求解分布式混合流水线调度问题的改进双层嵌套式遗传算法

针对分布式混合流水线生产的生产调度问题,模拟实际排产中的排产到线和排产到时的排产策略,提出了基于改进双层嵌套式遗传算法的两层优化模型。外层依据流水线分配平衡和准时交货等基本原则总体上解决生产订单在流水线之间的分配问题,内层以最小生产时间为主要目的求解流水线的生产订单生产次序问题。考虑到双层嵌套式遗传算法的时间复杂性,基于模糊逻辑理论设计了一种模糊控制器来动态调整遗传算子,并采用主动检测停止方法,提高算法效率。使用某空调工厂的实际生产数据验证了算法的可行性、计算结果的准确性及排产策略的有效性,为高级计划与排程(Advanced Planning and Scheduling,APS)中大规模复杂供应链调度问题提供了可借鉴的方法。     

A hybrid differential evolution method for permutation flow-shop scheduling

The permutation flow-shop scheduling problem (PFSSP) is a typical combinational optimization problem, which is of wide engineering background and has been proved to be strongly NP-hard. In this paper, a hybrid algorithm based on differential evolution (DE), named HDE, is proposed for the single-objective PFSSPs. Firstly, to make DE suitable for solving PFSSPs, a largest-order-value (LOV) rule is presented to convert the continuous values of individuals in DE to job permutations. Secondly, after the DE-based exploration, a simple but efficient local search, which is designed according to the PFSSPs’ landscape, is applied to emphasize exploitation. Thus, not only does the HDE apply the parallel evolution mechanism of DE to perform effective exploration (global search), but it also adopts problem-dependent local search methodology to adequately perform exploitation (local search). Based on the theory of finite Markov chains, the convergence property of the HDE is analyzed. Then, the HDE is extended to a multi-objective HDE (MHDE) to solve the multi-objective PFSSPs. Simulations and comparisons based on benchmarks for both single-objective and multi-objective PFSSPs are carried out, which show the effectiveness, efficiency, and robustness of the proposed HDE and MHDE.     

A novel hybrid genetic algorithm for the open shop scheduling problem

In this paper, a hybrid genetic algorithm is proposed for the open shop scheduling problem with the objective of minimizing the makespan. In the proposed algorithm, a specialized crossover operator is used that preserves the relative order of jobs on machines and a strategy is applied to prevent from searching redundant solutions in the mutation operator. Moreover, an iterative optimization heuristic is employed which uses the concept of randomized active schedules, a dispatching index based on the longest remaining processing time rule and a lower bound to further decrease the search space. Computational results show that the proposed algorithm outperforms other genetic algorithms and is very competitive with well-known metaheuristics available in the literature.     

多目标混合流水车间作业调度的演化算法

针对多目标条件下混合流水车间作业调度的优化问题,提出了一种在优化进程中能够动态调整适应度分配的演化算法。该算法采用矩阵编码描述多阶段并行机调度方案,结合问题的优化模型,对每一代Pareto解在各目标方向上的改善程度进行度量,进而通过多目标的选择性权重系数计算种群个体的适应度,以获得在改善指示方向上的选择压力。通过BENCHMARK问题测试和实际算例分析,表明新算法的性能优于现有的求解算法,特别是对于高维多目标优化问题,能够获得较高的演化收敛速度。     

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.     

A branch and bound procedure for the reentrant permutation flow-shop scheduling problem

This investigation considers a reentrant permutation flow-shop (RPFS) scheduling problem whose performance criterion is makespan. A reentrant flow-shop (RFS) refers to situations in which every job must be processed on machines in the order, M ₁, M ₂, ..., M _m , M ₁, M ₂, ..., M _m , ..., and M ₁, M ₂, ..., M _m . Every job can be decomposed into several layers each of which starts on M ₁ and finishes on M _m . In the RFS case, if the job ordering is the same on any machine at each layer, then no passing is said to be allowed, since no job is allowed to pass any former job. The RFS scheduling problem in which no passing is allowed, is called an RPFS problem. A branch and bound algorithm is presented and an example is also given to illustrate the solution procedure. To compare the proposed algorithm, a series of computational experiments are done on randomly generated test problems and the results show that the developed algorithm is efficient.     

