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。     

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.     

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.     

A novel hybrid meta-heuristic algorithm for solving multi objective flexible job shop scheduling

Finding feasible scheduling that optimize all objective functions for flexible job shop scheduling problem (FJSP) is considered by many researchers. In this paper, the novel hybrid genetic algorithm and simulated annealing (NHGASA) is introduced to solve FJSP. The NHGASA is a combination of genetic algorithm and simulated annealing to propose the algorithm that is more efficient than others. The three objective functions in this paper are: minimize the maximum completion time of all the operations (makespan), minimize the workload of the most loaded machine and minimize the total workload of all machines. Pareto optimal solution approach is used in NHGASA for solving FJSP. Contrary to the other methods that assign weights to all objective functions to reduce them to one objective function, in the NHGASA and during all steps, problems are solved by three objectives. Experimental results prove that the NHGASA that uses Pareto optimal solutions for solving multi-objective FJSP overcome previous methods for solving the same benchmarks in the shorter computational time and higher quality.     

A Pareto-based two-stage evolutionary algorithm for flexible job shop scheduling problem with worker cooperation flexibility

The previous studies on the flexible job shop scheduling problems (FJSP) with machine flexibility and worker flexibility normally assume that each machine is operated by one worker at any time. However, it is not accurate in many cases because many workers may be required for machines in processing complex operations. Hence, this paper studies a universal version, i.e., FJSP with worker cooperation flexibility (FJSPWC), which defines that each machine can be used only if their required workers are prepared. A mixed-integer linear programming model tuned by CPLEX is established for the problem aiming to collaboratively minimize the makespan, maximum workload of machines and maximum workload of workers. To solve the problem efficiently, a Pareto-based two-stage evolutionary algorithm (PTEA) is proposed. In the PTEA, a well-tailored initialization operator and the NSGA-II structure are designed for global exploration in the first stage, and a competitive objective-based local search operator is developed to improve its local search ability and accelerate the convergence in the second stage. Extensive experiments based on fifty-eight newly formulated benchmarks are carried out to validate the effectiveness of the well-designed initialization operator and two-stage architecture. Comprehensive experiments are performed to evaluate the proposed PTEA, and the results reveal that the PTEA is superior to four comparison algorithms concerning the distribution, convergence, and overall performance.     

Process plan and part routing optimization in a dynamic flexible job shop scheduling environment: an optimization via simulation approach

This paper presents an optimization via simulation approach to solve dynamic flexible job shop scheduling problems. In most real-life problems, certain operation of a part can be processed on more than one machine, which makes the considered system (i.e., job shops) flexible. On one hand, flexibility provides alternative part routings which most of the time relaxes shop floor operations. On the other hand, increased flexibility makes operation machine pairing decisions (i.e., the most suitable part routing) much more complex. This study deals with both determining the best process plan for each part and then finding the best machine for each operation in a dynamic flexible job shop scheduling environment. In this respect, a genetic algorithm approach is adapted to determine best part processing plan for each part and then select appropriate machines for each operation of each part according to the determined part processing plan. Genetic algorithm solves the optimization phase of solution methodology. Then, these machine-operation pairings are utilized by discrete-event system simulation model to estimate their performances. These two phases of the study follow each other iteratively. The goal of methodology is to find the solution that minimizes total of average flowtimes for all parts. The results reveal that optimization via simulation approach is a good way to cope with dynamic flexible job shop scheduling problems, which usually takes NP-Hard form.     

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.     

自适应Jaya算法求解多目标柔性车间绿色调度问题

针对多目标柔性作业车间绿色调度问题(MO-FJGSP),建立优化目标为最大完工时间、机器总负荷和能耗最小的多目标数学模型,并设计一种基于Pareto最优解的自适应多目标Jaya算法(SAMO-Jaya)对该问题进行优化求解.算法采用两级实数编码方式实现工序排序与机器分配的编码表示,并设计一种转换机制实现将Jaya连续解空间映射至FJSP离散解空间;然后设计一种混沌序列与均匀分布相结合的混合策略以提高初始种群的质量与全局分散性;此外,在Jaya算法中嵌入自适应调整种群规模的方法以提高算法求解速度.通过10个单目标与3个多目标基准算例测试,并与7个已有算法进行对比分析,结果表明SAMO-Jaya算法能够对MO-FJGSP进行有效求解.     

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.     

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.     

Research on flexible job shop scheduling under finite transportation conditions for digital twin workshop

Flexible job shop scheduling is one of the most effective methods for solving multiple varieties and small batch production problems in discrete manufacturing enterprises. However, limitations of actual transportation conditions in the flexible job shop scheduling problem (FJSP) are neglected, which limits its application in actual production. In this paper, the constraint influence imposed by finite transportation conditions in the FJSP is addressed. The coupling relationship between transportation and processing stages is analyzed, and a finite transportation conditions model is established. Then, a three-layer encoding with redundancy and decoding with correction is designed to improve the genetic algorithm and solve the FJSP model. Furthermore, an entity-JavaScript Object Notation (JSON) method is proposed for transmission between scheduling services and Digital Twin (DT) virtual equipment to apply the scheduling results to the DT system. The results confirm that the proposed finite transportation conditions have a significant impact on scheduling under different scales of scheduling problems and transportation times.     

