Estimation of Optimum Genetic Control Parameters for Job Shop Scheduling

Genetic algorithms (GA) have demonstrated considerable success in providing good solutions to many non-polynomial hard optimization problems. GAs are applied for identifying efficient solutions for a set of numerical optimization problems. Job shop scheduling (JSS) has earned a reputation for being difficult to solve. Many workers have used various values of genetic parameters. This paper attempts to tune the control parameters for efficiency, that are used to acceleate the genetic algorithm (applied to JSS) to converge on an optimal solution. The genetic parameters, namely, number of generations, probability of crossover, probability of mutation, are optimized relating to the size of problems. The results are validated in job shop scheduling problems. The results indicate that by using an appropriate range of parameters, the genetic algorithm is able to find an optimal solution faster. RID=" ID=" <E5>Correspondence and offprint requests to</E5>: Dr S. G. Ponnambalam, Department of Production Engineering, Regional Engineering College, Tiruchirapalli, 620 015, India. E-mail: pons&commat;rect.ernet.in     

The ordinal optimisation of genetic control parameters for flow shop scheduling

Genetic algorithms (GAs) have been widely applied for many non-polynomial hard optimisation problems, such as flow shop and job shop scheduling. It is well known that the efficiency and effectiveness of a GA is highly depend on its control parameters, but setting suitable parameters often involves tedious trial and error. Currently, setting optimal parameters is still a substantial problem and is one of the most important and promising areas for GAs. In this paper, the determination of optimal GA control parameters with limited computational effort and simulation replication constraints, namely, population size, crossover and mutation probabilities, is firstly formulated as a stochastic optimisation problem. Then, the ordinal optimisation (OO) and the optimal computing budget allocation (OCBA) are applied to select the optimal GA control parameters, thereby providing a reasonable performance evaluation for hard flow shop scheduling problems. The effectiveness of the methodology is demonstrated by simulation results based on benchmarks.     

Ordinal optimisation of genetic control parameters for flow shop scheduling

Genetic algorithm (GA) has been widely applied to many non-polynomial hard optimisation problems, such as flow shop and job shop scheduling. It is well known that the efficiency and effectiveness of GA highly depend on its control parameters, but even setting suitable parameters often suffers from tedious trial and error. Currently, setting optimal parameters is still an open problem and one of the most important and promising areas for GA. In this paper, the determination of optimal GA control parameters with limited computational effort and total simulation replication constraint, namely, population size, crossover and mutation probabilities, is firstly formulated as a stochastic optimisation problem. Ordinal optimisation and optimal computing budget allocation are then applied to select the optimal GA control parameters while providing reasonable performance evaluation for hard flow shop scheduling problems. Lastly the effectiveness of the methodology is demonstrated by simulation results based on benchmarks.     

Two-machine, no-wait job shop problem with separable setup times and single-server constraints

No-wait job shop scheduling problems refer to the set of problems in which a number of jobs are available for processing on a number of machines in a job shop context with the added constraint that there should be no waiting time between consecutive operations of the jobs. In this paper, a two-machine, no-wait job shop problem with separable setup times and a single-server constraint is considered. The considered performance measure is the makespan. This problem is strongly NP-hard. A mathematical model of the problem is developed and a number of propositions are proven for the special cases. Moreover, a genetic algorithm is proposed in this paper to find the optimal (or near-optimal) solutions. In order to evaluate the developed algorithm, a number of small instances are solved to optimality using the developed mathematical model. The proposed algorithm is able to find the optimal solution of all of these cases. For larger instances, the developed algorithm has been compared with the 2-opt algorithm as well as a proposed lower bound. Computational results show the efficiency of the proposed algorithm in generating good quality solutions compared to the developed lower bounds and 2-opt algorithm.     

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.     

Flexible job shop scheduling with tabu search algorithms

This paper presents a tabu search algorithm that solves the flexible job shop scheduling problem to minimize the makespan time. As a context for solving sequencing and scheduling problems, the flexible job shop model is highly complicated. Alternative operation sequences and sequence-dependent setups are two important factors that frequently appear in various manufacturing environments and in project scheduling. In this paper, we present a model for a flexible job shop scheduling problem while considering those factors simultaneously. The purpose of this paper is to minimize the makespan time and to find the best sequence of operations and the best choice of machine alternatives, simultaneously. The proposed tabu search algorithm is composed of two parts: a procedure that searches for the best sequence of job operations, and a procedure that finds the best choice of machine alternatives. Randomly generated test problems are used to evaluate the performance of the proposed algorithm. Results of the algorithm are compared with the optimal solution using a mathematical model solved by the traditional optimization technique (the branch and bound method). After modeling the scheduling problem, the model is verified and validated. Then the computational results are presented. Computational results indicate that the proposed algorithm can produce optimal solutions in a short computational time for small and medium sized problems. Moreover, it can be applied easily in real factory conditions and for large size problems. The proposed algorithm should thus be useful to both practitioners and researchers.     