求解混合流水车间调度问题的变量相关EDA算法

针对混合流水车间调度问题和分布估计算法的特点,提出将变量按工序分组,通过组内概率约束、组间概率耦合的方式建立混合流水车间调度问题变量间概率关系的新方法。对分布估计算法中的紧致遗传算法的种群产生和概率更新机制进行了改进,以解决流水车间调度问题等复杂问题。通过仿真实验、与其他算法比较以及在大规模生产实际问题中的应用,验证了该算法的有效性和鲁棒性。     

求解同顺序加工调度问题的一种启发式方法

为了更加有效地求解同顺序加工调度问题,分析了现有启发式求解方法,发现影响解的质量的主要因素是调整近似解的方法和初始解,其中调整近似解的方法对解的质量影响较大。对此,提出了一种新的启发式方法。新方法中的调整方法考虑了调整对最短总加工时间的影响,调整任意给定的近似解不会降低解的质量,经过迭代运算,可以逐步改善近似解;新方法采用了多起点策略,利用调整方法调整不同初始解,选取最好的近似解作为问题的解,从而减小了初始解对问题解的质量的影响。实验结果表明,这种方法是有效的。     

求解相同并行机混合流水线车间调度问题的分布估计算法

针对相同并行机混合流水车间调度问题,提出了一种有效的分布估计算法.针对基于排列的编码方式,设计了改进的启发式解码规则,进而提出了一种评价个体优劣的混合解码方式.建立了描述问题解空间分布的概率模型,通过对概率模型采样产生新个体,并基于优势种群更新概率模型的参数.通过基于标准测试集的数值仿真以及与已有算法的比较,验证了所提算法的有效性.     

Meta-heuristics to solve single-machine scheduling problem with sequence-dependent setup time and deteriorating jobs

This paper tackles the single-machine scheduling problem in which there are sequence-dependent setup times and deteriorating jobs. In this regard, a mathematical model has been formulated to minimize makespan (C _max). Afterwards, genetic and tabu search algorithms have been developed. Since the population diversity is a very important issue in preventing neighborhood search from trapping in a local optimum, some methods have been applied to genetic algorithm in order to maintain population diversity, and the final results show the effectiveness of these methods. The calibration of genetic algorithm parameters and operators is performed using design of experiments. Finally, several examples are produced to illustrate the proposed approach.     

一种求解Flow-Shop调度问题的混合量子进化算法

针对Flow—Shop调度问题,在量子进化算法的基础上,提出了一种求解置换流水车间调度问题的混合量子进化算法（HQEA）,融合了量子进化算法和经典遗传算法的优点,并提出了一种新的针对置换流水车间调度问题的解码方法和一种新的量子门更新旋转角策略,最后针对一系列典型置换流水车间调度问题进行了对比仿真。研究结果表明,所提出的混合量子进化算法HQEA具有良好的全局搜索能力和较快的收敛速度。     

A hybrid genetic algorithm to minimize makespan for the single batch machine dynamic scheduling problem

This paper considers a single batch machine dynamic scheduling problem, which is readily found in the burn-in operation of semiconductor manufacturing. The batch machine can process several jobs as a batch simultaneously, within the capacity limit of the machine, and the processing time is represented by the longest processing time among all jobs in a batch. For a single batch machine problem with arbitrary job release time, we proposed an improved algorithm (merge-split procedure) to refine the solution obtained by the LPT-BFF heuristic, and two versions of a hybrid genetic algorithm (GA) are introduced in this paper. Each version of the hybrid GA diversifies job sequences using the GA operators in stage 1, forms batches in stage 2, and finally sequence the batches in stage 3. The difference is that merge-split procedures are involved in the second version of the hybrid GA. Computational experiments showed that the hybrid GA would obtain satisfactory average solution quality and the merge-split procedures would be good at reinforcing the solution consistency of the hybrid GA.     

An effective hybrid genetic algorithm for the job shop scheduling problem

From the computational point of view, the job shop scheduling problem (JSP) is one of the most notoriously intractable NP-hard optimization problems. This paper applies an effective hybrid genetic algorithm for the JSP. We proposed three novel features for this algorithm to solve the JSP. Firstly, a new full active schedule (FAS) procedure based on the operation-based representation is presented to construct a schedule. After a schedule is obtained, a local search heuristic is applied to improve the solution. Secondly, a new crossover operator, called the precedence operation crossover (POX), is proposed for the operation-based representation, which can preserve the meaningful characteristics of the previous generation. Thirdly, in order to reduce the disruptive effects of genetic operators, the approach of an improved generation alteration model is introduced. The proposed approaches are tested on some standard instances and compared with other approaches. The superior results validate the effectiveness of the proposed algorithm.     

A TSP-GA multi-objective algorithm for flow-shop scheduling

A multi-objective evolutionary search algorithm using a travelling salesman algorithm and genetic algorithm for flow-shop scheduling is proposed in this paper. The initial sequence is obtained by solving the TSP. The initial population of the genetic algorithm is created with the help of a neighbourhood creation scheme known as a random insertion perturbation scheme, which uses the sequence obtained from TSP. The proposed algorithm uses a weighted sum of multiple objectives as a fitness function. The weights are randomly generated for each generation to enable a multi-directional search. The performance measures considered include minimising makespan, mean flow time and machine idle time. The performance of the proposed algorithm is demonstrated by applying it to benchmark problems available in the OR-Library.     

