A scheduling problem in blocking hybrid flow shop robotic cells with multiple robots

This paper addresses the robotic scheduling problem in blocking hybrid flow shop cells that consider multiple part types, unrelated parallel machines, multiple robots and machine eligibility constraints. Initially, a mixed integer linear programming (MILP) model is proposed to minimize the makespan for this problem. Due to the complexity of the model, a simulated annealing (SA) based solution approach is developed for its solution. To increase the efficiency of the SA algorithm, a new neighborhood structure based on block properties is applied. The performance of the proposed SA is assessed over a set of randomly generated instances. The computational results demonstrate that the SA algorithm is effective with the employed neighborhood structure. Additionally, this study shows that the appropriate number of robots depends on the sequence of processing operations to be performed at each stage.     

Optimizing distributed no-wait flow shop scheduling problem with setup times and maintenance operations via iterated greedy algorithm

Nowadays, distributed scheduling problem is a reality in many companies. Over the last years, an increasingly attention has been given to the distributed flow shop scheduling problem and the addition of constraints to the problem. This article introduces the distributed no-wait flow shop scheduling problem with sequence-dependent setup times and maintenance operations to minimize makespan. A mixed-integer linear programming (MILP) is to mathematically describe the problem and heuristic procedures to incorporate maintenance operations to job scheduling are proposed. An Iterated Greedy with Variable Search Neighborhood (VNS), named IG_NM, is proposed to solve small and large instances with size of 4,800 and 13,200 problems, respectively. Computational experiments were conducted to evaluate the performance of IG_NM in comparison with MILP and the most recent methods of literature of distributed flow shop scheduling problems. Statistical results show that in the trade-off between effectiveness and efficiency the proposed IG_NM outperformed other metaheuristics of the literature.     

求解工件车间调度问题的一种新的邻域搜索算法

该文提出了一种新的求解工件车间调度(job shop scheduling)问题的邻域搜索算法．问题的目标是：在满足约束条件的前提下使得调度的makespan尽可能地小．定义了一种新的优先分配规则以生成初始解;定义了一种新的邻域结构;将邻域搜索跟单机调度结合在一起;提出了跳坑策略以跳出局部最优解并且将搜索引向有希望的方向．计算了当前国际文献中的一组共58个benchmark问题实例,算法的优度高于当前国外学者提出的两种著名的先进算法．其中对18个10工件10机器的实例,包括最著名的难解实例ft10,在可接受的时间内都找到了最优解．这些实例是当前文献中报导的所有规模为10工件10机器的实例．     

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。     

Maintenance costs and makespan minimization for assembly permutation flow shop scheduling by considering preventive and corrective maintenance

The joint optimization of production scheduling and maintenance planning has a significant influence on production continuity and machine reliability. However, limited research considers preventive maintenance (PM) and corrective maintenance (CM) in assembly permutation flow shop scheduling. This paper addresses the bi-objective joint optimization of both PM and CM costs in assembly permutation flow shop scheduling. We also propose a new mixed integer linear programming model for the minimization of the makespan and maintenance costs. Two lemmas are inferred to relax the expected number of failures and CM cost to make the model linear. A restarted iterated Pareto greedy (RIPG) algorithm is applied to solve the problem by including a new evaluation of the solutions, based on a PM strategy. The RIPG algorithm makes use of novel bi-objective-oriented greedy and referenced local search phases to find non-dominated solutions. Three types of experiments are conducted to evaluate the proposed MILP model and the performance of the RIPG algorithm. In the first experiment, the MILP model is solved with an epsilon-constraint method, showing the effectiveness of the MILP model in small-scale instances. In the remaining two experiments, the RIPG algorithm shows its superiority for all the instances with respect to four well-known multi-objective metaheuristics.     

求解柔性机器人车间调度问题的混合蚁群算法

在柔性作业车间调度问题的基础上,考虑多台搬运机器人执行不同工序在不同机床之间的搬运,形成柔性机器人作业车间调度问题,提出混合蚁群算法。用改进析取图对问题进行描述,使用混合选择策略、自适应伪随机比例规则和改进信息素更新规则优化蚁群算法,结合遗传算子完成机床选择和工序排序。使用一种多机器人排序算法完成搬运机器人分配和搬运工序排序。通过多组算例仿真测试并与其他算法进行比较,验证了算法的有效性和可靠性。     

Bacterial memetic algorithm for simultaneous optimization of path planning and flow shop scheduling problems

The paper deals with simultaneous optimization of path planning of mobile robots and flow shop scheduling problem. The goal of the path planning problem is to determine an optimal collision-free path between a start and a target point for a mobile robot in an environment surrounded by obstacles. The objective is to minimize the path length without colliding with an obstacle. On the other hand, shop scheduling problems deal with processing a given set of jobs on a given number of machines. Each operation has an associated machine on which it has to be processed for a given length of time. The problem is to minimize the overall time demand of the whole process. In this paper, we deal with two robots carrying items between the machines. Bacterial memetic algorithm is proposed for solving this combined problem. The algorithm is verified by experimental simulations and compared to classical techniques.     

