Ant colony optimization for unrelated parallel machine scheduling

Meeting due dates is a major issue in most manufacturing systems, and one effective measure for due dates is total weighted tardiness. In this research, we consider an ant colony optimization (ACO) algorithm incorporating a number of new ideas (heuristic initial solution, machine reselection step, and local search procedure) to solve the problem of scheduling unrelated parallel machines to minimize total weighted tardiness. The problem is NP-hard in the strong sense, because the single machine case is already NP-hard in the strong sense. Computational results show that the proposed ACO algorithm outperforms other existing algorithms in terms of total weighted tardiness.     

Scheduling Jobs on Parallel Machines with Sequence-Dependent Family Set-up Times

This paper proposes an efficient heuristic to minimise the total weighted tardiness of a set of tasks with known processing times, due dates, weights and family types for parallel machines. A three-phase heuristic is presented to minimise total weighted tardiness. In the first phase, jobs are listed by the earliest due date and then divided into small job-sets according to a decision parameter. In the second phase, jobs are grouped by the due date within applicable families using apparent tardiness cost with set-up (ATCS), and the sequence of jobs within families is improved through the use of the tabu search method. In the third phase, jobs are allocated to machines using a threshold value and a look-ahead parameter. The comprehensive simulation results show that the proposed heuristic performs better than the ATCS and rolling horizon procedure at a significantly reduced total weighted tardiness.     

The tricriteria flowshop scheduling problem

Multicriteria flowshop scheduling problems have been one of the most attractive subjects in recent years. In the multicriteria flowshop scheduling literature, a very limited number of studies have been performed on problems which include a tardiness criterion. In this paper a multicriteria (tricriteria) two-machine flowshop scheduling problem with a tardiness criterion is tackled. The objective is to minimise a weighted sum of total completion time, total tardiness and makespan. An integer programming model is proposed for the problem which belongs to NP-hard class. The modified NEH (Nawaz, Enscore and Ham) algorithm, a tabu search-based heuristic method, random search and the EDD rule (the earliest due date rule) are used to solve problems with up to 2,500 jobs. A computational analysis is conducted to evaluate the performance of the heuristics. The analysis shows that the heuristics are quite efficient, and the performance of the tabu search based heuristic is the best of all in terms of solution quality.     

A due date density-based categorising heuristic for parallel machines scheduling

The effective management of shop floor resources is an important factor in achieving the goals of a manufacturing company. The need for effective scheduling is particularly strong in complex manufacturing environments. This paper presents an efficient due date density-based categorising heuristic to minimise the total weighted tardiness (TWT) of a set of tasks with known processing times, due dates, weights and sequence-dependent setup times for parallel machines scheduling. The proposed heuristic is composed of four phases. In the first phase, jobs are listed by the earliest due date (EDD). The second phase computes the due date gaps between listed jobs and categorises the jobs based on the due date density. In the third phase, the sequence of jobs is improved by a tabu search (TS) method. The fourth phase allocates each job to machines. The comprehensive simulation results show that the proposed heuristic performs better than other existing heuristics at a significantly reduced total weighted tardiness.     

Parallel processor scheduling for minimizing total weighted tardiness using ant colony optimization

In the modern business environment, meeting due dates and avoiding delay penalties are very important goals that can be accomplished by minimizing total weighted tardiness. We consider a scheduling problem in a system of parallel processors with the objective of minimizing total weighted tardiness. Our aim in the present work is to develop an efficient algorithm for solving the parallel processor problem as compared to the available heuristics in the literature and we propose the ant colony optimization approach for this problem. An extensive experimentation is conducted to evaluate the performance of the ACO approach on different problem sizes with the varied tardiness factors. Our experimentation shows that the proposed ant colony optimization algorithm is giving promising results compared to the best of the available heuristics.     

