Single CNC machine scheduling with controllable processing times to minimize total weighted tardiness

Advanced manufacturing technologies, such as CNC machines, require significant investments, but also offer new capabilities to the manufacturers. One of the important capabilities of a CNC machine is the controllable processing times. By using this capability, the due date requirements of customers can be satisfied much more effectively. Processing times of the jobs on a CNC machine can be easily controlled via machining conditions such that they can be increased or decreased at the expense of tooling cost. Since scheduling decisions are very sensitive to the processing times, we solve the process planning and scheduling problems simultaneously. In this study, we consider the problem of scheduling a set of jobs on a single CNC machine to minimize the sum of total weighted tardiness, tooling and machining costs. We formulated the joint problem, which is NP-hard since the total weighted tardiness problem (with fixed processing times) is strongly NP-hard alone, as a nonlinear mixed integer program. We proposed a DP-based heuristic to solve the problem for a given sequence and designed a local search algorithm that uses it as a base heuristic.     

考虑多目标的柔性工艺与调度集成优化算法

针对工艺规划与车间调度集成优化问题,在考虑零件的加工工序柔性、工序次序柔性及加工机器柔性的基础上,以最大完工时间、总加工成本和总拖期时间为优化目标,对多目标柔性工艺与车间调度集成问题建模,提出一种基于改进人工蜂群算法的多目标柔性工艺与车间调度集成优化策略,并提出邻域变异操作以及全局交叉操作,对种群进行更新。引入Pareto方法,通过对适应度评价、贪婪准则、Pareto最优解集构造和保存以及解得多样性维护等方面进行改进,设计了一种基于Pareto方法的多目标人工蜂群算法。最后,通过采用基本人工蜂群算法及改进人工蜂群算法对六个工件、五台机床的柔性工艺与车间调度集成问题进行优化,验证了改进算法的有效性。     

Multi-skilled project scheduling with level-dependent rework risk; three multi-objective mechanisms based on cuckoo search

In many projects, multi-skilled workforces are able to perform different tasks with different quality levels. In this paper, a real-life version of the multi-skilled resource constrained project scheduling problem is investigated, in which the reworking risk of each activity depends on the assigned level of multi-skilled workforces. The problem is formulated mathematically as a bi-objective optimization model to minimize total costs of processing the activities and to minimize reworking risks of the activities, concurrently. In order to solve the resulting problem, three cuckoo-search-based multi-objective mechanisms are developed based on non-dominance sorting genetic algorithm, multi-objective particle swarm and multi-objective invasive weeds optimization algorithm. The parameters of the algorithms are tuned using the Taguchi method to improve the efficiency of the solution procedures. Furthermore, a competitive multi-objective invasive weeds optimization algorithm is used to evaluate the performance of the proposed methodologies. Finally, a priority based method is employed to compare the proposed algorithms in terms of different metrics.     

区际救援物资中转调度的多目标优化问题研究

针对大规模、远距离和多品种的区际救援物资联动调运问题,以区际救援物资送达受灾城市总时间最短和总成本最小为目标,建立了一个区际救援物资中转调度的多目标优化模型,并设计了一种多目标协进化遗传算法。算例分析验证了该算法能够较好地获取问题的Pareto最优解。     

基于蚁群粒子群算法求解多目标柔性调度问题

通过分析多目标柔性作业车间调度问题中各目标的相互关系,提出一种主、从递阶结构的蚁群粒子群求解算法。算法中,主级为蚁群算法,在选择工件加工路径过程中实现设备总负荷和关键设备负荷最小化的目标;从级为粒子群算法,在主级工艺路径约束下的设备排产中实现工件流通时间最小化的目标。然后,以设备负荷和工序加工时间为启发式信息设计蚂蚁在工序可用设备间转移概率;基于粒子向量优先权值的大小关系设计解码方法实现设备上的工序排产。最后,通过仿真和比较实验,验证了该算法的有效性。     

