A novel MILP model for job shop scheduling problem with mobile robots

The mobile robot is the essential equipment for automated logistics in the intelligent workshop, but the literature on shop scheduling rarely considers transport resources. This paper studies the integrated scheduling of machines and mobile robots, which can facilitate the efficiency of production systems. For the job shop scheduling problem with mobile robots (JSPMR), the existing mathematical models are too complex to obtain the optimal solution in an efficient time. Therefore, a novel mixed integer linear programming (MILP) model is proposed to minimize the makespan. Firstly, in view of the property of the problem, a disjunctive graph model is modified to describe the relationship between transport and processing tasks. Secondly, a more accurate and simplified MILP is proposed based on the modified disjunctive graph model. Two related proofs are given to prove the proposed model satisfies all special situations. Thirdly, the proposed MILP is tested on the well-known benchmark, including 82 instances. The proposed model is the first MILP model to obtain optimal solutions for all instances. Finally, 40 larger-scale instances are presented based on a real-world engineering case and used to validate the performance of models further. The comparison results verify the effectiveness and superior computational performance of the proposed model.     

Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm

Most flexible job shop scheduling models assume that the machines are available all of the time. However, in most realistic situations, machines may be unavailable due to maintenances, pre-schedules and so on. In this paper, we study the flexible job shop scheduling problem with availability constraints. The availability constraints are non-fixed in that the completion time of the maintenance tasks is not fixed and has to be determined during the scheduling procedure. We then propose a hybrid genetic algorithm to solve the flexible job shop scheduling problem with non-fixed availability constraints (fJSP-nfa). The genetic algorithm uses an innovative representation method and applies genetic operations in phenotype space in order to enhance the inheritability. We also define two kinds of neighbourhood for the problem based on the concept of critical path. A local search procedure is then integrated under the framework of the genetic algorithm. Representative flexible job shop scheduling benchmark problems and fJSP-nfa problems are solved in order to test the effectiveness and efficiency of the suggested methodology. Received: June 2005 /Accepted: December 2005     

A heuristic for job shop scheduling to minimize total weighted tardiness

This paper considers the job shop scheduling problem to minimize the total weighted tardiness with job-specific due dates and delay penalties, and a heuristic algorithm based on the tree search procedure is developed for solving the problem. A certain job shop scheduling to minimize the maximum tardiness subject to fixed sub-schedules is solved at each node of the search tree, and the successor nodes are generated, where the sub-schedules of the operations are fixed. Thus, a schedule is obtained at each node, and the sub-optimum solution is determined among the obtained schedules. Computational results on some 10 jobs and 10 machines problems and 15 jobs and 15 machines problems show that the proposed algorithm can find the sub-optimum solutions with a little computation time.     

Irreducible bin packing and normality in routing open shop

The open shop is a classical scheduling problem known since 1976, which can be described as follows. A number of jobs have to be processed by a given set of machines, each machine should perform an operation on every job, and the processing times of all the operations are given. One has to construct a schedule to perform all the operations to minimize finish time also known as the makespan. The open shop problem is known to be NP-hard for three and more machines, while is polynomially solvable in the case of two machines. We consider the routing open shop problem, being a generalization of both the open shop problem and the metric traveling salesman problem. In this setting, jobs are located at nodes of a transportation network and have to be processed by mobile machines, initially located at a predefined depot. Machines have to process all the jobs and return to the depot to minimize makespan. A feasible schedule is referred to as normal if its makespan coincides with the standard lower bound. We introduce the Irreducible Bin Packing decision problem, use it to describe new sufficient conditions of normality for the two machine problem, and discuss the possibility to extend these results on the problem with three and more machines. To that end, we present two new computer-aided optima localization results.

