Digital twin-based job shop anomaly detection and dynamic scheduling

Scheduling scheme is one of the critical factors affecting the production efficiency. In the actual production, anomalies will lead to scheduling deviation and influence scheme execution, which makes the traditional job shop scheduling methods are not sufficient to meet the needs of real-time and accuracy. By introducing digital twin (DT), further convergence between physical and virtual space can be achieved, which enormously reinforces real-time performance of job shop scheduling. For flexible job shop, an anomaly detection and dynamic scheduling framework based on DT is proposed in this paper. Previously, a multi-level production process monitoring model is proposed to detect anomaly. Then, a real-time optimization strategy of scheduling scheme based on rolling window mechanism is explored to enforce dynamic scheduling optimization. Finally, the improved grey wolf optimization algorithm is introduced to solve the scheduling problem. Under this framework, it is possible to monitor the deviation between the actual processing state and the planned processing state in real time and effectively reduce the deviation. An equipment manufacturing job shop is taken as a case study to illustrate the effectiveness and advantages of the proposed framework.     

Discrepancy search for the flexible job shop scheduling problem

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop problem in which each operation must be processed on a given machine chosen among a finite subset of candidate machines. The aim is to find an allocation for each operation and to define the sequence of operations on each machine, so that the resulting schedule has a minimal completion time. We propose a variant of the climbing discrepancy search approach for solving this problem. We also present various neighborhood structures related to assignment and sequencing problems. We report the results of extensive computational experiments carried out on well-known benchmarks for flexible job shop scheduling. The results demonstrate that the proposed approach outperforms the best-known algorithms for the FJSP on some types of benchmarks and remains comparable with them on other ones.     

A hybrid Jaya algorithm for solving flexible job shop scheduling problem considering multiple critical paths

As an extension of the classical job shop scheduling problem, flexible job shop scheduling problem (FJSP) is considered as a challenge in manufacturing systems for its complexity and flexibility. Meta-heuristic algorithms are shown effective in solving FJSP. However, the multiple critical paths issue, which has not been formally discussed in the existing literature, is discovered to be a primary obstacle for further optimization by meta-heuristics. In this paper, a hybrid Jaya algorithm integrated with Tabu search is proposed to solve FJSP for makespan minimization. Two Jaya operators are designed to improve solutions under a two-vector encoding scheme. During the local search phase, three approaches are proposed to deal with multiple critical paths and have been evaluated by experimental study and qualitative analyses. An incremental parameter setting strategy and a makespan estimation method are employed to speed up the searching process. The proposed algorithm is compared with several state-of-the-art algorithms on three well-known FJSP benchmark sets. Extensive experimental results suggest its superiority in both optimality and stability. Additionally, a real world scheduling problem, including six instances with different scales, is applied to further prove its ability in handling large-scale scheduling problems.     

批量生产柔性作业车间多目标精细化调度方法

提出了一种批量生产柔性作业车间多目标精细化调度方法。针对批量生产柔性作业车间多目标调度问题特点,建立了一类以完工时间最短和制造成本最低为优化目标的等量分批柔性作业车间调度多目标优化模型。提出了5种批量生产柔性作业车间精细化调度技术;设计了一种改进的NSGA II算法对模型进行求解。算法中引入面向对象技术处理复杂的实体逻辑关系,使用矩阵编码技术进行编码,采用分段交叉和分段变异的遗传算子实现遗传进化,应用上述5种精细化调度技术于解码过程以提高设备利用率。通过案例分析验证了该方法的有效性。     

Effective ensembles of heuristics for scheduling flexible job shop problem with new job insertion

This study investigates the flexible job shop scheduling problem (FJSP) with new job insertion. FJSP with new job insertion includes two phases: initializing schedules and rescheduling after each new job insertion. Initializing schedules is the standard FJSP problem while rescheduling is an FJSP with different job start time and different machine start time. The time to do rescheduling is the same as the time of new job insertion. Four ensembles of heuristics are proposed for scheduling FJSP with new job insertion. The objectives are to minimize maximum completion time (makespan), to minimize the average of earliness and tardiness (E/T), to minimize maximum machine workload (Mworkload) and total machine workload (Tworkload). Extensive computational experiments are carried out on eight real instances from remanufacturing enterprise. The results and comparisons show the effectiveness of the proposed heuristics for solving FJSP with new job insertion.     