Solving a bi-objective unrelated parallel batch processing machines scheduling problem: A comparison study

Nowadays in competitive markets, production organizations are looking to increase their efficiency and optimize manufacturing operations. In addition, batch processor machines (BPMs) are faster and cheaper to carry out operations; thus the performance of manufacturing systems is increased. This paper studies a production scheduling problem on unrelated parallel BPMs with considering the release time and ready time for jobs as well as batch capacity constraints. In unrelated parallel BPMs, modern machines are used in a production line side by side with older machines that have different purchasing costs; so this factor is introduced as a novel objective to calculate the optimum cost for purchasing various machines due to the budget. Thus, a new bi-objective mathematical model is presented to minimize the makespan (i.e., C_max), tardiness/earliness penalties and the purchasing cost of machines simultaneously. The presented model is first coded and solved by the ε-constraint‌ method. Because of the complexity of the NP-hard problem, exact methods are not able to optimally solve large-sized problems in a reasonable time. Therefore, we propose a multi-objective harmony search (MOHS) algorithm. the results are compared with the multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective ant colony optimization algorithm (MOACO). To tune their parameters, the Taguchi method is used. The results are compared by five metrics that show the effectiveness of the proposed MOHS algorithm compared with the MOPSO, NSGA-II and MOACO. At last, the sensitivity of the model is analyzed on new parameters and impacts of each parameter are illustrated on bi- objective functions.     

Multi-objective genetic algorithm and its applications to flowshop scheduling

In this paper, we propose a multi-objective genetic algorithm and apply it to flowshop scheduling. The characteristic features of our algorithm are its selection procedure and elite preserve strategy. The selection procedure in our multi-objective genetic algorithm selects individuals for a crossover operation based on a weighted sum of multiple objective functions with variable weights. The elite preserve strategy in our algorithm uses multiple elite solutions instead of a single elite solution. That is, a certain number of individuals are selected from a tentative set of Pareto optimal solutions and inherited to the next generation as elite individuals. In order to show that our approach can handle multi-objective optimization problems with concave Pareto fronts, we apply the proposed genetic algorithm to a two-objective function optimization problem with a concave Pareto front. Last, the performance of our multi-objective genetic algorithm is examined by applying it to the flowshop scheduling problem with two objectives: to minimize the makespan and to minimize the total tardiness. We also apply our algorithm to the flowshop scheduling problem with three objectives: to minimize the makespan, to minimize the total tardiness, and to minimize the total flowtime.     

智能RGV动态调度多目标规划模型

智能轨道式自动引导车(Rail Guided Vehicle,RGV)的动态调度模型及其算法研究是一个热门的加工规划问题。针对智能RGV的动态调度问题的不同情形,建立线性加权情况下时间函数与相对稳定性的多目标规划模型,并使用多段遗传编码的遗传算法进行求解。用多组序机器在一定加工件数内最小完成时间与单组序机器最小完成时间之比验证模型。根据加工系统作业参数均值以及与两种调度方案所需时间进行对比,与传统算法相比时间平均缩短13%,证明算法优化的执行具有可行性,在保证加工时间的同时提高了加工系统的稳定性。     

考虑恶化效应的MapReduce模型下的同类机调度

本文研究了MapReduce模型中考虑恶化效应的同类机调度问题. 在MapReduce模型中每个工件加工必须经 过两道工序. 其中在第1道工序中每个工件加工任务可分割成若干个子任务且能并行加工, 当某个工件中的所有子 任务全部完成后, 才允许启动第2道工序, 且第2道工序只能在一台机器上连续加工. 本文考虑了工件实际加工时间 与其开工前的等待时间呈线性函数关系的恶化效应, 构建了以最小化所有工件的逗留时间和为目标函数的混合整 数规划模型, 同时给出了问题的一个下界, 最后设计了采用正余弦差分扰动机制的改进蝙蝠优化算法来求解模型. 通过数值仿真对蝙蝠优化算法、遗传算法、CPLEX结果与下界进行对比, 验证了模型的正确性和改进算法的有效 性.     

