A multi-objective genetic algorithm for scheduling in flow shops to minimize the makespan and total flow time of jobs

In this paper the problem of permutation flow shop scheduling with the objectives of minimizing the makespan and total flow time of jobs is considered. A Pareto-ranking based multi-objective genetic algorithm, called a Pareto genetic algorithm (GA) with an archive of non-dominated solutions subjected to a local search (PGA-ALS) is proposed. The proposed algorithm makes use of the principle of non-dominated sorting, coupled with the use of a metric for crowding distance being used as a secondary criterion. This approach is intended to alleviate the problem of genetic drift in GA methodology. In addition, the proposed genetic algorithm maintains an archive of non-dominated solutions that are being updated and improved through the implementation of local search techniques at the end of every generation. A relative evaluation of the proposed genetic algorithm and the existing best multi-objective algorithms for flow shop scheduling is carried by considering the benchmark flow shop scheduling problems. The non-dominated sets obtained from each of the existing algorithms and the proposed PGA-ALS algorithm are compared, and subsequently combined to obtain a net non-dominated front. It is found that most of the solutions in the net non-dominated front are yielded by the proposed PGA-ALS.     

结合混合进化算法和知识的多目标车间调度

提出了一种结合混合进化算法和知识的新型多目标车间调度方法,在有限的时间或迭代次数下可以得到更好的非支配Pareto解以服务于生产调度。由优化目标和属性归纳演绎法确定了知识挖掘的工件属性,通过优先级权重得到了规则初始种群。所提出的增减排序方法通过重新局部排序初始种群中工序的位置来克服优先级下工序不足或过饱和的问题。最后由一标准案例和非支配排序遗传算法-Ⅱ（NSGA-Ⅱ）混合模拟退火算法对所提调度方法进行了验证,得到的结果无论是优化目标值还是解集的分布在不同迭代次数和初始种群尺寸下都要优于传统随机进化方法。     

A simulated annealing algorithm to find approximate Pareto optimal solutions for the multi-objective facility layout problem

In this article, we consider the facility layout problem which combines the objective of minimization of the total material handling cost and the maximization of total closeness rating scores. Multi-objective optimization is the way to consider the two objectives at the same time. A simulated annealing (SA) algorithm is proposed to find the non-dominated solution (Pareto optimal) set approximately for the multi-objective facility layout problem we tackle. The Pareto optimal sets generated by the proposed algorithm was compared with the solutions of the previous algorithms for multi-objective facility layout problem. The results showed that the approximate Pareto optimal sets we have found include almost all the previously obtained results and many more approximate Pareto optimal solutions.     

多目标柔性作业车间调度决策精选机制研究

针对多目标柔性作业车间调度优化无法找到唯一最优解的问题，提出多目标遗传算法和层次分析法模糊综合评判的分阶段优化策略。提出优化阶段和精选阶段的优化任务，优化阶段选出一组Pareto解集，精选阶段从Pareto解集中选出最优解；在精选阶段运用层次分析法和模糊评判集成的策略精选调度决策。决策算例证明提出的方法是可行的，可很好地帮助决策者选择出一个最满意的解。     

Pareto-based discrete artificial bee colony algorithm for multi-objective flexible job shop scheduling problems

This paper presents a hybrid Pareto-based discrete artificial bee colony algorithm for solving the multi-objective flexible job shop scheduling problem. In the hybrid algorithm, each solution corresponds to a food source, which composes of two components, i.e., the routing component and the scheduling component. Each component is filled with discrete values. A crossover operator is developed for the employed bees to learn valuable information from each other. An external Pareto archive set is designed to record the non-dominated solutions found so far. A fast Pareto set update function is introduced in the algorithm. Several local search approaches are designed to balance the exploration and exploitation capability of the algorithm. Experimental results on the well-known benchmark instances and comparisons with other recently published algorithms show the efficiency and effectiveness of the proposed algorithm.     

