A memetic algorithm-based heuristic for a scheduling problem in printed circuit board assembly

This research develops a memetic algorithm to solve Printed Circuit Board (PCB) scheduling with sequence-dependent setup times on a single machine with constrained feeder capacity. The objective of the scheduling problem is to minimize the total weighted tardiness. A memetic algorithm-based heuristics is developed by integrating a genetic algorithm, Minimum Slack Time (MST) scheduling rule, “Keep Tool Needed Soonest” (KTNS) policy, and a local search procedure. Application of the MA results in two outcome plans: a scheduling plan and a feeder setup plan.Numerical experiments show that compared to a number of commonly used dispatching rules, the memetic algorithm provides better solutions in term of minimum total weighted tardiness. Even the computation is the highest, it still practical. Calibration of MA parameter values is also explored in this study.     

A variable neighborhood search for minimizing total weighted tardiness with sequence dependent setup times on a single machine

This paper deals with the single machine scheduling problem to minimize the total weighted tardiness in the presence of sequence dependent setup. Firstly, a mathematical model is given to describe the problem formally. Since the problem is NP-hard, a general variable neighborhood search (GVNS) heuristic is proposed to solve it. Initial solution for the GVNS algorithm is obtained by using a constructive heuristic that is widely used in the literature for the problem. The proposed algorithm is tested on 120 benchmark instances. The results show that 37 out of 120 best known solutions in the literature are improved while 64 instances are solved equally. Next, the GVNS algorithm is applied to single machine scheduling problem with sequence dependent setup times to minimize the total tardiness problem without changing any implementation issues and the parameters of the GVNS algorithm. For this problem, 64 test instances are solved varying from small to large sizes. Among these 64 instances, 35 instances are solved to the optimality, 16 instances' best-known results are improved, and 6 instances are solved equally compared to the best-known results. Hence, it can be concluded that the GVNS algorithm is an effective, efficient and a robust algorithm for minimizing tardiness on a single machine in the presence of setup times.     

A tabu search algorithm for order acceptance and scheduling

We consider a make-to-order production system, where limited production capacity and order delivery requirements necessitate selective acceptance of the orders. Since tardiness penalties cause loss of revenue, scheduling and order acceptance decisions must be taken jointly to maximize total revenue. We present a tabu search algorithm that solves the order acceptance and scheduling problem on a single machine with release dates and sequence dependent setup times. We analyze the performance of the tabu search algorithm on an extensive set of test instances with up to 100 orders and compare it with two heuristics from the literature. In the comparison, we report optimality gaps which are calculated with respect to bounds generated from a mixed integer programming formulation. The results show that the tabu search algorithm gives near optimal solutions that are significantly better compared to the solutions given by the two heuristics. Furthermore, the run time of the tabu search algorithm is very small, even for 100 orders. The success of the proposed heuristic largely depends on its capability to incorporate in its search acceptance and scheduling decisions simultaneously.     

多目标和声搜索算法求解序依赖单机调度问题

针对一种具有序依赖设置时间的单机调度问题,建立了目标为总机器设置时间最小、总交货延误时间最短和交货延误率最小的多目标优化模型,提出了一种自适应多目标和声搜索算法,算法中引入了信息熵的概念来评价种群中个体的多样性和拥挤度。实例计算结果表明该算法可行、有效。     

Efficient heuristic algorithms for the blocking flow shop scheduling problem with total flow time minimization

This paper proposes two constructive heuristics, i.e. HPF1 and HPF2, for the blocking flow shop problem in order to minimize the total flow time. They differ mainly in the criterion used to select the first job in the sequence since, as it is shown, its contribution to the total flow time is not negligible. Both procedures were combined with the insertion phase of NEH to improve the sequence. However, as the insertion procedure does not always improve the solution, in the resulting heuristics, named NHPF1 and NHPF2, the sequence was evaluated before and after the insertion to keep the best of both solutions. The structure of these heuristics was used in Greedy Randomized Adaptive Search Procedures (GRASP) with variable neighborhood search in the improvement phase to generate greedy randomized solutions. The performance of the constructive heuristics and of the proposed GRASPs was evaluated against other heuristics from the literature. Our computational analysis showed that the presented heuristics are very competitive and able to improve 68 out of 120 best known solutions of Taillard’s instances for the blocking flow shop scheduling problem with the total flow time criterion.     

A hybrid discrete artificial bee colony algorithm for permutation flowshop scheduling problem

To minimize the makespan in permutation flowshop scheduling problems, a hybrid discrete artificial bee colony (HDABC) algorithm is presented. In the HDABC, each solution to the problem is called a food source and represented by a discrete job permutation. First, the initial population with certain quality and diversity is generated from Greedy Randomized Adaptive Search Procedure (GRASP) based on Nawaz–Enscore–Ham (NEH) heuristics. Second, the discrete operators and algorithm, such as insert, swap, path relinking and GRASP are applied to generate new solution for the employed bees, onlookers and scouts. Moreover, local search is applied to the best one. The presented algorithm is tested on scheduling problem benchmarks. Experimental results show its efficiency.     