Two-generation Pareto ant colony algorithm for multi-objective job shop scheduling problem with alternative process plans and unrelated parallel machines

The flexibilities of alternative process plans and unrelated parallel machines are benefit for the optimization of the job shop scheduling problem, but meanwhile increase the complexity of the problem. This paper constructs the mathematical model for the multi-objective job shop scheduling problem with alternative process plans and unrelated parallel machines, splits the problem into two sub-problems, namely flexible processing route decision and task sorting, and proposes a two-generation (father and children) Pareto ant colony algorithm to generate a feasible scheduling solution. The father ant colony system solves the flexible processing route decision problem, which selects the most appropriate process node set from the alternative process node set. The children ant colony system solves the sorting problem of the process task set generated by the father ant colony system. The Pareto ant colony system constructs the applicable pheromone matrixes and heuristic information with respect to the sub-problems and objectives. And NSGAII is used as comparison whose genetic operators are re-defined. The experiment confirms the validation of the proposed algorithm. By comparing the result of the algorithm to NSGAII, we can see the proposed algorithm has a better performance.     

Multi-objective optimization model for multi-project scheduling on critical chain

In this paper, a multi-project scheduling in critical chain problem is addressed. This problem considers the influence of uncertainty factors and different objectives to achieve completion rate on time of the whole projects. This paper introduces a multi-objective optimization model for multi-project scheduling on critical chain, which takes into consideration multi-objective, such as overall duration, financing costs and whole robustness. The proposed model can be used to generate alternative schedules based on the relative magnitude and importance of different objectives. To respond to this need, a cloud genetic algorithm is proposed. This algorithm using randomness and stability of Normal Cloud Model, cloud genetic algorithm was designed to generate priority of multi-project scheduling activities and obtain plan of multi-project scheduling on critical chain. The performance comparison shows that the cloud genetic algorithm significantly outperforms the previous multi-objective algorithm.     

Minimizing total earliness and tardiness through unrelated parallel machine scheduling using distributed release time control

Using unrelated parallel machine scheduling to minimize the total earliness and tardiness of jobs with distinct due dates is a nondeterministic polynomial-hard problem. Delayed customer orders may result in penalties and reduce customer satisfaction. On the other hand, early completion creates inventory storage costs, which increase the total cost. Although parallel machines can increase productivity, machine assignments also increase the complexity of production. Therefore, the challenge in parallel machine scheduling is to dynamically adjust the machine assignment to complete the job within the shortest possible time. In this paper, we address an unrelated parallel machine scheduling problem for jobs with distinct due dates and dedicated machines. The objective is to dynamically allocate jobs to unrelated parallel machines in order to minimize the total earliness and tardiness time. We formulate the problem as a mixed integer linear programming (MILP) model and develop a modified genetic algorithm (GA) with a distributed release time control (GARTC) mechanism to obtain the near-optimal solution. A preliminary computational study indicates that the developed GARTC not only provides good quality solutions within a reasonable amount of time, but also outperforms the MILP model, a classic GA and heuristic approaches described in the literature.     

基于度值和聚类系数的跨单元调度问题优化

针对工业互联网大环境下的跨单元调度存在协作效率差、生产成本过高等问题,在机器设备归置存在重叠的情况下,首先使用分层网络设计思想构造以机器和制造单元为节点的双层有向加工网络,通过分析网络中全局协作效率、单元间冗余加工路径与一阶度值的相关性,构建最小化平均度值、完工时间和加工成本的多目标调度模型.其次根据麻雀搜索算法局部搜索能力强的特点,提出了一种非支配排序遗传算法和麻雀搜索算法融合策略以及基于聚类系数的初始解生成机制.最后通过实例计算说明网络特征与跨单元调度目标呈相关性,所提模型和算法求解质量更高.     

