A genetic algorithm application using fuzzy processing times in non-identical parallel machine scheduling problem

There are many scheduling problems which are NP-hard in the literature. Several heuristics and dispatching rules are proposed to solve such hard combinatorial optimization problems. Genetic algorithms (GA) have shown great advantages in solving the combinatorial optimization problems in view of its characteristic that has high efficiency and that is fit for practical application [1]. Two different scale numerical examples demonstrate the genetic algorithm proposed is efficient and fit for larger scale identical parallel machine scheduling problem for minimizing the makespan. But, even though it is a common problem in the industry, only a small number of studies deal with non-identical parallel machines. In this article, a kind of genetic algorithm based on machine code for minimizing the processing times in non-identical machine scheduling problem is presented. Also triangular fuzzy processing times are used in order to adapt the GA to non-identical parallel machine scheduling problem in the paper. Fuzzy systems are excellent tools for representing heuristic, commonsense rules. That is why we try to use fuzzy systems in this study.     

基于递阶遗传算法的并行多机调度优化

针对最小化完工时间的等同和非等同并行多机调度一类问题，提出了一种递阶遗传算法。该算法根据问题的特点，采用一种递阶编码方案，此编码与调度方案一一对应。用递阶遗传算法优化并行多机调度不需设计专门的遗传算子，操作简单。计算结果表明，递阶遗传算法是有效的，能适用于大规模等同和非等同并行多机调度问题。     

用并行遗传算法解决带约束并行多机调度问题

遗传算法是一种全局优化的数值计算方法,它存在自然并行性,本文提出了一种解带约束并行多机调度问题的主从式控制网络并行遗传算法,并在PVM环境下实现。计算结果表明,并行遗传算法是有效的,且能适用于大规模并行多机调度问题。     

用并行遗传算法解决带约束并行多机调度问题

遗传算法是一种全局优化的数值计算方法。它存在自然并行性。本文提出一种解带约束并行多机调度问题的主从式控制网络并行遗传算法,并在PVM环境下实现。计算结果表明,并行遗传算法是有效的,且能适用于大规模并行多机调度问题。     

解决并行多机提前/拖后调度问题的混合遗传算法方法

研究了带有公共交货期的并行多机提前/拖后调度问题.提出了一种混合遗传算法 方法,以便于确定公共交货期和每台机器上加工的任务代号及其加工顺序,即找到一个最优 公共交货期和最优调度,使加工完所有任务后交货期安排的成本、提前交货成本和拖后交货 成本的总和最小.数值计算结果表明了该混合遗传算法优于启发式算法,并能适用于较大规 模并行多机提前/拖后调度问题.算法计算量小,鲁棒性强.     

Scheduling algorithm based on evolutionary computing in identical parallel machine production line

Evolutionary programming is a kind of evolutionary computing method based on stochastic search suitable for solving system optimization. In this paper, evolutionary programming method is applied to the identical parallel machine production line scheduling problem of minimizing the number of tardy jobs, which is a very important optimization problem in the field of research on CIMS and industrial engineering, and researches on problem formulation, expression of feasible solution, methods for the generation of the initial population, the mutation and improvement on the local search ability of evolutionary programming. Computational results of different scales of problems show that the evolutionary programming algorithm proposed in this paper is efficient, and that it is fit for solving large-scale identical parallel machine production line scheduling problems, and that the quality of its solution has advantage over so far the best heuristic procedure.     

Genetic algorithms for the optimal common due date assignment and the optimal scheduling policy in parallel machine earliness/tardiness scheduling problems

Earliness/tardiness scheduling problems with undetermined common due date which have wide application background in textile industry, mechanical industry, electronic industry and so on, are very important in the research fields such as industry engineering and CIMS. In this paper, a kind of genetic algorithm based on sectional code for minimizing the total cost of assignment of due date, earliness and tardiness in this kind of scheduling problem is proposed to determine the optimal common due date and the optimal scheduling policy for determining the job number and their processing order on each machine. Also, simulated annealing mechanism and the iterative heuristic fine-tuning operator are introduced into the genetic algorithm so as to construct three kinds of hybrid genetic algorithms with good performance. Numerical computational results focusing on the identical parallel machine scheduling problem and the general parallel machine scheduling problem shows that these algorithms outperform heuristic procedures, and fit for larger scale parallel machine earliness/tardiness scheduling problem. Moreover, with practical application data from one of the largest cotton colored weaving enterprises in China, numerical computational results show that these genetic algorithms are effective and robust, and that especially the performance of the hybrid genetic algorithm based on simulated annealing and the iterative heuristic fine-tuning operator is the best among them.     

带特殊工艺约束的并行机器生产线调度问题的一种遗传算法

研究带特殊工艺约束的并行机器生产线的调度方法.以完工时间、拖期时间和超库 存时间的惩罚量之和最小为调度目标,对该优化调度问题提出了一种遗传算法,并在问题建 模、遗传算法编码、初始种群的产生办法、交叉及变异方法等方面作了研究.数值计算结果表 明所提出的遗传算法是有效的.     