An intensive search evolutionary algorithm for single-machine total-weighted-tardiness scheduling problems

In this paper, an intensive search evolutionary algorithm is proposed to solve single machine total weighted tardiness scheduling problems. A specialised locally improved random swap mutation operator and an ordered crossover operator are used for evolution. The proposed algorithm starts with a pair of sequences: one generated by a greedy heuristic, namely, a backward phase heuristic acts as one parent, and a randomly generated sequence acts as the other. A computational experiment is conducted by applying the mutation operator on the backward phase sequence and the proposed algorithm with the same number of generations as the termination criteria. A total of 125 benchmark instances for sizes 40, 50 and 100 available in the OR library are solved and the results are compared with the available best-known results. It is observed that the proposed evolutionary algorithm provides better results than others .     

一种求解变速机调度问题的混合蚁群优化算法

针对一类变速机总加权拖期调度问题,提出一种混合蚁群优化算法.引人单机拖期调度问题中性能良好的修正预计完成时间的一种修改版本启发式规则,计算信息素初值,有利于算法跳出局部极值,并在局部搜索阶段,采用单亲遗传算法基因移位算子,有效优化当代最优解.通过均匀试验设计和统计分析,确定算法的关键参数组合,将算法应用于随机生成的不同规模的40个算例,并将其结果与同类文献中算法的优化结果进行对比分析.结果表明,在相同迭代次数下,混合算法优于对比算法.     

Minimizing total weighted tardiness on a batch-processing machine with non-agreeable release times and due dates

This study considers the scheduling problem observed in the burn-in operation of semiconductor final testing, where jobs are associated with release times, due dates, processing times, sizes, and non-agreeable release times and due dates. The burn-in oven is modeled as a batch-processing machine which can process a batch of several jobs as long as the total sizes of the jobs do not exceed the machine capacity and the processing time of a batch is equal to the longest time among all the jobs in the batch. Due to the importance of on-time delivery in semiconductor manufacturing, the objective measure of this problem is to minimize total weighted tardiness. We have formulated the scheduling problem into an integer linear programming model and empirically show its computational intractability. Due to the computational intractability, we propose a few simple greedy heuristic algorithms and meta-heuristic algorithm, simulated annealing (SA). A series of computational experiments are conducted to evaluate the performance of the proposed heuristic algorithms in comparison with exact solution on various small-size problem instances and in comparison with estimated optimal solution on various real-life large size problem instances. The computational results show that the SA algorithm, with initial solution obtained using our own proposed greedy heuristic algorithm, consistently finds a robust solution in a reasonable amount of computation time.     

互替机床提前/延期惩罚调度问题的启发式算法

对以作业提前或延期惩罚因素之和最小为目标函数的互替机床调度问题进行了描述，提出和阐述了一种四段式启发式算法，并通过大量不同规模的问题仿真对该算法进行了评价分析，结果表明该算法可行、有效。     

Solving a multi-objective no-wait flow shop scheduling problem with an immune algorithm

Flow shop scheduling problems have gained wide attention both in practical and academic fields. In this paper, we consider a multi-objective no-wait flow shop scheduling problem by minimizing the weighted mean completion time and weighted mean tardiness simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in a strong sense, an effective immune algorithm (IA) is proposed for searching locally the Pareto-optimal frontier for the given problem. To validate the performance of the proposed algorithm in terms of solution quality and diversity level, various test problems are carried out and the efficiency of the proposed algorithm, based on some comparison metrics, is compared with a prominent multi-objective genetic algorithm, i.e., strength Pareto evolutionary algorithm II (SPEA-II). The computational results show that the proposed IA outperforms the above genetic algorithm, especially for large problems.     

Job shop scheduling based on earliness and tardiness penalties with due dates and deadlines: an enhanced genetic algorithm

This paper studies a job shop scheduling problem with due dates and deadlines in the presence of tardiness and earliness penalties. Due dates are desired completion dates of jobs given by the customer, while deadlines are determined by the manufacturer based on customer due dates. Due dates can be violated at the cost of tardiness, whereas deadlines must be met and cannot be violated. The aforementioned scheduling problem, which is NP-hard, can be formulated with the objective function of minimizing the sum of weighted earliness and weighted tardiness of jobs subject to due dates and deadlines. In order to solve this problem, an enhanced genetic algorithm (EGA) is introduced in this paper. EGA utilizes an operation-based scheme to represent schedules as chromosomes. After the initial population of chromosomes is randomly generated, each chromosome is processed through a three-stage decoder, which first reduces tardiness based on due dates, second ensures deadlines are not violated, and finally reduces earliness based on due dates. After the population size is reached, EGA continues with selection, crossover, and mutation. The proposed algorithm is tested on 180 job shop scheduling problems of varying sizes and its performance is discussed.     