     

The total completion time open shop scheduling problem with a given sequence of jobs on one machine

This paper addresses the open shop scheduling problem to minimize the total completion time, provided that one of the machines has to process the jobs in a given sequence. The problem is NP-hard in the strong sense even for the two-machine case. A lower bound is derived based on the optimal solution of a relaxed problem in which the operations on every machine may overlap except for the machine with a given sequence of jobs. This relaxed problem is NP-hard in the ordinary sense, however it can be quickly solved via a decomposition into subset-sum problems. Both heuristic and branch-and-bound algorithm are proposed. Experimental results show that the heuristic is efficient for solving large-scaled problems, and the branch-and-bound algorithm performs well on small-scaled problems.Scope and purposeShop scheduling problems, widely used in the modeling of industrial production processes, are receiving an increasing amount of attention from researchers. To model practical production processes more closely, additional processing restrictions can be introduced, e.g., the resource constraints, the no-wait in process requirement, the precedence constraints, etc. This paper considers the total completion time open shop scheduling problem with a given sequence of jobs on one machine. This model belongs to a new class of shop scheduling problems under machine-dependent precedence constraints. This problem is NP-hard in the strong sense. A heuristic is proposed to efficiently solve large-scaled problems and a branch-and-bound algorithm is presented to optimally solve small-scaled problems. Computational experience is also reported.     

智能仓储中的多机器人调度方法

近年来,传统仓储系统已满足不了日益增长的订单需求并已渐渐向智能仓储转变。针对智能仓储中移动机器人的调度问题,以移动机器人执行任务时的转向次数、路程代价、最大任务等待时间为优化目标,提出一种兼顾任务分配和路径规划的调度算法。算法采用遗传算法进行任务分配,同时以多个移动机器人为目标进行任务分配,保证每个机器人分配到的任务没有重复。然后采用Q-learning算法对机器人分配到的任务进行路径规划,根据转向次数和路程代价约束路径,对于路径转向和每一步可行的动作均设有惩罚值,最终形成一条转向次数少、行程较短的路径。通过将该算法与其他算法进行对比,证实了该算法的有效性。     

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.     

基于信息物理系统的多分拣移动机器人调度策略

研究基于信息物理系统建模的多分拣移动机器人(multi-SMR)调度策略.首先,在基于实际应用场景的拓扑地图建模中加入新的路径弧时间损耗指标,以实现对货物不均匀比例和多机器人拥堵状态的精确估计;其次,提出一种改进的启发式路径规划算法,并在路径评估过程中增加目的地距离和时间损耗指标;最后,将完整的调度过程以分层式结构部署在信息物理系统模型中,包括控制层的时间损耗指标更新、交通管制监测,以及物理层的分布式路径规划和机器人状态更新.仿真实验结果表明,改进的调度策略可以进一步提升系统分拣效率,降低计算成本,有效解决机器人拥堵和安全问题.     

带工序跳跃的绿色混合流水车间机器与AGV联合调度

针对带工序跳跃的绿色混合流水车间机器和自动引导车(AGV)联合调度问题,提出改进memetic algorithm (MA)以同时最小化最大完工时间和总能耗.首先,设计基于工序、机器和转速的三层编码策略,最大程度保证算法在整个解空间中搜索;然后,设计混合种群初始化方法以提高初始种群解的质量,同时设计交叉和变异算子以及两种基于问题的邻域搜索策略来平衡算法的全局搜索和局部搜索能力;最后,通过大量仿真实验验证MA算法求解该问题的有效性和优越性.     

求解柔性作业车间调度的GATOC混合方法

柔性作业车间调度问题是经典作业车间调度问题的扩展,它允许工序在可选加工机器集中任意一台上加工,加工时间随加工机器不同而不同。针对柔性作业车间调度问题的特点,提出一种基于约束理论的局部搜索方法,对关键路径上的机器的负荷率进行比较,寻找瓶颈机器,以保证各机器之间的负荷平衡。为了克服传统遗传算法早熟和收敛慢的缺点,设计多种变异操作,增加种群多样性。为了更好保留每代中的优良解,设计了基于海明距离的精英解保留策略。运用提出的算法求解基准测试问题,验证了算法的可行性和有效性。     

