Multi-objective Flexible Job Shop Scheduling Research Articles

A reinforcement learning enhanced memetic algorithm for multi-objective flexible job shop scheduling toward Industry 5.0

Flexible job shop scheduling problem (FJSP) with worker flexibility has gained significant attention in the upcoming Industry 5.0 era because of its computational complexity and its importance in production processes. It is normally assumed that each machine is typically operated by one worker at any time; therefore, shop-floor managers need to decide on the most efficient assignments for machines and workers. However, the processing time is variable and uncertain due to the fluctuating production environment caused by unsteady operating conditions of machines and learning effect of workers. Meanwhile, they also need to balance the worker workload while meeting production efficiency. Thus a dual resource-constrained FJSP with worker’s learning effect and fuzzy processing time (F-DRCFJSP-WL) is investigated to simultaneously minimise makespan, total machine workloads and maximum worker workload. Subsequently, the reinforcement learning enhanced multi-objective memetic algorithm based on decomposition (RL-MOMA/D) is proposed for solving F-DRCFJSP-WL. For RL-MOMA/D, the Q-learning is incorporated into memetic algorithm to perform variable neighbourhood search and further strengthen the exploitation capability for the algorithm. Finally, comprehensive experiments on extensive test instances and a case study of aircraft overhaul shop-floor are conducted to demonstrate effectiveness and superiority of the proposed method.

Fast Pareto set approximation for multi-objective flexible job shop scheduling via parallel preference-conditioned graph reinforcement learning

The Multi-Objective Flexible Job Shop Scheduling Problem (MOFJSP) is a complex challenge in manufacturing, requiring balancing multiple, often conflicting objectives. Traditional methods, such as Multi-Objective Evolutionary Algorithms (MOEA), can be time-consuming and unsuitable for real-time applications. This paper introduces a novel Graph Reinforcement Learning (GRL) approach, named Preference-Conditioned GRL, which efficiently approximates the Pareto set for MOFJSP in a parallelized manner. By decomposing the MOFJSP into distinct sub-problems based on preferences and leveraging a parallel multi-objective training algorithm, our method efficiently produces high-quality Pareto sets, significantly outperforming MOEA methods in both solution quality and speed, especially for large-scale problems. Extensive experiments demonstrate the superiority of our approach, with remarkable results on large instances, showcasing its potential for real-time scheduling in dynamic manufacturing environments. Notably, for large instances (50 × 20), our approach outperforms MOEA baselines with remarkably shorter computation time (less than 1% of that of MOEA baselines). The robust generalization performance across various instances also highlights the practical value of our method for decision-makers seeking optimized production resource utilization.

An improved MOEA/D for multi-objective flexible job shop scheduling by considering efficiency and cost

To achieve cost reduction and efficiency improvement in the production process of the aerospace industry, this study establishes a mathematical model for the multi-objective flexible job shop scheduling problem (MOFJSP). The model comprehensively considers four optimisation objectives: completion time, tool number, machine load, and machine energy consumption. For solving the MOFJSP, an improved MOEA/D (IMOEA/D) algorithm is proposed. To improve the quality of solutions, the algorithm introduces another global update strategy in addition to the original substitution operation. The population is initialised using four allocation rules, and the neighbourhood is dynamically updated based on the degree of population evolution. The simulation results on a single instance indicate that the simulation time of IMOEA/D has decreased by 10.5% and machine energy consumption has reduced by 9.5%. Moreover, when compared to various classic multi-objective algorithms on 25 benchmark instances, the IMOEA/D algorithm achieved optimal results in 19 instances for inverted generational distance comparisons, 15 instances for hypervolume comparisons and nearly all instances for set coverage comparisons. The results reveal that the proposed IMOEA/D is effective and competitive in solving MOFJSP.

Bi-objective flexible job shop scheduling on machines considering condition-based maintenance activities

This paper investigates multi-objective flexible job shop scheduling considering maintenance activities. The condition-based maintenance strategy is used to reduce machines breakdown. After maintenance activities are completed, the machine degradation model’s parameters are updated using Bayesian inference to make it more realistic. A novel multi-objective evolutionary algorithm is designed to address the multi-criteria scheduling problem. An innovative insertion algorithm is proposed in this paper to balance production plan and maintenance activities. According to the experimental results, the designed evolutionary algorithm performs better than the other two traditional algorithms, and the insertion approach can reduce the impact of maintenance activities on production plan by up to 200%.