Scheduling in a two-machine flow-shop for earliness/tardiness under learning effect

In the literature, earliness/tardiness (E/T) problem was known as weighted absolute deviation problem, and both tardiness and earliness is very important performance criteria for scheduling problem. While total tardiness criteria provides adaptation for due date (ignoring results of earliness done jobs), it deals with only cost of tardiness. However this phenomenon has been started to change with just-in-time (JIT) production concept. On JIT production, earliness is as important as tardiness. The phenomenon of the learning effect has been extensively studied in many different areas of operational research. However, there have been a few studies in the general context of production scheduling such as flow-shop scheduling. This paper addresses the minimization of the total earliness/tardiness penalties under learning effects in a two-machine flow-shop scheduling problem. Jobs have a common due date. We present mathematical model to obtain an optimal schedule for a given job sequence. We also present heuristics that use genetic algorithm and tabu search, based on proposed properties. Furthermore, random search was used for showing the significance of the study by comparison purpose. A new set of benchmark problems is presented with the purpose of evaluating the heuristics. The experimental results show that the performance of proposed approach is quite well, especially for the instances of large size.     

A novel hybrid multi-objective shuffled frog-leaping algorithm for a bi-criteria permutation flow shop scheduling problem

This paper investigates a novel multi-objective model for a permutation flow shop scheduling problem that minimizes both the weighted mean earliness and the weighted mean tardiness. Since a flow shop scheduling problem has been proved to be NP-hard in a strong sense, a new hybrid multi-objective algorithm based on shuffled frog-leaping algorithm (SFLA) and variable neighborhood search (VNS) is devised to find Pareto optimal solutions for the given problem. To validate the performance of the proposed hybrid multi-objective shuffled frog-leaping algorithm (HMOSFLA) in terms of solution quality and diversity level, various test problems are examined. Further, the efficiency of the proposed algorithm, based on various salient metrics, is compared against two well-known multi-objective genetic algorithms: NSGA-II and SPEA-II. Our computational results suggest that the proposed HMOSFLA outperforms the two foregoing algorithms, especially for large-sized problems.     

用遗传算法求解一类不确定性作业车间调度问题

对具有不确定加工时间和交货期窗口的一类作业车间调度问题进行了研究.不确定加工时间用区间数来表示,以工件提前或者拖期遭受惩罚的可能性的总加权和最小作为优化目标.设计了带精英交叉策略的遗传算法求解此类问题.仿真实验验证了该算法的有效性.计算结果表明,该遗传算法有更快的收敛速度、更高的优化精度和更好的初值鲁棒性.     

[车间调度]新型蛙跳算法求解总能耗约束FJSP

针对具有总能耗约束且以总延迟时间为目标的柔性作业车间调度问题(job shop scheduling problem,FJSP),首先将该问题转化为具有总能耗和总延迟时间的两目标问题,从而有效地处理能耗约束,然后提出了一种新型蛙跳算法直接优化转化后的两目标FJSP,该算法利用模因组构建和模因组搜索的新策略以及模因组内最好解的强化搜索以提高求解质量。计算实验和分析结果表明,新型蛙跳算法对所研究的FJSP具有较强的搜索能力和优势。     

ACO-based multi-objective scheduling of parallel batch processing machines with advanced process control constraints