Multi-degree cyclic scheduling of two robots in a no-wait flowshop

This paper addresses multi-degree cyclic scheduling of two robots in a no-wait flowshop, where exactly r(r > 1) identical parts with constant processing times enter and leave the production line during each cycle, and transportation of the parts between machines is performed by two robots on parallel tracks. The objective is to minimize the cycle time. The problem is transformed into enumeration of pairs of overlapping moves that cannot be performed by the same robot. This enumeration is accomplished by enumerating intervals for some linear functions of decision variables. The algorithm developed is polynomial in the number of machines for a fixed r, but exponential if r is arbitrary. Computational results with benchmark instances are reported. Note to Practitioners-This paper was motivated by the problem of cyclic scheduling of a no-wait production line, where a part must be processed without any interruption either on or between machines due to characteristics of the processing technology itself or the absences of storage capacity between operations of a part. Multi-degree schedules, in which multiple parts enter and leave the line during a cycle, usually have larger throughput rate than simple ones. This paper proposes an algorithm for multi-degree cyclic scheduling of a no-wait flowshop with two robots. Computational results show that the throughput rate can be really improved by using multi-degree schedules with two robots. However, we have not addressed the decision of the optimal value of the degree of the cycle. Furthermore, since we consider that the two robots travel along parallel tracks, the collision-avoidance constraints have been relaxed in the algorithm. In future research, we will address the two problems and generalize the algorithm to multi-robot cases.     

Neural computation for collision-free path planning

Automatic path planning plays an essential role in planning of assembly or disassembly of products, motions of robot manipulators handling part, and material transfer by mobile robots in an intelligent and flexible manufacturing environment. The conventional methodologies based on geometric reasoning suffer not only from the algorithmic difficulty but also from the excessive time complexity in dealing with 3-D path planning. This paper presents a massively parallel, connectionist algorithm for collision-free path planning. The path planning algorithm is based on representing a path as a series ofvia points or beads connected by elastic strings which are subject to displacement due to a potential field or a collision penalty function generated by polyhedral obstacles. Mathematically, this is equivalent to optimizing a cost function, defined in terms of the total path length and the collision penalty function, by moving thevia points simultaneously but individually in the direction that minimizes the cost function. Massive parallelism comes mainly from: (1) the connectionist model representation of obstacles and (2) the parallel computation of individualvia-point motions with only local information. The algorithm has power to deal effectively with path planning of three-dimensional objects with translational and rotational motions. Finally, the algorithm incorporates simulated annealing to solve a local minimum problem. Simulation results are shown.     

The Machine Duplication Problem in a Job Shop with Two Jobs

This paper addresses a problem related to the classical job shop scheduling problem with two jobs. The problem consists in concurrently determining the best subset of machines to be duplicated and the optimal scheduling of the operations in order to minimize completion time. Such a problem arises in the tool management for a class of flexible manufacturing cells. The job shop with two jobs is first reviewed, the application of the classical search algorithm A* to this problem is discussed and its performance compared with a previous approach. The complexity of the machine duplication problem is then analysed. The problem is proved to be in general NP-hard in the strong sense, but in a class of special cases, relevant from the applications viewpoint, it can be solved in polynomial time by a dynamic programming algorithm. A heuristic based on such an algorithm and on A* is proposed for the general problem; the results are satisfactory in terms of both efficiency and quality of the solution.     

异构多目标差分-动态窗口算法 及其在移动机器人中的应用

为了实现在多移动机器人和多窄通道的复杂动态环境中机器人的节能运动规划,提出异构多目标差分-动态窗口法(heterogeneous multi-objective differential evolution-dynamic window algorithm,HMODE-DWA).首先,建立行驶时间、执行器作用力和平滑度的3目标优化模型,设计具有碰撞约束的异构多目标差分进化算法来获得3个目标函数的最优解,进而在已知的静态环境中获得帕累托前沿,利用平均隶属度函数获得起点与终点间最优的全局路径;其次,定义基于环境缓冲区域的模糊动态窗口法使机器人完成动态复杂环境中避障,利用所提出的HMODE-DWA算法动态避障的同时实现节能规划.仿真和实验结果表明,所提出的混合路径规划控制策略能够有效降低移动机器人动态避障过程中的能耗.     