An integrated search heuristic for large-scale flexible job shop scheduling problems

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop scheduling problem (JSP), where each operation is allowed to be processed by any machine from a given set, rather than one specified machine. In this paper, two algorithm modules, namely hybrid harmony search (HHS) and large neighborhood search (LNS), are developed for the FJSP with makespan criterion. The HHS is an evolutionary-based algorithm with the memetic paradigm, while the LNS is typical of constraint-based approaches. To form a stronger search mechanism, an integrated search heuristic, denoted as HHS/LNS, is proposed for the FJSP based on the two algorithms, which starts with the HHS, and then the solution is further improved by the LNS. Computational simulations and comparisons demonstrate that the proposed HHS/LNS shows competitive performance with state-of-the-art algorithms on large-scale FJSP problems, and some new upper bounds among the unsolved benchmark instances have even been found.     

改进的离散型萤火虫优化算法求解柔性作业车间调度问题

针对传统的群智能优化算法在求解柔性作业车间调度问题(FJSP)时,存在寻优能力不足且易陷入局部最优等缺点,本文以最小化最大完工时间为目标,将萤火虫算法(FA)用于求解柔性作业车间调度问题,提出一种改进的离散型萤火虫算法(DFA)。首先,通过两段式编码建立FA连续优化问题与FJSP离散优化问题之间的联系;其次,设计一种群初始化方法,以确保初始解的质量以及多样性;然后,提出改进离散型萤火虫优化算法并引入局部搜索算法,加强算法的全局搜索能力和局部搜索能力;最后,对标准算例进行仿真,验证DFA算法求解FJSP的有效性。通过与遗传算法和粒子群优化算法进行仿真对比,表明了DFA求解FJSP的优越性。     

Mathematical modeling and heuristic approaches to flexible job shop scheduling problems

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, it is quite difficult to achieve an optimal solution to this problem in medium and actual size problem with traditional optimization approaches owing to the high computational complexity. For solving the realistic case with more than two jobs, two types of approaches have been used: hierarchical approaches and integrated approaches. In hierarchical approaches assignment of operations to machines and the sequencing of operations on the resources or machines are treated separately, i.e., assignment and sequencing are considered independently, where in integrated approaches, assignment and sequencing are not differentiated. In this paper, a mathematical model and heuristic approaches for flexible job shop scheduling problems (FJSP) are considered. Mathematical model is used to achieve optimal solution for small size problems. Since FJSP is NP-hard problem, two heuristics approaches involve of integrated and hierarchical approaches are developed to solve the real size problems. Six different hybrid searching structures depending on used searching approach and heuristics are presented in this paper. Numerical experiments are used to evaluate the performance of the developed algorithms. It is concluded that, the hierarchical algorithms have better performance than integrated algorithms and the algorithm which use tabu search and simulated annealing heuristics for assignment and sequencing problems consecutively is more suitable than the other algorithms. Also the numerical experiments validate the quality of the proposed algorithms.     

A new immune multi-agent system for the flexible job shop scheduling problem

Scheduling for the flexible job shop is very important and challenging in manufacturing field. Multi-agent-based approaches have been used to solve the flexible job shop scheduling problem (FJSP), in order to reduce complexity and cost, increase flexibility, and enhance robustness. However, the quality of solution obtained by the multi-agent approach is always worse than the centralized meta-heuristic algorithms. The immune system is a distributed and complicated information processing system, which can protect body from foreign antigens by immune responses. In this paper, we analyze the similarities between the FJSP and humoral immunity, which is one of the immune responses. Based on the similarities, we develop a new immune multi-agent scheduling system (NIMASS) to solve the FJSP with the objective of minimizing the maximal completion time (makespan). In order to acquire the higher-quality solution of the FJSP, we simulate humoral immunity to establish the architecture of NIMASS and the negotiation strategies of NIMASS, which are proposed for negotiation among agents. NIMASS was tested on different benchmark instances of the FJSP. In comparison with the multi-agent approaches and the centralized heuristic algorithms, the computational results indicate that NIMASS can effectively improve the quality of solution in very short time. And the computational time of NIMASS is superior to that of the centralized meta-heuristic algorithms, especially for the complex FJSPs. These results indicate that NIMASS can be very useful in applications that deal with real-time FJSPs.     