Hybrid discrete particle swarm optimization for multi-objective flexible job-shop scheduling problem

Flexible job-shop problem has been widely addressed in literature. Due to its complexity, it is still under consideration for research. This paper addresses flexible job-shop scheduling problem (FJSP) with three objectives to be minimized simultaneously: makespan, maximal machine workload, and total workload. Due to the discrete nature of the FJSP problem, conventional particle swarm optimization (PSO) fails to address this problem and therefore, a variant of PSO for discrete problems is presented. A hybrid discrete particle swarm optimization (DPSO) and simulated annealing (SA) algorithm is proposed to identify an approximation of the Pareto front for FJSP. In the proposed hybrid algorithm, DPSO is significant for global search and SA is used for local search. Furthermore, Pareto ranking and crowding distance method are incorporated to identify the fitness of particles in the proposed algorithm. The displacement of particles is redefined and a new strategy is presented to retain all non-dominated solutions during iterations. In the presented algorithm, pbest of particles are used to store the fixed number of non-dominated solutions instead of using an external archive. Experiments are performed to identify the performance of the proposed algorithm compared to some famous algorithms in literature. Two benchmark sets are presented to study the efficiency of the proposed algorithm. Computational results indicate that the proposed algorithm is significant in terms of the number and quality of non-dominated solutions compared to other algorithms in the literature.     

A genetic algorithmic approach to multi-objective scheduling in a kanban-controlled flowshop with intermediate buffer and transport constraints

In this paper, we consider the problem of extended permutation flowshop scheduling with the intermediate buffers. The Kanban flowshop problem considered involves dual-blocking by both part type and queue size acting on machines, as well as on material handling. The objectives considered in this study include the minimization of mean completion time of containers, mean completion time of part types, and the standard deviation of mean completion time of part types. An attempt is made to solve the multi-objective problem by using a proposed genetic algorithm, called the “non-dominated and normalized distanceranked sorting multi-objective genetic algorithm” (NDSMGA). In order to evaluate the NDSMGA, we have made use of randomly generated flowshop scheduling problems with input and output buffer constraints in the flowshop. The non-dominated solutions for these problems are obtained from each of the existing methods, namely multi-objective genetic local search (MOGLS), elitist non-dominated sorting genetic algorithm (ENGA), gradual priority weighting genetic algorithm (GPWGA), modified MOGLS, and the NDSMGA. These non-dominated solutions are combined to obtain a net non-dominated solution set for a given problem. Contribution in terms of number of solutions to the net non-dominated solution set from each of these algorithms is tabulated, and the results reveal that a substantial number of non-dominated solutions are contributed by the NDSMGA.     

A genetic algorithmic approach to multi-objective scheduling in a Kanban-controlled flowshop with intermediate buffer and transport constraints

In this paper, we consider the problem of extended permutation flowshop scheduling with the intermediate buffers. The Kanban flowshop problem considered involves dual-blocking by both part type and queue size acting on machines, as well as on material handling. The objectives considered in this study include the minimization of mean completion time of containers, mean completion time of part types, and the standard deviation of mean completion time of part types. An attempt is made to solve the multi-objective problem by using a proposed genetic algorithm, called the “non-dominated and normalized distance-ranked sorting multi-objective genetic algorithm” (NDSMGA). In order to evaluate the NDSMGA, we have made use of randomly generated flowshop scheduling problems with input and output buffer constraints in the flowshop. The non-dominated solutions for these problems are obtained from each of the existing methods, namely multi-objective genetic local search (MOGLS), elitist non-dominated sorting genetic algorithm (ENGA), gradual priority weighting genetic algorithm (GPWGA), modified MOGLS, and the NDSMGA. These non-dominated solutions are combined to obtain a net non-dominated solution set for a given problem. Contribution in terms of number of solutions to the net non-dominated solution set from each of these algorithms is tabulated, and the results reveal that a substantial number of non-dominated solutions are contributed by the NDSMGA.     

Multi-objective artificial bee colony for interval job shop scheduling with flexible maintenance

In scheduling problem with uncertainty, flexible preventive maintenance (PM) and multiple objectives are seldom investigated. In this study, interval job shop scheduling problem with non-resumable jobs and flexible maintenance is considered and an effective multi-objective artificial bee colony (MOABC) is proposed, in which an effective decoding procedure is used to build the schedule and handle PM operation. The objective is to minimize interval makespan and a newly defined objective called total interval tardiness. In each cycle, a dominance-based greedy principle is adopted, a dominance-based tournament is utilized to choose solution for onlooker bee, and the non-dominated ranking is applied to update the non-dominated set. A solution with the highest rank is replaced with a non-dominated solution every certain cycle. Computational results show the good performance of MOABC on the considered problem.     