Distributed assembly permutation flow shop problem; Single seekers society algorithm

The distributed manufacturing and assembly systems have an important role at the point of overcoming the difficulties faced by today's mass-production industry. By using both of these systems together in the same production system, the advantages of this integration can make industries more flexible and stronger. Besides, optimizing these systems is more complicated since the multiple production systems can undoubtfully affect the production system’s performance. In this paper, two new mixed-integer linear programming (MILP) models are proposed for the distributed assembly permutation flow shop problem (DAPFSP), inspiring by the multiple-travelling salesman structure. Moreover, a single seekers society (SSS) algorithm is proposed for solving the DAPFSP to minimize the maximum completion time of all products. The performance of the proposed MILP models is evaluated using 900 small-sized benchmark instances. The proposed MILP models were effective and were able to find more optimal solutions or improve the best-found solutions for the small-sized DAPFSP benchmark instances. Similarly, the SSS algorithm is statistically compared with the best-known algorithms developed for solving the DAPFSP on 900 small and 810 large-sized benchmark instances. The proposed SSS algorithm shows superior performance compared to other algorithms in solving the small-sized DAPFSP instances in terms of finding better solutions. In addition, it is as effective as the best performing algorithms developed to solve the large-sized DAPFSP instances. Furthermore, the best-found solutions for 40 numbers of test problems reported to be improved in this paper.     

基于深度强化学习求解作业车间机器与 AGV联合调度问题

针对作业车间中自动引导运输车(automated guided vehicle, AGV)与机器联合调度问题,以完工时间最小化为目标,提出一种基于卷积神经网络和深度强化学习的集成算法框架.首先,对含AGV的作业车间调度析取图进行分析,将问题转化为一个序列决策问题,并将其表述为马尔可夫决策过程.接着,针对问题的求解特点,设计一种基于析取图的空间状态与5个直接状态特征;在动作空间的设置上,设计包含工序选择和AGV指派的二维动作空间;根据作业车间中加工时间与有效运输时间为定值这一特点,构造奖励函数来引导智能体进行学习.最后,设计针对二维动作空间的2D-PPO算法进行训练和学习,以快速响应AGV与机器的联合调度决策.通过实例验证,基于2D-PPO算法的调度算法具有较好的学习性能和可扩展性效果.     

考虑非确定加工时间的柔性作业车间调度问题研究

加工时间不确定的柔性作业车间调度问题已逐渐成为生产调度研究的热点。采用区间表示加工时间范围,利用时间Petri网建立区间柔性作业车间调度问题形式化模型,并运用网模型的状态类图进行可达性分析,计算出所有可行变迁触发序列。通过对触发序列的时序分析,提出一种有效的逆向分步法来构造触发序列的时间约束不等式,进而求解线性规划问题来获得最小完工时间下界(上界)的优化调度策略。最后利用实例分析验证了模型及所提方法的正确性和可行性,为实际的区间柔性作业车间调度问题提供有效方案。     

一种用于车间作业调度问题的智能枚举算法

车间作业调度问题是优化组合中一个著名的难题,即使规模不大的算例,优化算法的时间也很长。文章提出了一种求解车间作业调度问题的快速智能枚举算法,选取了22个标准算例作为算法的测试试验集,该算法在较短的时间内找到了17个算例的最优解,试验结果表明智能枚举算法确实是一种快速的、有效的求解车间作业调度问题的近似算法。     

Modeling and scheduling a case of flexible flowshops: Total weighted tardiness minimization

Two of the most realistic assumptions in the field of scheduling are the consideration of setup and transportation times. In this paper, we study the flexible flowshop scheduling where setup times are anticipatory sequence-dependent and transportation times are job-independent. We also assume that there are several transporters to carry jobs. The objective is to minimize total weighted tardiness. We first formulate the problem as a mixed integer linear programming (MILP) model. With this, we solve small-sized instances to optimality. Since this problem is known to be NP-hard, we then propose an effective metaheuristic to tackle large-sized instances. This metaheuristic, called electromagnetism algorithm (EMA), originates from the attraction–repulsion mechanism of the electromagnetism theory. We conduct a series of experiments and complete statistical analyses to evaluate the performance of the proposed MILP model and EMA. On a set of instances, we first tune the parameters of EMA. Then, the efficiency of the model and general performance of the proposed EMA are assessed over a set of small-sized instances. To further evaluate EMA, we compare it against two high performing metaheuristics existing in the literature over a set of large-sized instances. The results demonstrate that the proposed MILP model and EMA are effective for this problem.     