Optimization method with large leap steps for job shop scheduling

Local search methods have the characteristic of obtaining decent solution with short or acceptable time for job shop scheduling problems. They improve solution by searching iteratively neighbors of initial solution. But, they tend to get trapped in local optimal solutions, usually far away from the global optimal solution. Simulated annealing methods try to improve on this by accepting uphill moves depending on a decreasing probability controlled by the temperature parameter. But, at small temperatures, they also tend to get stuck in valleys of the cost function. In this paper, we proposed an optimization method with large leap steps. The large leap steps of the optimization method allow one to leave these valleys even at small temperatures. Experiments on some job shop scheduling benchmark problems demonstrated the effectiveness and efficiency of the optimization method with large leap steps.     

Solving job shop scheduling problems using artificial immune system

The n-job, m-machine job shop scheduling (JSS) problem is one of the general production scheduling problems. Many existing heuristics give solutions for small size problems with near optimal solutions. This paper deals with the criterion of makespan minimization for the job shop scheduling of different size problems. The proposed computational method of artificial immune system algorithm (AIS) is used for finding optimal makespan values of different size problems. The artificial immune system algorithm is tested with 130 benchmark problems [10 (ORB1-ORB5 & ARZ5-ARZ9), 40 (LA01-LA40) and 80 (TA01-TA80)]. The results show that the AIS algorithm is an efficient and effective algorithm which gives better results than the Tabu search shifting bottleneck procedure (TSSB) as well as the best solution of shifting bottleneck procedure ( SB-GLS1 ) of Balas and Vazacopoulos.     

Determining optimal combination of genetic operators for flow shop scheduling

Genetic algorithms (GAs) have gained wide research and applications in production scheduling fields, but the efficiency and effectiveness of a GA significantly depend on its parameters and operators. In contrast to the rich research on determination of optimal and adaptive parameters, little research has been done on determining optimal combination of genetic operators. Different from the traditional way by trial and error, this paper presents a novel and systematical approach based on ordinal optimisation (OO) and optimal computing budget allocation (OCBA) technique to determine optimal combination of genetic operators for flow shop scheduling problems. Simulation results show that the proposed methodology is able to determine optimal combination of genetic operators and simultaneously to provide a good solution with reasonable performance evaluation for scheduling problem.     

A class of hypothesis-test-based genetic algorithms for flow shop scheduling with stochastic processing time

As an important optimisation problem with a strong engineering background, stochastic flow shop scheduling with uncertain processing time is difficult because of inaccurate objective estimation, huge search space, and multiple local minima, especially NP-hardness. As an effective meta-heuristic, genetic algorithms (GAs) have been widely studied and applied in scheduling fields, but so far seldom for stochastic cases. In this paper, a hypothesis-test method, an effective methodology in statistics, is employed and incorporated into a GA to solve the stochastic flow shop scheduling problem and to avoid premature convergence of the GA. The proposed approach is based on statistical performance and a hypothesis test. It not only preserves the global search ability of a GA, but it can also reduce repeated searches for those solutions with similar performance in a statistical sense so as to enhance population diversity and achieve better results. Simulation results based on some benchmarks demonstrate the feasibility and effectiveness of the proposed method by comparison with traditional GAs. The effects of some parameters on the performance of the proposed algorithms are also discussed .     

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.     

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.     

Pareto archived simulated annealing for job shop scheduling with multiple objectives

In this paper, the job shop scheduling problem is studied with the objectives of minimizing the makespan and the mean flow time of jobs. The simultaneous consideration of these objectives is the multi-objective optimization problem under study. A metaheuristic procedure based on the simulated annealing algorithm called Pareto archived simulated annealing (PASA) is proposed to discover non-dominated solution sets for the job shop scheduling problems. The seed solution is generated randomly. A new perturbation mechanism called segment-random insertion (SRI) scheme is used to generate a set of neighbourhood solutions to the current solution. The PASA searches for the non-dominated set of solutions based on the Pareto dominance or through the implementation of a simple probability function. The performance of the proposed algorithm is evaluated by solving benchmark job shop scheduling problem instances provided by the OR-library. The results obtained are evaluated in terms of the number of non-dominated schedules generated by the algorithm and the proximity of the obtained non-dominated front to the Pareto front.     