A local-best harmony search algorithm with dynamic sub-harmony memories for lot-streaming flow shop scheduling problem

In this paper, a local-best harmony search (HS) algorithm with dynamic sub-harmony memories (HM), namely DLHS algorithm, is proposed to minimize the total weighted earliness and tardiness penalties for a lot-streaming flow shop scheduling problem with equal-size sub-lots. First of all, to make the HS algorithm suitable for solving the problem considered, a rank-of-value (ROV) rule is applied to convert the continuous harmony vectors to discrete job sequences, and a net benefit of movement (NBM) heuristic is utilized to yield the optimal sub-lot allocations for the obtained job sequences. Secondly, an efficient initialization scheme based on the NEH variants is presented to construct an initial HM with certain quality and diversity. Thirdly, during the evolution process, the HM is dynamically divided into many small-sized sub-HMs which evolve independently so as to balance the fast convergence and large diversity. Fourthly, a new improvisation scheme is developed to well inherit good structures from the local-best harmony vector in the sub-HM. Meanwhile, a chaotic sequence to produce decision variables for harmony vectors and a mutation scheme are utilized to enhance the diversity of the HM. In addition, a simple but effective local search approach is presented and embedded in the DLHS algorithm to enhance the local searching ability. Computational experiments and comparisons show that the proposed DLHS algorithm generates better or competitive results than the existing hybrid genetic algorithm (HGA) and hybrid discrete particle swarm optimization (HDPSO) for the lot-streaming flow shop scheduling problem with total weighted earliness and tardiness criterion.     

Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective

This paper presents several search heuristics and their performance in batch scheduling of parallel, unrelated machines. Identical or similar jobs are typically processed in batches in order to decrease setup times and/or processing times. The problem accounts for allotting batched work parts into unrelated parallel machines, where each batch consists of a fixed number of jobs. Some batches may contain different jobs but all jobs within each batch should have an identical processing time and a common due date. Processing time of each job of a batch is determined according to the machine group as well as the batch group to which the job belongs. Major or minor setup times are required between two subsequent batches depending on batch sequence but are independent of machines. The objective of our study is to minimize the total weighted tardiness for the unrelated parallel machine scheduling. Four search heuristics are proposed to address the problem, namely (1) the earliest weighted due date, (2) the shortest weighted processing time, (3) the two-level batch scheduling heuristic, and (4) the simulated annealing method. These proposed local search heuristics are tested through computational experiments with data from dicing operations of a compound semiconductor manufacturing facility.     

基于改进ACO算法的印制电路板装配研究

引入带顺序相关切换时间的单机带权延期模型,研究印制电路板(PCB)装配中单生产线多板型的调度问题,使用改进的蚁群优化(ACO)算法对其进行求解。在改进算法中,使用带禁忌表的信息素更新策略防止算法过早收敛,以多线程方式实现局部搜索,通过路径池使局部搜索与蚁群进行交互和通信。测试结果表明,改进算法可以有效提高PCB装配效率,降低生产任务延期率。     

求解异构并行机调度问题的混合多目标教-学优化算法

以异构并行机调度问题为研究对象,考虑了一类以优化总加权完工时间和加权延误总和的调度问题。首先,基于问题描述构建了该问题的混合整数规划模型。其次,提出了混合多目标教-学优化算法。在算法设计中,结合问题的特点设计序列编码方法,并采用分解技术来实现多目标调度问题的求解。此外,该算法通过融合多种交叉算子来定义个体进化过程,并通过与变邻域搜索算法的混合来提升其优化效果。最后,给出了仿真实验与分析,测试结果验证了多目标教-学优化算法求解该调度问题的优越性。     

基于滚动时域优化的机场起降动态调度

为了减少作战时军用飞机实际起降时刻与计划起降时刻产生的偏差,提出一种基于滚动时域优化原理的动态机场起降调度策略,分析军用飞机起降过程中的时间窗口约束和尾流间隔约束。对进入每个预测窗口内的飞机队列,以加权提前/延误时间和最小作为目标函数,将军用飞机起降调度模型转换为带到达时间的单机加权E/T调度模型。设计一种针对自然数域的离散粒子群算法,并应用该算法进行模型求解。通过仿真实验确定了算法的参数,仿真结果说明了模型和算法的有效性。     

一种高效的三维轮廓曲线匹配算法

针对三维碎片自动拼接中的碎片匹配问题,提出一种高效的轮廓曲线匹配算法。用B-样条曲线表示三维空间曲线,并计算轮廓曲线上各个点的曲率、挠率和法矢,在匹配过程中,对轮廓特征点按其邻域曲面片进行分类,根据特征点类型标志及特征段之间的欧式距离对不同轮廓上的特征段进行相似性度量,再利用法矢对相似性较高的轮廓段进行可匹配性验证。实验结果证明该算法是稳定、高效的。     

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 study of hybrid evolutionary algorithms for single machine scheduling problem with sequence-dependent setup times