Lateness minimization with Tabu search for job shop scheduling problem with sequence dependent setup times

We tackle the job shop scheduling problem with sequence dependent setup times and maximum lateness minimization by means of a tabu search algorithm. We start by defining a disjunctive model for this problem, which allows us to study some properties of the problem. Using these properties we define a new local search neighborhood structure, which is then incorporated into the proposed tabu search algorithm. To assess the performance of this algorithm, we present the results of an extensive experimental study, including an analysis of the tabu search algorithm under different running conditions and a comparison with the state-of-the-art algorithms. The experiments are performed across two sets of conventional benchmarks with 960 and 17 instances respectively. The results demonstrate that the proposed tabu search algorithm is superior to the state-of-the-art methods both in quality and stability. In particular, our algorithm establishes new best solutions for 817 of the 960 instances of the first set and reaches the best known solutions in 16 of the 17 instances of the second set.     

面向多目标流水车间调度的多种群多目标遗传算法

针对制造型企业普遍存在的流水车间调度问题,建立了以最小化最迟完成时间和总延迟时间为目标的多目标调度模型,并提出一种基于分解方法的多种群多目标遗传算法进行求解.该算法将多目标流水车间调度问题分解为多个单目标子问题,并分阶段地将这些子问题引入到算法迭代过程进行求解.算法在每次迭代时,依据种群的分布情况选择各子问题的最好解及与其相似的个体分别为当前求解的子问题构造子种群,通过多种群的进化完成对多个子问题最优解的并行搜索.通过对标准测试算例进行仿真实验,结果表明所提出的算法在求解该问题上能够获得较好的非支配解集.     

Fast scheduling of human-robot teams collaboration on synchronised production-logistics tasks in aircraft assembly

The deployment of human-robot teams (HRTs) promises to realise the potential of each team member regarding their distinct abilities and combines efficiency and flexibility in manufacturing operations. However, enabling effective coordination amongst collaborative tasks performed by humans and robots while ensuring safety and satisfying specific constraints is challenging. Motivated by real-world applications that Boeing and Airbus adopt HRTs in manufacturing operations, this paper investigates the allocating and coordinating of HRTs to support safe and efficient human-robot collaboration on synchronised production-logistics tasks in aircraft assembly. We connect the operations research and robotics communities by formulating the problem with precedence constraints, spatial constraints, temporal constraints, and synchronisation constraints that fits within the classic multi-robot task allocation (MRTA) category into a flexible job shop scheduling problem. Two exact approaches, including mixed-integer linear programming (MILP) and constraint programming (CP), are proposed to formulate and solve this problem. A benchmark set with 80 instances (e.g., small/medium-scale and large-scale instances) that corresponds to real dimensions of industrial problems with production tasks, subtasks, locations, deadlines, human worker eligibility and capacity, robot eligibility and capacity, material handling system capacity, and travel times is developed. Experimental evaluation with a total of 1200 independent tests on the benchmark set shows the superiority of the CP approach comparing the MILP approach for efficiently solving real-life scheduling problems of HRTs collaboration on synchronised production-logistics tasks in aircraft assembly.     

Tardiness minimization in a flexible job shop: A tabu search approach

This paper addresses the problem of scheduling jobs in a flexible job shop with the objective of minimizing total tardiness. The flexible job shop differs from the classical job shop in that each of the operations associated with a job can be processed on any of a set of alternative machines. Two heuristics based on tabu search are developed for this problem: a hierarchical procedure and a multiple start procedure. The procedures use dispatching rules to obtain an initial solution and then search for improved solutions in neighborhoods generated by the critical paths of the jobs in a disjunctive graph representation. Diversification strategies are also implemented and tested. The outcomes of extensive computational results are reported.     