遗传算法解柔性作业车间调度问题应用综述

柔性作业车间调度问题是典型的NP难问题,对实际生产应用具有指导作用。近年来,随着遗传算法的发展,利用遗传算法来解决柔性作业车间调度问题的思想和方法层出不穷。为了促进遗传算法求解柔性作业车间调度问题的进一步发展,阐述了柔性作业车间调度问题的研究理论,对已有改进方法进行了分类,通过对现存问题的分析,探讨了未来的发展方向。     

求解柔性作业调度问题的协同进化粒子群算法

柔性作业车间调度问题是典型的NP难题。柔性作业车间调度问题涉及到设备分配和作业分配两个问题,并且两问题之间具有较强的耦合性,提出了基于协同进化的粒子群算法。该算法将设备选择和工件调度分别作为两个寻优变量,利用PSO算法分别进行寻优,根据两个变量的内容进行互相评价。实验表明该算法对FJSP问题的有效性。     

一种动态双种群果蝇优化算法求解FJSP

为了有效解决柔性作业车间调度问题(FJSP),提出了一种具有较强进化机制的动态双种群果蝇优化算法(DDFOA),该算法采用自适应移动步长,并动态地将种群划分为先进子种群和后进子种群,其中先进子种群侧重局部搜索,后进子种群负责全局搜索。同时针对柔性作业车间调度问题,设计了合适的编码转化方案。最后,对算法的收敛性进行了证明,并选用经典算例对其进行仿真实验,仿真结果验证了DDFOA求解FJSP的有效性。     

考虑工件移动时间的柔性作业车间调度问题研究

分析生产车间的实际生产状况,建立了考虑工件移动时间的柔性作业车间调度问题模型,该模型考虑了以往柔性作业车间调度问题模型所没有考虑的工件在加工机器间的移动时间,使柔性作业车间调度问题更贴近实际生产,让调度理论更具现实性。通过对已有的改进遗传算法的遗传操作进行重构,设计出有效求解考虑工件移动时间的柔性作业车间调度问题的改进遗传算法。最后对实际案例进行求解,得到调度甘特图和析取图,通过对甘特图和析取图的分析验证了所建考虑工件移动时间的柔性作业车间调度问题模型的可行性和有效性。     

混合灰狼优化算法求解柔性作业车间调度问题

将灰狼优化算法(GWO)用于柔性作业车间调度问题(FJSP),以优化最大完工时间为目标,提出一种混合灰狼优化算法(HGWO).首先,采用两段式编码方式,建立GWO连续空间与FJSP离散空间的映射关系;其次,设计种群初始化方法,保证算法初始解的质量;然后,嵌入一种变邻域搜索策略,加强算法的局部搜索能力,引入遗传算子,提升算法的全局探索能力;最后,通过实验数据验证HGWO算法在求解FJSP问题方面的有效性.     

相关工件车间调度问题的拓扑算法

针对加工装配型离散制造企业实际生产的特点,提出了一类用于表示工序之间偏序关系的相关工件车间调度问题。为了利用已有的求解表示工序之间的线序关系的传统车间调度算法求解相关工件车间调度问题,设计了一种拓扑算法,该算法能够将工序之间的偏序关系转化为线序关系,将相关工件车间调度问题转化为传统的车间调度问题,通过实证研究,结果表明了拓扑算法是可行和高效的。     

Flexible job shop scheduling under condition-based maintenance: Improved version of imperialist competitive algorithm

Maintenance activities have been ignored in many studies on scheduling problems where all machines are assumed to be available without interruption in the planning horizon. However, in realistic situations, they might be unavailable due to preventive maintenance, basic maintenance or unforeseen breakdowns. In this paper, we simulate a condition-based maintenance (CBM) for flexible job shop scheduling problem (FJSP) and consider the combination of Sigmoid function and Gaussian distribution to improve the CBM simulation. This study proposes an improved imperialist competitive algorithm (ICA) for the FJSP scheduling problem with the objective of the makespan minimization. The performance of the proposed algorithm is enhanced with a hybridization of ICA with simulated annealing (SA), after diagnosing standard ICA disadvantages and shortcomings. This ICA also includes a simulation part to handle CBM requirements. Various parameters of the novel ICA are reviewed to calibrate the algorithm with the help of the Taguchi experimental design. Experimental results show the high performance of the novel ICA in comparison with the standard ICA. The obtained results demonstrate that the novel ICA is an effective algorithm for FJSP under CBM. Finally, the performance of ICA is evaluated compared to other popular algorithms.     