解决车间调度问题的改进模拟退火算法

结合作业车间调度问题的关键路径理论,设计了一种具有多次退火过程的调度算法。该算法利用记忆表记录下降过程中的平衡点,当一次退火过程结束后,从表中取出各平衡点的温度、状态和抽样长度重新开始退火过程,直到记忆表为空。仿真结果表明该算法在求解质量和求解效率方面均有优势。     

Developing two multi-objective evolutionary algorithms for the multi-objective flexible job shop scheduling problem

The aim of this paper is to study multi-objective flexible job shop scheduling problem (MOFJSP). Flexible job shop scheduling problem is a modified version of job shop scheduling problem (JSP) in which an operation is allowed to be processed by any machine from a given set of capable machines. The objectives that are considered in this study are makespan, critical machine work load, and total work load of machines. In the literature of the MOFJSP, since this problem is known as an NP-hard problem, most of the studies have developed metaheuristic algorithms to solve it. Most of them have integrated their objective functions and used an integrated single-objective metaheuristic algorithm though. In this study, two new version of multi-objective evolutionary algorithms including non-dominated sorting genetic algorithm and non-dominated ranking genetic algorithm are adapted for MOFJSP. These algorithms use new multi-objective Pareto-based modules instead of multi-criteria concepts to guide their process. Another contribution of this paper is introducing of famous metrics of the multi-objective evaluation to literature of the MOFJSP. A new measure is also proposed. Finally, through using numerous test problems, calculating a number of measures, performing different statistical tests, and plotting different types of figures, it is shown that proposed algorithms are at least as good as literature’s algorithm.     

多目标置换流水车间调度的改进食物链算法

针对目标函数为最小化最大完成时间和总延迟时间的多目标置换流水车间调度问题,提出了一种改进的食物链算法。该算法在食物链算法的基础上,引入基于Pareto最优解的快速非支配性排序和个体拥挤距离计算,增强了算法的寻优性能。对OR-Library三个典型算例的优化比较表明,该算法在解的质量上明显超越NSGA-Ⅱ算法。     

Pareto archive particle swarm optimization for multi-objective fuzzy job shop scheduling problems

This paper addresses multi-objective job shop scheduling problems with fuzzy processing time and due-date in such a way to provide the decision-maker with a group of Pareto optimal solutions. A new priority rule-based representation method is proposed and the problems are converted into continuous optimization ones to handle the problems by using particle swarm optimization. The conversion is implemented by constructing the corresponding relationship between real vector and the chromosome obtained with the new representation method. Pareto archive particle swarm optimization is proposed, in which the global best position selection is combined with the crowding measure-based archive maintenance, and the inclusion of mutation into the proposed algorithm is considered. The proposed algorithm is applied to eight benchmark problems for the following objectives: the minimum agreement index, the maximum fuzzy completion time and the mean fuzzy completion time. Computational results demonstrate that the proposal algorithm has a promising advantage in fuzzy job shop scheduling.     

A conflict-based priority dispatching rule and operation-based approaches to job shops

Job shop scheduling (JSS) problems consist of a set of machines and a collection of jobs to be scheduled. Each job consists of several operations with a specified processing order. In this paper, a job shop model problem is scheduled with the help of the Giffler and Thompson algorithm using a priority dispatching rule (PDR). A conflict based PDR is used to schedule the job shop model by using Genetic Algorithms (GAs). An iterative method is applied to the job model to find the optimal conflict-based PDR order and the operation sequence. The same job shop model is also scheduled based on an operation using simulated annealing (SA) and hybrid simulated annealing (HSA). A makespan of the job model is used as an objective. These four methods are considered as different solutions for each problem. A two-way analysis of variance (ANOVA) is applied to test its significance.     

An efficient bi-objective heuristic for scheduling of hybrid flow shops

This paper considers the problem of scheduling n independent jobs in hybrid flow shop environment with sequence-dependent setup times to minimize the makespan and total tardiness. For the optimization problem, an algorithm namely; bi-objective heuristic (BOH) is proposed for searching Pareto-optimal frontier. The aim of the proposed algorithm is to generate a good approximation of the set of efficient solutions. The BOH procedure initiates by generating a seed sequence. Since the output results are strongly dependent on the initial solution and in order to increase the quality of output results algorithm, we have considered how the generation of seed sequence with random way and particular sequencing rules. Two methods named Euclidean distance and percent error have been proposed to compare non-dominated solution sets obtain of each seed sequence. It is perceived from these methods that the generation of seed sequence using earliest due date rule is more effective. Then, the performance of the proposed BOH is compared with a simulated annealing proposed in the literature and a VNS heuristic on a set of test problems. The data envelopment analysis is used to evaluate the performance of approximation methods. From the results obtained, it can be seen that the proposed algorithm is efficient and effective.     