A Trans-Ptr-Nets Based Transfer Optimization Method for Multi-Objective Flexible Job Shop Scheduling in IIoT

A Trans-Ptr-Nets Based Transfer Optimization Method for Multi-Objective Flexible Job Shop Scheduling in IIoT

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

AbstractRising costs for energy are increasingly becoming a vital factor for the production planning of manufacturing companies. Manufacturers face the challenge to react to dynamic energy prices and design energy cost efficient schedules in their production planning. In the literature, the energy cost-aware Flexible Job Shop Scheduling Problem addresses minimization of both makespan and energy costs. Recent studies provide multi-objective approaches to model the trade-off of minimizing makespan and energy costs. However, the literature is limited to coarse-grained time periods and does not consider dynamic tariffs where costs change at short intervals, so that production schedules may fall short on energy costs. We aim to close this research gap by considering frequently changing real-time energy tariffs. We propose a multi-objective memetic algorithm based on the non-dominated sorting genetic algorithm (NSGA-II) with both makespan and energy cost minimization as the objectives. We evaluate our approach by conducting computational experiments using prominent FJSP-benchmark instances from the literature, which we supplement with empiric dynamic energy prices. We show results on method performance and compare the memetic NSGA-II with the results of an exact state-of-the-art solver. To investigate the trade-off between a short makespan and low energy costs, we present solutions on the approximated Pareto front and discuss our results.

MILP modeling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times

MILP modeling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times

Retracted: An Effective Hybrid Multiobjective Flexible Job Shop Scheduling Problem Based on Improved Genetic Algorithm

Retracted: An Effective Hybrid Multiobjective Flexible Job Shop Scheduling Problem Based on Improved Genetic Algorithm

Flexible Job Shop Scheduling Optimization for Green Manufacturing Based on Improved Multi-Objective Wolf Pack Algorithm

Green manufacturing has become a new production mode for the development and operation of modern and future manufacturing industries. The flexible job shop scheduling problem (FJSP), as one of the key core problems in the field of green manufacturing process planning, has become a hot topic and a difficult issue in manufacturing production research. In this paper, an improved multi-objective wolf pack algorithm (MOWPA) is proposed for solving a multi-objective flexible job shop scheduling problem with transportation constraints. Firstly, a multi-objective flexible job shop scheduling model with transportation constraints is established, which takes the maximum completion time and total energy consumption as the optimization objectives. Secondly, an improved wolf pack algorithm is proposed, which designs individual codes from two levels of process and machine. The precedence operation crossover (POX) operation is used to improve the intelligent behavior of wolves, and the optimal Pareto solution set is obtained by introducing non-dominated congestion ranking. Thirdly, the Pareto solution set is selected using the gray relational decision analysis method and analytic hierarchy process to obtain the optimal scheduling scheme. Finally, the proposed algorithm is compared with other algorithms through a variety of standard examples. The analysis results show that the improved multi-objective wolf pack algorithm is superior to other algorithms in terms of solving speed and convergence performance of the Pareto solution, which shows that the proposed algorithm has advantages when solving FJSPs.

An evolutionary algorithm for the multi-objective flexible job shop scheduling problem with uncertain processing time

在实际工业生产中, 调度环境的复杂性与不确定性使得调度问题求解难度大大提高. 针对加工时间不确定的柔性作业车间调度问题, 采用不确定参数描述随机工时波动程度和约束条件允许违背程度, 构建工时波动服从指数分布的机会约束规划模型, 将不确定调度问题模型转化为加工时间确定的柔性作业车间调度问题, 求解得到一定程度上具有鲁棒性能的调度方案. 并在执行过程中对工时扰动驱动下采用工序移动调整和重调度方法对作业排产方案进行动态调整. 基于双链式编码以及贪婪插入法解码规则, 提出了基于变邻域搜索的混合NSGA-II算法. 针对车间调度问题的多约束性和计算复杂度高等特点, 设计了基于机器选择的复合启发式规则以获取分布均匀且更加接近pareto前沿的初始种群, 包括依概率应用机器累计负载最小、工序加工时间最短规则, 采用改进工序和设备交叉策略以提高算法的全局搜索能力, 研究基于关键工序和机器选择的多种邻域结构设计变邻域搜索策略, 以进一步提高算法的局部搜索能力. 通过Kacem和Brandimarte标准算例的数值仿真以及与多种代表算法的统计比较, 验证了所提算法的有效性, 并为不确定柔性作业车间调度问题提供更优的调度方案.