Hybrid metaheuristics for scheduling of machines and transport robots in job shop environment

In real manufacturing environments, the control of some elements in systems based on robotic cells, such as transport robots has some difficulties when planning operations dynamically. The Job Shop scheduling Problem with Transportation times and Many Robots (JSPT-MR) is a generalization of the classical Job Shop scheduling Problem (JSP) where a set of jobs additionally have to be transported between machines by several transport robots. Hence, the JSPT-MR is more computationally difficult than the JSP presenting two NP-hard problems simultaneously: the job shop scheduling problem and the robot routing problem. This paper proposes a hybrid metaheuristic approach based on clustered holonic multiagent model for the JSPT-MR. Firstly, a scheduler agent applies a Neighborhood-based Genetic Algorithm (NGA) for a global exploration of the search space. Secondly, a set of cluster agents uses a tabu search technique to guide the research in promising regions. Computational results are presented using two sets of benchmark literature instances. New upper bounds are found, showing the effectiveness of the presented approach.     

An experimental analysis of local minima to improve neighbourhood search

The paper reports the results from a number of experiments on local search algorithms applied to job shop scheduling problems. The main aim was to get insights into the structure of the underlying configuration space. We consider the disjunctive graph representation where the objective function of job shop scheduling is equal to the length of longest paths. In particular, we analyse the number of longest paths, and our computational experiments on benchmark problems provide evidence that in most cases optimal and near optimal solutions do have a small number of longest paths. For example, our best solutions have one to five longest paths only while the maximum number is about sixty longest paths. Based on this observation, we investigate a non-uniform neighbourhood for simulated annealing procedures that gives preference to transitions where a decrease of the number of longest paths is most likely. The results indicate that the non-uniform strategy performs better than uniform methods, i.e. the non-uniform approach has a potential to find better solutions within the same number of transition steps. For example, we obtain the new upper bound 886 on the 20×20 benchmark problem YN1.

Scope and purpose

The paper reports a number of experiments with local search algorithms applied to job shop scheduling (JSS). The JSS problem is defined as follows: Given a number of l jobs, the jobs have to be processed on m machines. Each job consists of a sequence of m tasks, i.e., each task of a job is assigned to a particular machine. The tasks have to be processed during an uninterrupted time period of a fixed length on a given machine. A schedule is an allocation of the tasks to time intervals on the machines and the aim is to find a schedule that minimises the overall completion time which is called the makespan. The scheduling problem is one of the hardest combinatorial optimization problems (cf. M.R. Garey, D.S. Johnson, SIAM J. Comput. 4(4) (1975) 397. Many methods have been proposed to find good approximations of optimum solutions to job shop scheduling problems; for an overview (see E.H.L. Aarts, Local Search in Combinatorial Optimization, Wiley, New York, 1998). In our paper, the main aim is to get insights into the structure of the underlying configuration space. We consider the disjunctive graph representation where the objective function of job shop scheduling is equal to the length of longest paths. In particular, we analyse the number of longest paths, and our computational experiments on benchmark problems provide evidence that in most cases optimal and near optimal solutions do have a small number of longest paths. For example, our best solutions have one to five longest paths only while the maximum number is about sixty longest paths. Based on this observation, we investigate a non-uniform neighbourhood for simulated annealing procedures that gives preference to transitions where a decrease of the number of longest paths is most likely. The results indicate that the non-uniform strategy performs better than uniform methods, i.e., the non-uniform approach has a potential to find better solutions within the same number of transition steps. For example, we obtain the new upper bound 886 on the 20×20 benchmark problem YN1.     

Mathematical model and discrete artificial Bee Colony algorithm for distributed integrated process planning and scheduling

With the development of the globalization of economy and manufacturing industry, distributed manufacturing mode has become a hot topic in current production research. In the context of distributed manufacturing, one job has different process routes in different workshops because of heterogeneous manufacturing resources and manufacturing environments in each factory. Considering the heterogeneous process planning problems and shop scheduling problems simultaneously can take advantage of the characteristics of distributed factories to finish the processing task well. Thus, a novel network-based mixed-integer linear programming (MILP) model is established for distributed integrated process planning and scheduling problem (DIPPS). The paper designs a new encoding method based on the process network and its OR-nodes, and then proposes a discrete artificial bee colony algorithm (DABC) to solve the DIPPS problem. The proposed DABC can guarantee the feasibility of individuals via specially-designed mapping and switching operations, so that the process precedence constraints contained by the network graph can be satisfied in the entire procedure of the DABC algorithm. Finally, the proposed MILP model is verified and the proposed DABC is tested through some open benchmarks. By comparing with other powerful reported algorithms and obtaining new better solutions, the experiment results prove the effectiveness of the proposed model and DABC algorithm successfully.     

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.