A Pareto evolutionary algorithm approach to bi-objective unrelated parallel machine scheduling problems

This paper addresses the unrelated parallel machine scheduling problem with job sequence- and machine-dependent setup times. The preemption of jobs is not permitted, and the optimization criteria are to simultaneously minimize total weighted flow time and total weighted tardiness. The problem has applications in industries such as TFT-LCD, automobile, and textile manufactures. In this study, a Pareto evolutionary approach is proposed to solve the bi-objective scheduling problem. The performance of this approach using different encoding and decoding schemes is evaluated and is compared with that of two multi-objective simulated annealing algorithms via a set of instances generated by a method in the literature. The experimental results indicate that the Pareto evolutionary approach using random key representation and weighted bipartite matching optimization method outperforms the other algorithms in terms of closeness metric, based on similar computation times. Additionally, although the proposed method does not provide the best distribution in terms of diversity metric, it found most of the reference solutions.     

A general flow shop scheduling problem with consideration of position-based learning effect and multiple availability constraints

In this paper, a more general version of the flow shop scheduling problem with the objective of minimizing the total flow time is investigated. In order to get closer to the actual conditions of the problem, some realistic assumptions including non-permutation scheduling, learning effect, multiple availability constraints, and release times are considered. It is assumed that the real processing time of each job on a machine depends on the position of that job in the sequence, and after processing a specified number of jobs at each machine, an unavailability period is occurring because of maintenance activities. Moreover, it is supposed that each job may not be ready for processing at time zero and may have a release time. According to these assumptions, a new mixed integer linear programming (MILP) model is proposed to formulate the problem. Due to the high complexity of the problem, a heuristic method and a simulated annealing algorithm are presented to find the nearly optimal solutions for medium- and large-sized problems. To obtain better and more robust solutions, the Taguchi method is used in order to calibrate the simulated annealing algorithm parameters. Finally, the computational results are provided for evaluating the performance and effectiveness of the proposed solution methods.     

Bi-objective hybrid flow shop scheduling: a new local search

In this paper, we have considered the bi-objective hybrid flow shop scheduling problem with the objectives of minimizing makespan and minimizing total tardiness. The problem is, however, a combinatorial optimization problem which is too difficult to be solved optimally, and hence, heuristics are used to obtain good solutions in a reasonable time. On the other hand, local search is a method for solving computationally hard optimization problems. Hence, we introduce a novel bi-objective local search algorithm (BOLS) to solve the problem efficiently. This local search can perform an effective search in three phases. In the initial phase, the assigned job set of a machine is moved to other machines. In the second phase, the order of jobs is changed for a machine. Finally, in phase 3, a process is done to change the assigned job set of a machine and order of jobs for a machine simultaneously. A measure of performance in literature namely free disposal hull approach and a new technique proposed by authors called “triangle method” have been used to evaluate the quality of the obtained solutions. The experimental results of the comparison between the proposed algorithm and several effective algorithms show that the BOLS is attractive for solving the bi-objective scheduling problem.     

基于多目标遗传算法的高频磁致伸缩换能器优化设计

磁致伸缩换能器在高频激励下存在铁心涡流损耗大、磁场分布不均匀、电磁转化效率低等问题,需要从换能器本体优化设计方面寻求解决。首先对换能器的线圈高度和磁轭回路结构进行仿真分析以初步确定磁路结构;然后基于非支配排序遗传算法对换能器提出了一个整体的多目标优化设计模型,该模型以增大磁致伸缩棒内磁场强度、提高棒内的磁场分布均匀度和减少换能器高频损耗为优化目标,引入规范化排序和熵权法对该优化方法得到的Pareto前沿解进行决策支持,筛选一组最优设计方案;最后对该最优解进行仿真分析,磁场分布和数值计算结果验证了该优化方法的有效性,根据优化结果制作了一台换能器样机,样机输出特性的测试结果表明了优化设计方法的可行性。     

一种基于改进遗传算法的车间调度问题研究

作业车间调度是一类求解较困难的组合优化问题,在考虑遗传算法早熟收敛问题结合模拟退火算法局部最优时能概率性跳出的特性,该特性最终使算法能够趋于全局最优。在此基础上,将遗传算法和模拟退火算法相结合,提出了一种基于遗传和模拟退火的混合算法,该算法将模拟退火算法赋予搜索过程一种时变性融入其中,具有明显的概率跳跃性。同时。通过选取Brandimarte基准问题和经典的Benchmarks基准问题进行分析,并应用实例对该算法进行了仿真研究。该结果表明,通过模拟退火算法与遗产算法相集合,可以使计算的收敛精度明显提高,是行之有效的,与传统的算法相比较,有较明显的优越性。