Developing a multi-objective flexible job shop scheduling optimization model using Lexicographic procedure considering transportation time

A multi-objective flexible job shop scheduling problem (FJSSP) that considers transportation time using mathematical programming is proposed to optimise three conflicting objectives: minimising makespan, total cost, and total lateness. The proposed model was developed and verified in three stages. In the first stage, only one objective was considered. The minimisation of the makespan and total cost was considered separately in the first stage. In the second stage, only two objectives were considered. In this stage, the minimisation of the makespan and total cost was considered instantaneously. In the third stage, a model was developed to optimise the three objectives. The proposed model was formulated using mixed-integer nonlinear programming (MINLP) and solved using the DICOPT solver based on general algebraic modelling system (GAMS) optimisation software. This model includes the transportation times between machines in the FJSSP, and the problem is called the “flexible job shop scheduling problem with transportation time” (TT-FJSSP). The proposed model gave better results in comparison with the other recent developed models. The effect of changing the maximum allowable deviation when optimising the three objectives was studied to achieve more-practical results.

A Novel Collaborative Evolutionary Algorithm with Two-Population for Multi-Objective Flexible Job Shop Scheduling

A Novel Collaborative Evolutionary Algorithm with Two-Population for Multi-Objective Flexible Job Shop Scheduling

Memetic algorithm based on learning and decomposition for multiobjective flexible job shop scheduling considering human factors

Human factors, including worker flexibility and learning-forgetting effects, are crucial factors in modern manufacturing systems to reduce costs and improve efficiency. However, traditional flexible job shop scheduling problem (FJSP) only considers machine flexibility and ignores human factors. Therefore, this paper originally investigates a multi-objective FJSP considering human factors (MO-FJSPHF) to simultaneously minimize makespan, maximum machine workload, and total machine workload. Firstly, a multi-objective mixed-integer nonlinear programming (MINLP) model is established based on the characteristics of the MO-FJSPHF. Then, a multi-objective memetic algorithm based on learning and decomposition (MOMA-LD) is proposed to solve the model by incorporating the learning-based adaptive local search into the multi-objective evolutionary algorithm based on decomposition (MOEA/D). In MOMA-LD, the machine learning technique determines which solutions deserve to perform the local search. Meanwhile, the computational resources are allocated dynamically based on the degree of population convergency during the evolutionary process. Experimental results show that our proposed algorithm outperforms four state-of-the-art algorithms on forty-three test instances and three real-world cases from a casting workshop. The validity of the proposed MINLP model is examined by the exact solver Gurobi. • Flexible job shop scheduling problem considering human factors is considered. • Memetic algorithm based on learning and decomposition (MOMA-LD) is proposed. • Machine learning-based local search is designed and incorporated into the MOMA-LD. • Experiment results show that MOMA-LD is superior to the other compared algorithms.

Multi-objective reinforcement learning framework for dynamic flexible job shop scheduling problem with uncertain events

The economic benefits for manufacturing companies will be influenced by how it handles potential dynamic events and performs multi-objective real-time scheduling for existing dynamic events. Based on these, we propose a new dynamic multi-objective flexible job shop scheduling problem (DMFJSP) to simulate realistic production environment. Six dynamic events are involved in the problem including job insertion, job cancellation, job operation modification, machine addition, machine tool replacement and machine breakdown. As well as three objectives of longest job processing time (makespan), average machine utilization and average job processing delay rate with a set of constraints are also raised in the study. Then this research designs a novel dynamic multi-objective scheduling algorithm based on deep reinforcement learning. The algorithm uses two deep Q-learning networks and a real-time processing framework to process each dynamic event and generate complete scheduling scheme. In addition, an improved local search algorithm is adopted to further optimize the scheduling results and the idea of combination is used to make the scheduling rules more comprehensive. Experiments on 27 instances show the superiority and stability of our approach compared to each proposed combined rule, well-known scheduling rules and standard deep Q-learning based algorithms. Compared to the current optimal deep Q-learning method, the maximum performance improvement for our three objectives are approximately 57%, 164% and 28%.