Discrete harmony search algorithm for flexible job shop scheduling problem with multiple objectives

Flexible job-shop scheduling problem (FJSP) is a practically useful extension of the classical job shop scheduling problem. This paper proposes an effective discrete harmony search (DHS) algorithm to solve FJSP. The objectives are the weighted combination of two minimization criteria namely, the maximum of the completion time (Makespan) and the mean of earliness and tardiness. Firstly, we develop a new method for the initial machine assignment task. Some existing heuristics are also employed for initializing the harmony memory with discrete machine permutation for machine assignment and job permutation for operation sequencing. Secondly, we develop a new rule for the improvisation to produce a new harmony for FJSP incorporating machine assignment and operation sequencing. Thirdly, several local search methods are embedded to enhance the algorithm’s local exploitation ability. Finally, extensive computational experiments are carried out using well-known benchmark instances. Computational results and comparisons show the efficiency and effectiveness of the proposed DHS algorithm for solving the FJSP with weighted combination of two objectives.     

一种柔性车间快速启发式调度算法

柔性作业车间调度问题比传统的Job-shop问题更复杂也更符合实际生产实际.为了快速有效地求解这类问题,设计出一种基于综合分派规则的快速启发式调度算法.基于综合分派规则的调度算法,以一批工件总完工时间最短为目标,在调度过程中通过动态调整工件的加工优先级并为每道工序分配最适合的机器进行加工,可迅速求得满意的较优解.与其他方法进行对比实验结果证实了算法的有效性,在实际调度系统的应用中也证明了算法的实用性.     

Greedy randomized adaptive search for dynamic flexible job-shop scheduling

Dynamic flexible job shop scheduling problem is studied under the events such as new order arrivals, changes in due dates, machine breakdowns, order cancellations, and appearance of urgent orders. This paper presents a constructive algorithm which can solve FJSP and DFJSP with machine capacity constraints and sequence-dependent setup times, and employs greedy randomized adaptive search procedure (GRASP). Besides, Order Review Release (ORR) mechanism and order acceptance/rejection decisions are also incorporated into the proposed method in order to adjust capacity execution considering customer due date requirements. The lexicographic method is utilized to assess the objectives: schedule instability, makespan, mean tardiness and mean flow time. A group of experiments is also carried out in order to verify the suitability of the GRASP in solving the flexible job shop scheduling problem. Benchmark problems are formed for different problem scales with dynamic events. The event-driven rescheduling strategy is also compared with periodical rescheduling strategy. Results of the extensive computational experiment presents that proposed approach is very effective and can provide reasonable schedules under event-driven and periodic scheduling scenarios.     

A Review on Swarm Intelligence and Evolutionary Algorithms for Solving Flexible Job Shop Scheduling Problems

Flexible job shop scheduling problems (FJSP) have received much attention from academia and industry for many years. Due to their exponential complexity, swarm intelligence (SI) and evolutionary algorithms (EA) are developed, employed and improved for solving them. More than 60% of the publications are related to SI and EA. This paper intents to give a comprehensive literature review of SI and EA for solving FJSP. First, the mathematical model of FJSP is presented and the constraints in applications are summarized. Then, the encoding and decoding strategies for connecting the problem and algorithms are reviewed. The strategies for initializing algorithms? population and local search operators for improving convergence performance are summarized. Next, one classical hybrid genetic algorithm (GA) and one newest imperialist competitive algorithm (ICA) with variables neighborhood search (VNS) for solving FJSP are presented. Finally, we summarize, discus and analyze the status of SI and EA for solving FJSP and give insight into future research directions.