A swarm optimization approach for flexible flow shop scheduling with multiprocessor tasks

In simple flow shop problems, each machine operation center includes just one machine. If at least one machine center includes more than one machine, the scheduling problem becomes a flexible flow shop problem (FFSP). Flexible flow shops are thus generalization of simple flow shops. Flexible flow shop scheduling problems have a special structure combining some elements of both the flow shop and the parallel machine scheduling problems. FFSP can be stated as finding a schedule for a general task graph to execute on a multiprocessor system so that the schedule length can be minimized. FFSP is known to be NP-hard. In this study, we present a particle swarm optimization (PSO) algorithm to solve FFSP. PSO is an effective algorithm which gives quality solutions in a reasonable computational time and consists of less numbers parameters as compared to the other evolutionary metaheuristics. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast towards near-optimal solution and hence reduce computational efforts further. The performance of schedules is evaluated in terms of total completion time or makespan (C_max). The results are presented in terms of percentage deviation (PD) of the solution from the lower bound. The results are compared with different versions of genetic algorithm (GA) used for the purpose from open literature. The results indicate that the proposed PSO algorithm is quite effective in reducing makespan because average PD is observed as 2.961, whereas GA results in average percentage deviation of 3.559. Finally, influence of various PSO parameters on solution quality has been investigated.     

Genetic ordinal optimisation for stochastic flow shop scheduling

Stochastic flow shop scheduling is a typical and widely studied NP-hard stochastic optimisation problem with strong industrial roots. However, due to inaccurate estimation of objective values, NP-hardness and a limited computing budget, it is generally hard to solve such stochastic optimisation problems effectively and efficiently. Based on the idea of order comparison and goal softening, ordinal optimisation (OO) has been widely applied for stochastic optimisation. In this paper, OO and optimal computing budget allocation (OCBA) as well as a genetic algorithm (GA) are reasonably hybridised to propose an effective genetic ordinal optimisation (GOO) approach for flow shop scheduling with stochastic processing times. In GOO, limited computing effort can be intelligently allocated by OCBA to provide reliable and robust evaluation and identification of good solutions in a population, and the solution space can be well explored by an order-based evolutionary genetic search with the good solutions identified by OCBA. Simulation results based on benchmarks demonstrate the effectiveness of the GOO by comparison with traditional methods. Moreover, the effects of some parameters on the optimisation performance are discussed.     

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。     

[车间调度]并行多机开放车间调度问题的模型与算法

发光二极管制造过程中,晶粒分类拣选工序的调度问题是典型的并行多机开放车间调度问题,属于NP-hard问题。研究了该调度问题以最小化总加权完工时间为目标的求解模型与算法。根据问题特性构建了可获得最优解的混合整数规划模型,并设计了同时考虑质量与求解效率的启发式算法和改进粒子群优化算法。仿真结果显示,启发式算法和改进粒子群优化算法都能在合理的时间内迅速有效地获得较佳的调度解。     

Genetic algorithms for minimizing makespan in a flow shop with two capacitated batch processing machines

This paper considers a flow shop with two batch processing machines. The processing times of the job and their sizes are given. The batch processing machines can process multiple jobs simultaneously in a batch as long as the total size of all the jobs in a batch does not exceed its capacity. When the jobs are grouped into batches, the processing time of the batch is defined by the longest processing job in the batch. Batch processing machines are expensive and a bottleneck. Consequently, the objective is to minimize the makespan (or maximize the machine utilization). The scheduling problem under study is NP-hard, hence, a genetic algorithm (GA) is proposed. The effectiveness (in terms of solution quality and run time) of the GA approach is compared with a simulated annealing approach, a heuristic, and a commercial solver which was used to solve a mixed-integer formulation of the problem. Experimental study indicates that the GA approach outperforms the other approaches by reporting better solution.     

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.     

具有前成组约束的两阶段柔性流水车间的启发式算法

以模具加工车间为背景,分析具有前成组约束的两阶段柔性流水车间的特点,在对前成组约束进行定义和数学描述的基础上,以最少化最大完工时间为目标,建立具有前成组约束的、工件批量到达的两阶段柔性流水车间调度问题的数学模型,并且在第一阶段由两个成组加工单元构成;接着针对这一模型,提出一种启发式求解算法H′;运用数学分析的手段,给出该算法优化结果的一个下界;设计大量的实例测试集,将启发式算法H′与其他三种改造后的经典启发式算法进行性能比较,不仅验证启发式算法H′的有效性,而且还发现随着任务规模的增大,启发式算法H′的优越性更加明显,这一结论对H′算法在模具加工车间调度上的应用具有重要意义。