Real-Time Scheduling for Dynamic Partial-No-Wait Multiobjective Flexible Job Shop by Deep Reinforcement Learning

In modern discrete flexible manufacturing systems, dynamic disturbances frequently occur in real time and each job may contain several special operations in partial-no-wait constraint due to technological requirements. In this regard, a hierarchical multiagent deep reinforcement learning (DRL)-based real-time scheduling method named hierarchical multi-agent proximal policy optimization (HMAPPO) is developed to address the dynamic partial-no-wait multiobjective flexible job shop scheduling problem (DMOFJSP-PNW) with new job insertions and machine breakdowns. The proposed HMAPPO contains three proximal policy optimization (PPO)-based agents operating in different spatiotemporal scales, namely, objective agent, job agent, and machine agent. The objective agent acts as a higher controller periodically determining the temporary objectives to be optimized. The job agent and machine agent are lower actuators, respectively, choosing a job selection rule and machine assignment rule to achieve the temporary objective at each rescheduling point. Five job selection rules and six machine assignment rules are designed to select an uncompleted job and assign the next operation of which together with its successors in no-wait constraint on the corresponding processing machines. A hierarchical PPO-based training algorithm is developed. Extensive numerical experiments have confirmed the effectiveness and superiority of the proposed HMAPPO compared with other well-known dynamic scheduling methods. Note to Practitioners—The motivation of this article stems from the need to develop real-time scheduling methods for modern discrete flexible manufacturing factories, such as aerospace product manufacturing and steel manufacturing, where dynamic events frequently occur, and each job may contain several operations subjected to the no-wait constraint. Traditional dynamic scheduling methods, such as metaheuristics or dispatching rules, either suffer from poor time efficiency or fail to ensure good solution quality for multiple objectives in the long-term run. Meanwhile, few of the previous studies have considered the partial-no-wait constraint among several operations from the same job, which widely exists in many industries. In this article, we propose a hierarchical multiagent deep reinforcement learning (DRL)-based real-time scheduling method named HMAPPO to address the dynamic partial-no-wait multiobjective flexible job shop scheduling problem (DMOFJSP-PNW) with new job insertions and machine breakdowns. The proposed HMAPPO uses three DRL-based agents to adaptively select the temporary objectives and choose the most feasible dispatching rules to achieve them at different rescheduling points, through which the rescheduling can be made in real time and a good compromise among different objectives can be obtained in the long-term schedule. Extensive experimental results have demonstrated the effectiveness and superiority of the proposed HMAPPO. For industrial applications, this method can be extended to many other production scheduling problems, such as hybrid flow shops and open shop with different uncertainties and objectives.

Digital twin oriented multi-objective flexible job shop scheduling model and its hybrid particle swarm optimization

To solve the problems of low efficiency and insufficient dynamic response of job shop scheduling in the discrete manufacturing process, a multi-objective flexible job shop scheduling model for digital twin and its solution method are proposed. Firstly, a digital twin scheduling model with physical entity, virtual model and production plan is constructed, and four factors are taken as optimization goals. Then, a hybrid particle swarm optimization method is designed to increase the refined optimization ability, and the obtained Pareto optimal solution set is analyzed by grey relational analysis to obtain a satisfactory solution which coincides with the actual production. Finally, a three-dimensional model which is completely mapped with the real job shop scheduling is built by Plant Simulation software. The scheduling process is simulated and optimized by combining with the production data of an enterprise, which verifies the feasibility and applicability of this method, and will effectively guide the production practice.

Integrating preferences within multiobjective flexible job shop scheduling

When faced with a multiobjective optimization problem, it is necessary to consider the decision-maker preferences in order to propose the best compromise solution. We consider the multiobjective flexible job shop scheduling problem and a decision-maker that is best represented using a non-compensatory reference level-based preference model. We show how integrating this model into a multiobjective genetic algorithm allows to obtain solutions that surpass more aspiration levels when compared to classical multiobjective optimization approaches. Furthermore, these solutions are found faster and in greater numbers which facilitates their integration within the workshop.

