Flexible Job Shop Scheduling Problem (FJSSP) is a challenging issue for industries and manufacturers. However, the transportation tasks in this problem should not be underestimated, as their impact is substantial, and they are frequently overlooked in the literature. In this paper, the FJSSP with multi-AMR (Autonomous mobile robot) transportation constraints is addressed. We developed a genetic algorithm with dispatching rules to solve the Flexible Job Shop Scheduling Problem with Multi-AMR Transportation Constraints by minimizing the total completion time. Two dispatching rules are used to assign transportation robots. The first rule is random assignment and the second rule is AMR per Job assignment. Our encoding and decoding process utilizes a three-layer sequence (machine sequence, operation sequence, and AMR sequence). Finally, we conducted comprehensive experiments on different benchmarks to assess the performance of the proposed algorithm with a variable number of AMR to transport the operations. The experimental results indicate that the proposed algorithm effectively and efficiently solve the problem.

The Flexible Job Shop Scheduling Problem with Setups and Operator Skills: an application in the textile industry

The Flexible Job Shop Scheduling Problem (FJSSP) is one of the most studied problems in the literature thanks to its practical relevance. Many industrial production scheduling problems can be seen as a FJSSP with different constraints and objectives. The studied problem arises in a textile factory, precisely in the sewing process. Multiple real-world constraints are tackled. Individual skills of operators and different types of setup times are considered: machine-change setup time for operators, colour-change setup times and configuration-change setup times. The objective is to minimize the total tardiness. To the best of the authors’ knowledge, this is the first study that tackles this variant of the problem. This paper presents a preliminary study to validate the approach and evaluate the tractability of the industrial problem. A mixed-integer linear programming (MILP) model is proposed and solved using a commercial solver. Real-world data are used to generate more than 1000 problems that are clustered in 4 groups based on the number of jobs to be scheduled, the number of operators and flexibility of their skills. The results show that the proposed MILP model can reach optimality for the small size instances but it is intractable for most large-sized instances. Moreover, the results highlight how diversifying the operators’ skills can help find better solutions.

Evaluate Flexible Job Scheduling Problem Using Elitist Ant

One significant approach that is frequently utilized in many applications, particularly in industry, is scheduling .An extension of job scheduling, the Flexible Job Shop Scheduling Problem (FJSP), has a number of real-world uses .This subject has received a lot of attention due to its significance and complexity .This research discusses the importance of scheduling in real-life operations, particularly in production scheduling. It presents a model using Elitist Ant (EAS) to compute the maximum value (makspane) of the flexible job shop scheduling problem(FJSP). The model programmed by Python ver. (3.) with two instance from Brandimarte dataset to optimize logistics costs and meet customer demand. The study deduce that there are two relations by using two new formula. Firstly, the relation between number of elitist ant and total ants . Also, the evaporate value is effected by the first relation directly.

A multi-objective fuzzy flexible job shop scheduling problem considering the maximization of processing quality

This paper analyzes practical production characteristics, including customer's stringent quality requirements and uncertain processing time in aircraft shaft parts manufacturing. Considering the above characteristics, we propose a multi-objective fuzzy aircraft shaft parts production scheduling problem considering the maximization of production quality. We define this problem as a multi-objective fuzzy flexible job shop scheduling problem (MO-fFJSP) with fuzzy processing time. To address this problem, we developed an improved multi-objective spider monkey optimization (IMOSMO) algorithm. IMOSMO integrates strategies such as genetic operators, variable neighborhood search and Pareto optimization theory on the framework of the conventional Spider Monkey Optimization (SMO) framework and discretize the continuous SMO algorithm to solve MO-fFJSP. To enhance the efficiency of the algorithm, we further adjust the sequence of the local leader learning phase and the global leader learning phase within the proposed IMOSMO framework. We conduct a comparative analysis between the performance of IMOSMO and NSGA-Ⅱ using 28 cases of varying scales. The computational results demonstrate the superiority of our algorithm over NSGA-Ⅱ in terms of both solution diversity and quality. Moreover, the performance of the proposed algorithm upgrades as the problem scale increases.

A novel hybrid algorithm of genetic algorithm, variable neighborhood search and constraint programming for distributed flexible job shop scheduling problem

A novel hybrid algorithm of genetic algorithm, variable neighborhood search and constraint programming for distributed flexible job shop scheduling problem

Large-Scale Dynamic Scheduling for Flexible Job-Shop With Random Arrivals of New Jobs by Hierarchical Reinforcement Learning

As the intelligent manufacturing paradigm evolves, it is urgent to design a near real-time decision-making framework for handling the uncertainty and complexity of production line control. The dynamic flexible job shop scheduling problem (DFJSP) is frequently encountered in the manufacturing industry. However, it is still challenging to obtain high-quality schedules for DFJSP with dynamic job arrivals in real-time, especially facing thousands of operations from a large-scale scene with complex contexts in an assembly plant. This paper aims to propose a novel end-to-end hierarchical reinforcement learning framework for solving the large-scale DFJSP in near real-time. In the DFJSP, the processing information of newly arrived jobs is unknown in advance. Besides, two optimization tasks, including job operation selection and job-to-machine assignment, have to be handled, which means multiple actions must be controlled simultaneously. In our framework, a higher-level layer is designed to automatically divide the DFJSP into sub-problems, i.e., static FJSPs with different scales. And two lower-level layers are constructed to solve the sub-problems. In particular, one layer based on a graph neural network is in charge of sequencing job operations, and another layer based on a multi-layer perceptron is used to assign a machine to process the job operations. Numerical experiments, including offline training and online testing, are conducted on several instances with different scales. The results verify the superior performance of the proposed framework compared with existing dynamic scheduling methods, such as well-known dispatching rules and meta-heuristics.