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。     

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.     

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.     

Co-evolutionary genetic algorithm for fuzzy flexible job shop scheduling

Fuzzy flexible job shop scheduling problem (FfJSP) is the combination of fuzzy scheduling and flexible scheduling in job shop environment, which is seldom investigated for its high complexity. We developed an effective co-evolutionary genetic algorithm (CGA) for the minimization of fuzzy makespan. In CGA, the chromosome of a novel representation consists of ordered operation list and machine assignment string, a new crossover operator and a modified tournament selection are proposed, and the population of job sequencing and the population of machine assignment independently evolve and cooperate for converging to the best solutions of the problem. CGA is finally applied and compared with other algorithms. Computational results show that CGA outperforms those algorithms compared.     

Optimisation of distributed manufacturing flexible job shop scheduling by using hybrid genetic algorithms

In contrast to traditional job-shop scheduling problems, various complex constraints must be considered in distributed manufacturing environments; therefore, developing a novel scheduling solution is necessary. This paper proposes a hybrid genetic algorithm (HGA) for solving the distributed and flexible job-shop scheduling problem (DFJSP). Compared with previous studies on HGAs, the HGA approach proposed in this study uses the Taguchi method to optimize the parameters of a genetic algorithm (GA). Furthermore, a novel encoding mechanism is proposed to solve invalid job assignments, where a GA is employed to solve complex flexible job-shop scheduling problems (FJSPs). In addition, various crossover and mutation operators are adopted for increasing the probability of finding the optimal solution and diversity of chromosomes and for refining a makespan solution. To evaluate the performance of the proposed approach, three classic DFJSP benchmarks and three virtual DFJSPs were adapted from classical FJSP benchmarks. The experimental results indicate that the proposed approach is considerably robust, outperforming previous algorithms after 50 runs.     

A GEP-based reactive scheduling policies constructing approach for dynamic flexible job shop scheduling problem with job release dates

Flexible job shop scheduling problem (FJSSP) is generalization of job shop scheduling problem (JSSP), in which an operation may be processed on more than one machine each of which has the same function. Most previous researches on FJSSP assumed that all jobs to be processed are available at the beginning of scheduling horizon. The assumption, however, is always violated in practical industries because jobs usually arrive over time and can not be predicted before their arrivals. In the paper, dynamic flexible job shop scheduling problem (DFJSSP) with job release dates is studied. A heuristic is proposed to implement reactive scheduling for the dynamic scheduling problem. An approach based on gene expression programming (GEP) is also proposed which automatically constructs reactive scheduling policies for the dynamic scheduling. In order to evaluate the performance of the reactive scheduling policies constructed by the proposed GEP-based approach under a variety of processing conditions three factors, such as the shop utilization, due date tightness, problem flexibility, are considered in the simulation experiments. The scheduling performance measure considered in the simulation is the minimization of makespan, mean flowtime and mean tardiness, respectively. The results show that GEP-based approach can construct more efficient reactive scheduling policies for DFJSSP with job release dates under a big range of processing conditions and performance measures in the comparison with previous approaches.     

Group shops scheduling with makespan criterion subject to random release dates and processing times

This paper deals with a stochastic group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the other shop scheduling problems such as the flow shop, the job shop and the open shop scheduling problems. Both the release date of each job and the processing time of each job on each machine are random variables with known distributions. The objective is to find a job schedule which minimizes the expected makespan. First, the problem is formulated in a form of stochastic programming and then a lower bound on the expected makespan is proposed which may be used as a measure for evaluating the performance of a solution without simulating. To solve the stochastic problem efficiently, a simulation optimization approach is developed that is a hybrid of an ant colony optimization algorithm and a heuristic algorithm to generate good solutions and a discrete event simulation model to evaluate the expected makespan. The proposed approach is tested on instances where the random variables are normally, exponentially or uniformly distributed and gives promising results.     

Using multiple objective tabu search and grammars to model and solve multi-objective flexible job shop scheduling problems

A linguistic-based meta-heuristic modeling and solution approach for solving the flexible job shop scheduling problem (FJSSP) is presented in this study. FJSSP is an extension of the classical job-shop scheduling problem. The problem definition is to assign each operation to a machine out of a set of capable machines (the routing problem) and to order the operations on the machines (the sequencing problem), such that predefined performance measures are optimized. In this research, the scope of the problem is widened by taking into account the alternative process plans for each part (process plan selection problem). Probabilistic selection of alternative process plans and machines are also considered. The FJSSP is presented as a grammar and the productions in the grammar are defined as controls (Baykasolu, 2002). Using these controls and Giffler and Thompson's (1960) priority rule-based heuristic along with the multiple objective tabu search algorithm of Baykasolu et al. (1999) FJSSP is solved. This novel approach simplifies the modeling process of the FJSSP and enables usage of existing job shop scheduling algorithms for its fast solution. Instead of scheduling job shops with inflexible algorithms that cannot take into account the flexibility which is available in the job shop, the present algorithm is developed which can take into account the flexibility during scheduling. Such an approach will considerably increase the responsiveness of the job shops.     

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。