多目标等量分批柔性作业车间调度集成优化方法

针对多目标等量分批柔性作业车间调度问题,提出了一种集成优化方法。构建了一种以完工时间最短、生产成本最低为优化目标的多目标等量分批柔性调度集成优化模型。提出并设计了一种改进的非支配排序遗传算法对模型加以求解。算法中引入面向对象技术处理复杂的实体逻辑关系,采用三段式分段编码技术分别对分批方案、加工顺序、设备进行编码,采用三段式分段交叉和变异的混合遗传算子实现遗传进化,采用两种精细化调度技术进行解码以缩短流程时间。通过案例分析验证了所提方法的有效性。     

A hybrid genetic heuristic for scheduling parallel batch processing machines with arbitrary job sizes

This paper investigates the scheduling problem of parallel identical batch processing machines in which each machine can process a group of jobs simultaneously as a batch. Each job is characterized by its size and processing time. The processing time of a batch is given by the longest processing time among all jobs in the batch. Based on developing heuristic approaches, we proposed a hybrid genetic heuristic (HGH) to minimize makespan objective. To verify the performance of our algorithm, comparisons are made through using a simulated annealing (SA) approach addressed in the literature as a comparator algorithm. Computational experiments reveal that affording the knowledge of problem through using heuristic procedures, gives HGH the ability of finding optimal or near optimal solutions in a reasonable time.     

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.     

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。     

Minimizing makespan subject to minimum flowtime on two identical parallel machines

We consider the problem of scheduling jobs on two parallel identical machines where an optimal schedule is defined as one that gives the smallest makespan (the completion time of the last job) among the set of schedules with optimal total flowtime (the sum of the completion times of all jobs). We propose an algorithm to determine optimal schedules for the problem, and describe a modified multifit algorithm to find an approximate solution to the problem in polynomial computational time. Results of a computational study to compare the performance of the proposed algorithms with a known heuristic shows that the proposed heuristic and optimization algorithms are quite effective and efficient in solving the problem.Scope and purposeMultiple objective optimization problems are quite common in practice. However, while solving scheduling problems, optimization algorithms often consider only a single objective function. Consideration of multiple objectives makes even the simplest multi-machine scheduling problems NP-hard. Therefore, enumerative optimization techniques and heuristic solution procedures are required to solve multi-objective scheduling problems. This paper illustrates the development of an optimization algorithm and polynomially bounded heuristic solution procedures for the scheduling jobs on two identical parallel machines to hierarchically minimize the makespan subject to the optimality of the total flowtime.     

带机器人制造单元的作业车间调度仿真

针对带有机器人制造单元的作业车间调度优化问题, 在若干加工机器上可以加工具有特定加工工序的若干工件, 并且搬运机器人可以将工件在装卸载站与各加工机器间进行搬运. 在实际生产过程中, 由于不确定性, 特别是带有存货的加工单元, 要求工件的完工时间在一个时间窗内, 而不是一个特定的时间点. 因此针对此情况的作业车间, 考虑到其在求解问题过程中的复杂性和约束性等特点, 研究了在时间窗约束下, 目标值为最小化工件完成时间提前量和延迟量的总权重. 提出了一种将文化基因算法与邻域搜索技术(变邻域下降搜索)相结合的改进元启发式算法, 在求得最优目标值的同时, 可得到最优值的工件加工序列及机器人搬运序列. 通过实验结果表明, 所提出的算法有效且优于传统文化基因算法与遗传算法.     

求解区间柔性作业车间调度的多目标进化算法

针对不确定多目标柔性作业车间调度问题,将工序加工时间采用区间数表示,以区间最大完工时间和区间机器总负荷为优化目标,构建多目标区间柔性作业车间调度模型,并设计一种多目标进化优化算法对该模型进行求解.算法采用混合策略生成初始化种群,并采用贪婪插入法对染色体进行解码,通过基于可能度的占优关系评价个体性能,将区间目标归一化结合拥挤距离反映优化解的分布情况.实验结果验证了所提出算法的有效性.