The Implementation of Multiobjective Flexible Workshop Scheduling Based on Genetic Simulated Annealing-Inspired Clustering Algorithm

Multiobjective flexible workshop scheduling is an important subject to improve resource utilization and production efficiency and enhance the competitiveness of enterprises. As the situation of resource constraints becomes more and more severe, the problem of companies rationally allocating limited resources in production is becoming more and more serious. Today, the manufacturing industry widely adopts advanced manufacturing modes such as computer-integrated manufacturing and intelligent manufacturing, but in these semi-intelligent manufacturing modes with a high degree of uncertainty and a high degree of personnel dependence, it is difficult to adapt to the work of large-scale production. Therefore, suitable clustering algorithms are urgently needed to help solve these problems, and this paper selects a clustering algorithm based on the genetic simulation annealing algorithm. This article is aimed at studying the problem of efficiency improvement in the production process of large-scale manufacturing and at finding a stronger and more effective production mode for the manufacturing industry. Firstly, this paper introduces the basic principles of simulated annealing genetic algorithm and regularized clustering algorithm. These algorithms have excellent performance in searching for global optimal solutions. They can be constantly tested and computed to keep the calculation results close to the global optimal solution. In this paper, the K -means clustering algorithm is used to select the shortest completion time to represent the clustering target. According to the minimum distance principle, the machine, workpiece, and other objects are input into the clustering of the algorithm, and the K -means algorithm will send out the sorting plan. Therefore, a multiobjective flexible job shop scheduling model based on genetic simulated annealing algorithm and clustering algorithm is established. Then, by using hypothetical production data to simulate the operation of the workshop, the scheduling model was applied to conduct a deduction and empirical comparative study. The experimental results showed that the model shortened the completion time of the workpiece by 4.4% and increased the average load rate of the machine by 10%.

Multi-objective flexible job-shop scheduling problem researching based on improved adaptive NSGA-II

To solve the scheduling problem of products manufacturing in the military electronic equipment enterprises, a multi-objective flexible job-shop scheduling model was established with the objective of minimum the make span, production costs and equipment load. According to the characteristics of flexible job-shop scheduling problem, an adaptive NSGA-II algorithm was proposed in this paper, which could change the probabilities of crossover and mutation operation at different stages of genetic processes. To improve the diversity of population, the algorithm performed independent crossover and mutation operations on the working processes and equipment. Besides, a population independent elite retention strategy was adopted to avoid the loss of optimum solutions. At last, the feasibility and validity of the improved adaptive NSGA-II are verified by a flexible job-shop example.

An Effective Hybrid Multiobjective Flexible Job Shop Scheduling Problem Based on Improved Genetic Algorithm

Multiobjective Flexible Job Shop Scheduling Problem (MO-FJSP) is a scheduling problem used in manufacturing sectors to use energy efficiently and thriftily. The scheduling problem aims to increase productivity and reduce energy consumption via a mathematical model. With this paper, an effective genetic algorithm is proposed for MO-FJSP based on maximum completion time, total machine load, and bottleneck machine load. The solution method utilizes a hybrid multiobjective genetic algorithm. A combination of global selection and fast selection is used for initialization and obtaining a uniformly distributed initial population. The cross-variance operator is adaptively improved to enhance the searching in the population. Following that an elite retention mechanism is designed to address the possible limitations of the elite strategy in maintaining population diversity. As a result, an improved harmonic search algorithm is introduced to improve the quality of individuals in the elite pool. The proposed hybrid method is implemented in MATLAB R2018a. Tests were conducted using the benchmark Kacem test set, the BR data data set, and with the actual production cases. The algorithm succeeded in achieving 13 nondominated solutions in the initial 20 runs. Moreover, the method obtains the optimal value criterion for the solution accuracy factor. As a whole, results of the evaluation testify that the proposed method can be used to solve the MO-FJSP with high accuracy and fast convergence. The method also provides feasible and effective scheduling solutions for the decision-makers in actual production. Based on the promising results obtained, it is deduced that the method has a wide applicability range particularly in manufacturing sector.