An enhanced estimation of distribution algorithm for solving hybrid flow-shop scheduling problem with identical parallel machines

In this paper, an enhanced estimation of distribution algorithm (EEDA) is proposed to solve the hybrid flow-shop scheduling problem with identical parallel machines to minimize makespan. To evaluate the individuals, some decoding rules including the improved permutation scheduling rule, the improved list scheduling rule and the backward scheduling rule are designed for the permutation-based encoding scheme, and then a hybrid decoding method is proposed. To describe the distribution of the solution space for the EEDA, a probability model is built and used to generate new individuals by sampling. To well trace the region with promising solutions, a mechanism is provided to update the model with the superior sub-population. To enhance the exploitation capability, multiple local search operators are incorporated in the framework of the EEDA. The influence of the parameter setting is investigated based on the Taguchi method of design-of-experiment. Extensive numerical testing results based on sets of the well-known benchmarks and the comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm.     

基于混合遗传算法的柔性作业车间调度研究

为更有效地求解柔性作业车间调度问题,提出一种混合遗传算法(蚁群-遗传算法)。在分层法的基础上,首先采用蚁群算法解决工艺路线选择问题,再通过遗传算法解决传统的作业车间调度问题。在混合遗传算法求解过程中,不断地在前期优化中获取调度知识,用于指导后期的优化过程。通过标准案例测试,验证了混合遗传算法对于解决柔性作业车间调度问题的有效性。     

An immune algorithm for hybrid flow shop scheduling problem with time lags and sequence-dependent setup times

This paper deals with hybrid flow shop scheduling problems considering time lags and sequence-dependent setup times which have wide application in real-world problems. Most of the researches on operations scheduling problems have ignored time lags. A mathematical model is presented which is capable of solving the small size of the considered problem in a reasonable time. Since these problems are strongly NP-hard, a meta-heuristic algorithm based on the immune algorithm is developed. The optimization criterion considered in this paper is the minimization of the makespan. Numerical experiments are used to evaluate the performance and effectiveness of the proposed algorithm. The results of the proposed algorithm are compared with the presented mathematical programming model and a benchmark algorithm. Computational results indicate that the proposed algorithm can produce near-optimal solutions in a short computational time. Moreover, it can be applied easily in real factory conditions and for large-sized problems.     

A hybrid genetic algorithm for integrated process planning and scheduling problem with precedence constraints

Process planning and scheduling are two important functions in a modern manufacturing system. Although integrating decisions related to these functions gives rise to a hard combinatorial problem, due to the impressive improvement in system performance which is resulted through this integration, developing effective methods to solve this problem is of great theoretical and practical importance. In this research, after formulating the integrated process planning and scheduling problem as a mathematical program, we propose a hybrid genetic algorithm (GA) for the problem. In the proposed algorithm, problem-specific genetic operators are designed to enhance the global search power of GA. Also, a local search procedure has been incorporated into the GA to improve the performance of the algorithm. The model considers precedence relations among job operations, based on which feasible process plans for each job can be represented implicitly. A novel neighborhood function, considering the constraints of a flexible job shop environment and nonlinear precedence relations among operations, is presented to speed up the local search process. In experimental study, the performance of the proposed algorithm has been evaluated based on a number of problems adopted from the literature. The experimental results demonstrate the efficiency of the proposed algorithm to find optimal or near-optimal solutions.     

An improved genetic algorithm for robust permutation flowshop scheduling

In order to deal with uncertainties, a robust schedule for M-machine permutation flowshop is proposed. The presented robust schedule is aimed to maximize the probability of ensuring that makespan will not exceed the expected completion time. An improved genetic algorithm (GA) with a new generation scheme is developed, which can preserve good characteristics of parents in the new generation. Experiments are performed to get robust schedules for well-known Car and Rec permutation flowshop problems, taken from OR library. The schedules obtained from the improved GA are compared with the schedules formed by well-known heuristic in literature. Computational results show that the permutation flowshop schedules obtained from improved GA are robust to produce an affirmative percentage increase in the probability of getting makespan less than expected completion time.     

基于改进遗传算法的柔性作业车间调度方法研究

针对柔性作业车间调度问题,提出了一种自适应的遗传机制,构造出自适应的适值函数定义方法,设计了相应的自适应选择、交叉和变异3种算子。为了解决同一工序的不同机器的负荷平衡,提出了表征机器加工能力的能力系数。通过轮换方法实现了相同工序不同机器之间的调度。仿真实验结果表明,该调度算法具有可行性。