We present a systematic comparison of hybrid evolutionary algorithms (HEAs), which independently use six combinations of three crossover operators and two population updating strategies, for solving the single machine scheduling problem with sequence-dependent setup times. Experiments show the competitive performance of the combination of the linear order crossover operator and the similarity-and-quality based population updating strategy. Applying the selected HEA to solve 120 public benchmark instances of the single machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness widely used in the literature, we achieve highly competitive results compared with the exact algorithm and other state-of-the-art metaheuristic algorithms in the literature. Meanwhile, we apply the selected HEA in its original form to deal with the unweighted 64 public benchmark instances. Our HEA is able to improve the previous best known results for one instance and match the optimal or the best known results for the remaining 63 instances in a reasonable time.     

A particle swarm optimization for a fuzzy multi-objective unrelated parallel machines scheduling problem

This paper proposes a novel multi-objective model for an unrelated parallel machine scheduling problem considering inherent uncertainty in processing times and due dates. The problem is characterized by non-zero ready times, sequence and machine-dependent setup times, and secondary resource constraints for jobs. Each job can be processed only if its required machine and secondary resource (if any) are available at the same time. Finding optimal solution for this complex problem in a reasonable time using exact optimization tools is prohibitive. This paper presents an effective multi-objective particle swarm optimization (MOPSO) algorithm to find a good approximation of Pareto frontier where total weighted flow time, total weighted tardiness, and total machine load variation are to be minimized simultaneously. The proposed MOPSO exploits new selection regimes for preserving global as well as personal best solutions. Moreover, a generalized dominance concept in a fuzzy environment is employed to find locally Pareto-optimal frontier. Performance of the proposed MOPSO is compared against a conventional multi-objective particle swarm optimization (CMOPSO) algorithm over a number of randomly generated test problems. Statistical analyses based on the effect of each algorithm on each objective space show that the proposed MOPSO outperforms the CMOPSO in terms of quality, diversity and spacing metrics.     

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.     

混合离散人工蜂群算法求解含不相关并行机的分布式柔性流水线调度

研究每阶段含不相关并行机的分布式柔性流水线调度问题.考虑顺序相关准备时间和工件动态到达时间,以最小化总加权提前/拖期惩罚为目标建立整数规划模型,提出一种融合离散差分进化算法、变邻域下降算法和局域搜索的混合离散人工蜂群算法以获取近优解.该算法采用基于工厂-工件号的编码以及基于机器最早空闲时间的动态解码机制,通过随机规则和均衡分派策略生成初始工厂-工件序列群,在引领蜂阶段引入离散差分进化算法产生优质工厂-工件序列,在跟随蜂阶段利用变邻域下降算法在被选择序列附近继续搜索以得到邻域序列,在侦察蜂阶段设计基于关键/非关键工厂间插入的局域搜索提高算法搜索能力.通过仿真实验测试不同规模的算例,实验结果表明,所提出的混合离散人工蜂群算法表现出较好的求解性能.     

Heuristics for minimizing regular performance measures in unrelated parallel machine scheduling problems

This research compares the performance of various heuristics and one metaheuristic for unrelated parallel machine scheduling problems. The objective functions to be minimized are makespan, total weighted completion time, and total weighted tardiness. We use the least significant difference (LSD) test to identify robust heuristics that perform significantly better than others for a variety of parallel machine environments with these three performance measures. Computational results show that the proposed metaheuristic outperforms other existing heuristics for each of the three objectives when run with a parameter setting appropriate for the objective.     

A hybrid genetic algorithm for the single machine scheduling problem with sequence-dependent setup times

This paper presents a hybrid approach based on the integration between a genetic algorithm (GA) and concepts from constraint programming, multi-objective evolutionary algorithms and ant colony optimization for solving a scheduling problem. The main contributions are the integration of these concepts in a GA crossover operator. The proposed methodology is applied to a single machine scheduling problem with sequence-dependent setup times for the objective of minimizing the total tardiness. A sensitivity analysis of the hybrid approach is carried out to compare the performance of the GA and the hybrid genetic algorithm (HGA) approaches on different benchmarks from the literature. The numerical experiments demonstrate the HGA efficiency and effectiveness which generates solutions that approach those of the known reference sets and improves several lower bounds.     

求解置换流水线调度问题的改进萤火虫优化算法

针对最小化最大完成时间的置换流水线调度问题,提出了一种改进的离散萤火虫优化算法。在传统萤火虫优化算法的基础上,采用基于升序排序的随机键编码方式对萤火虫种群进行离散化处理,使用NEH算法对萤火虫种群进行初始化处理,结合遗传算法的交叉变异思想改进位置更新策略,采用个体变异方式解决孤立个体问题,提高算法的寻优能力。最后通过典型算例对改进算法进行仿真测试,实验结果表明该算法求解置换流水线调度问题时具备很强的寻优能力和鲁棒性,明显优于传统萤火虫优化算法和遗传算法,是解决置换流水线调度问题的一种有效算法。