This research was motivated by a scheduling problem in the dry strip operations of a semiconductor wafer fabrication facility. The machines were modeled as parallel batch processing machines with incompatible job families and dynamic job arrivals, and constraints on the sequence-dependent setup time and the qual-run requirements of advanced process control. The optimization had multiple objectives, the total weighted tardiness (TWT) and makespan, to consider simultaneously. Since the problem is NP-hard, we used an Ant Colony Optimization (ACO) algorithm to achieve a satisfactory solution in a reasonable computation time. A variety of simulation experiments were run to choose ACO parameter values and to demonstrate the performance of the proposed method. The simulation results showed that the proposed ACO algorithm is superior to the common Apparent Tardiness Cost-Batched Apparent Tardiness Cost rule for minimizing the TWT and makespan. The arrival time distribution and the number of jobs strongly affected the ACO algorithm’s performance.     

考虑节能的改进多目标樽海鞘群算法TFT-LCD面板阵列制程调度问题

TFT-LCD面板生产的阵列制程是可重入混合流水车间调度问题,采用一种改进多目标樽海鞘群算法对其进行优化求解。构建以最大完工时间、总拖期时间和总耗能为优化目标的数学规划模型;针对该问题结构特点,对基本多目标樽海鞘群算法进行了一系列改进操作,包括基于升序排列的随机键编码、PS方法解码、基于Lévy飞行的领导者个体位置更新方式,以及外部档案中非支配个体的变邻域搜索操作,并采用田口方法进行算法参数设置;最后通过对基准算例的数值实验,将改进多目标樽海鞘群算法与基本多目标樽海鞘群算法、多目标粒子群优化算法、快速非支配排序遗传算法进行对比,实验结果表明了改进多目标樽海鞘群算法的有效性。     

A branch-and-bound parallel algorithm for single-machine total weighted tardiness problem

This paper presents the branch-and-bound algorithm for the single-machine total weighted tardiness problem. Among exact solution approaches, the branch-and-bound algorithm from Potts and Van Wassenhove solves problems of up to 40 jobs and the algorithm from Babu et al. for 50 jobs (not for all instances). We have taken advantage of the properties of permutation broken into blocks. These properties are much stronger than elimination criteria (Potts CN, Van Wassenhove LN, 1991. IIE Trans 23:346–354; Rinnoy Kan AGH, Lageweg BJ, Lenstra JK 1975 Minimizing total cost one-machine scheduling. Oper Res 26:908–972) applied so far and they allow us to eliminate many branches of the solution tree. Parallel implementation of the algorithm enables us to reduce computational time significantly and to solve larger problems. We have tested the algorithms on randomly generated instances (of up to 80 jobs) and benchmark instances taken from the OR-Library [4]. The solutions obtained have been compared with the results yielded by the best algorithms discussed in the literature. The results show that the proposed algorithm solves the problem instances with high accuracy in a very short time.     

A Tabu Search Algorithm for Single Machine Scheduling with Release Times,Due Dates,and Sequence-Dependent Set-up Times

In this paper, we present a tabu search algorithm that schedules N jobs to a single machine in order to minimise the maximum lateness of the jobs. The release times, due dates, and sequence-dependent set-up times of the jobs are assumed to exist. We modified the original tabu search method to be suitable for the scheduling problem. The proposed tabu search algorithm is composed of two parts: a MATCS (modified apparent tardiness cost with set-ups) rule for finding an efficient initial solution, and the tabu search method to seek a near optimal solution from the initial solution. The experimental results show that the tabu search algorithm obtains much better solutions more quickly than the RHP (rolling horizon procedure) heuristic suggested by Ovacik and Uzsoy.     

Bicriteria parallel flow line scheduling using hybrid population-based heuristics

The objective of this paper is to determine a schedule for parallel flow line with bicriteria objective of minimizing the total tardiness and earliness of jobs. An enhancement to its basic greedy randomized adaptive search procedure (GRASP) is used in conjunction with genetic algorithm (GA) and particle swarm optimization (PSO). The feasible solution of GRASP construction phase is used as initial population for both GA and PSO. A number of problems are solved, by varying the number of jobs, lines, and machines, using the hybrid PSO, hybrid GA, PSO, and GA-based methods and the results are compared.