Scheduling Flexible Flow Shop in Labeling Companies to Minimize the Makespan

In the competitive global marketplace, production scheduling plays a vital role in planning in manufacturing. Scheduling deals directly with the time to output products quickly and with a low production cost. This research examines case study of a Radio-Frequency Identification labeling department at Avery Dennison. The main objective of the company is to have a method that allows for the sequencing and scheduling of a set of jobs so it can be completed on or before the customer’s due date to minimize the number of late orders. This study analyzes the flexible flow shop scheduling problem with a sequence dependent setup by modifying the processing time and setup time to minimize the makespan on multiple machines. Based on the defined mathematical model, this study includes an alternative approach and application of heuristic algorithm with the input being big data. Both optimization programs are used in this study and compared to determine which method can better solve the company’s problems. The proposed algorithm is able to improve machine utilization with large-scale problems.     

Path planning approach in unknown environment

This paper presents a new algorithm of path planning for mobile robots, which utilises the characteristics of the obstacle border and fuzzy logical reasoning. The environment topology or working space is described by the time-variable grid method that can be further described by the moving obstacles and the variation of path safety. Based on the algorithm, a new path planning approach for mobile robots in an unknown environment has been developed. The path planning approach can let a mobile robot find a safe path from the current position to the goal based on a sensor system. The two types of machine learning: advancing learning and exploitation learning or trial learning are explored, and both are applied to the learning of mobile robot path planning algorithm. Comparison with A* path planning approach and various simulation results are given to demonstrate the efficiency of the algorithm. This path planning approach can also be applied to computer games.     

Dyna-Q-based vector direction for path planning problem of autonomous mobile robots in unknown environments

Reinforcement learning (RL) is a popular method for solving the path planning problem of autonomous mobile robots in unknown environments. However, the primary difficulty faced by learning robots using the RL method is that they learn too slowly in obstacle-dense environments. To more efficiently solve the path planning problem of autonomous mobile robots in such environments, this paper presents a novel approach in which the robot’s learning process is divided into two phases. The first one is to accelerate the learning process for obtaining an optimal policy by developing the well-known Dyna-Q algorithm that trains the robot in learning actions for avoiding obstacles when following the vector direction. In this phase, the robot’s position is represented as a uniform grid. At each time step, the robot performs an action to move to one of its eight adjacent cells, so the path obtained from the optimal policy may be longer than the true shortest path. The second one is to train the robot in learning a collision-free smooth path for decreasing the number of the heading changes of the robot. The simulation results show that the proposed approach is efficient for the path planning problem of autonomous mobile robots in unknown environments with dense obstacles.     

A spatio-temporal constrained hierarchical scheduling strategy for multiple warehouse mobile robots under industrial cyber–physical system

The industrial cyber–physical system (ICPS) framework can reduce the computational load and improve task efficiency. This paper studies the ICPS-based scheduling strategy for multi-warehouse mobile robots (multi-WMRs). First of all, the possible congestion problem is considered in topological map modeling, which is transformed into a new path time cost index. Second, each robot independently executes the path planning algorithm, which realizes distributed path computation and takes time cost and destination distance into account. The improved task assignment strategy includes task evaluation and decision-making, which are considered part of the planning and help to improve task efficiency. Finally, the complete scheduling process is applied to the novel ICPS architecture, including cost evaluation, path planning, task assignment, and collision avoidance. In numerical experiments, the task efficiency has been increased by 24.8% to recent research and 14.59% to previous work. The average congestion time is reduced by 28.41%, and the planning time is reduced to 10.13% of the traditional method.     

Tighter Bounds on Preemptive Job Shop Scheduling with Two Machines

We consider the preemptive job shop scheduling problem with two machines, with the objective to minimize the makespan. We present an algorithm that finds a schedule of length at most P _max/2 greater than the optimal schedule length, where P _max is the length of the longest job. Received June 13, 2000     

柔性作业调度的串并行模型对比与求解

作业处理中的柔性使得作业调度更为灵活,作业中操作的执行顺序满足拓扑排序是作业调度的前提。是否允许没有优先关系的操作在不同的机器上同时执行是区分串行和并行调度的条件。文中以共生进化算法求解一个复杂的作业调度模型为例,给出了算法实现串行调度和并行调度的具体区别,并给出了串行和并行调度的结果。结果表明,并行相对于串行对算法效率的提高与柔性大小相关,与作业的规模成反比。