解不同交货期并行机调度问题的并行遗传算法

为有效地解决不同交货期窗口下的非等同并行多机提前/拖后调度问题,设计了一种分段编码的混合遗传算法。此编码方式能反映工件的分配序列,并利用调度优先级规则和最好适应值规则相结合的启发式算法对其顺序进行了调整,加快了收敛速度。同时为了更好地适应调度实时性和解大规模此类问题的需要,基于遗传算法自然并行性特点的基础上,实现了主从式控制网络模式下并行混合遗传算法。计算结果表明,此算法是有效的,优于遗传算法,有着较高的并行性,并能适用于大规模不同交货期窗口下非等同并行多机提前/拖后调度问题。     

解非等同并行多机调度问题的并行遗传算法

针对最小化完工时间的非等同并行多机调度一类问题,提出了一种混合遗传算法。该算法根据问题的特点,采用一种自然编码方案,此编码与调度方案一一对应,并对初始种群、交叉和变异等方法进行了研究。在鉴于遗传算法自然的并行性特点的基础上,实现了主从式控制网络模式下并行混合遗传算法。计算结果表明,并行混合遗传算法是有效的,优于启发式算法和遗传算法,有着较高的并行性,能适用于大规模非等同并行多机调度问题。     

Parallel machine scheduling with splitting jobs by a hybrid differential evolution algorithm

The problem of parallel machine scheduling for minimizing the makespan is an open scheduling problem with extensive practical relevance. It has been proved to be non-deterministic polynomial hard. Considering a job’s batch size greater than one in the real manufacturing environment, this paper investigates into the parallel machine scheduling with splitting jobs. Differential evolution is employed as a solution approach due to its distinctive feature, and a new crossover method and a new mutation method are brought forward in the global search procedure, according to the job splitting constraint. A specific local search method is further designed to gain a better performance, based on the analytical result from the single product problem. Numerical experiments on the performance of the proposed hybrid DE on parallel machine scheduling problems with splitting jobs covering identical and unrelated machine kinds and a realistic problem are performed, and the results indicate that the algorithm is feasible and efficient.     

A computer simulation model for job shop scheduling problems minimizing makespan

One of the basic and significant problems, that a shop or a factory manager is encountered, is a suitable scheduling and sequencing of jobs on machines. One type of scheduling problem is job shop scheduling. There are different machines in a shop of which a job may require some or all these machines in some specific sequence. For solving this problem, the objective may be to minimize the makespan. After optimizing the makespan, the jobs sequencing must be carried out for each machine. The above problem can be solved by a number of different methods such as branch and bound, cutting plane, heuristic methods, etc. In recent years, researches have used genetic algorithms, simulated annealing, and machine learning methods for solving such problems. In this paper, a simulation model is presented to work out job shop scheduling problems with the objective of minimizing makespan. The model has been coded by Visual SLAM which is a special simulation language. The structure of this language is based on the network modeling. After modeling the scheduling problem, the model is verified and validated. Then the computational results are presented and compared with other results reported in the literature. Finally, the model output is analyzed.     

A novel artificial immune system for solving multiobjective scheduling problems subject to special process constraint

This study presents a novel artificial immune system for solving a multiobjective scheduling problem on parallel machines (MOSP), which has the following characteristics: (1) parallel machines are nonidentical, (2) the type of jobs processed on each machine can be restricted, and (3) the multiobjective scheduling problem includes minimizing the maximum completion time among all the machines (makespan) and minimizing the total earliness/tardiness penalty of all the jobs. In this proposed algorithm, the cells are represented by a vector group, and a local search algorithm is incorporated to facilitate the exploitation of the search space. Specially, a new diversity technique is proposed to preserve the diversity of the population and enhance the exploration of the solution space. Simulation results show the proposed algorithm outperforms the vector immune genetic algorithm (VIGA).     

Tight bounds for the identical parallel machine scheduling problem

We address the problem of minimizing makespan on identical parallel machines. We propose new lower bounding strategies and heuristics for this fundamental scheduling problem. The lower bounds are based on the so‐called lifting procedure. In addition, two optimization‐based heuristics are proposed. These heuristics require iteratively solving a subset‐sum problem. We present the results of computational experiments that provide strong evidence that the new proposed lower and upper bounds consistently outperform the best bounds from the literature.     

Scheduling with multiple servers

In this paper, we consider the problem of scheduling a set of jobs on a set of identical parallel machines. Before the processing of a job can start, a setup is required which has to be performed by a given set of servers. We consider the complexity of such problems for the minimization of the makespan. For the problem with equal processing times and equal setup times we give a polynomial algorithm. For the problem with unit setup times, m machines and m − 1 servers, we give a pseudopolynomial algorithm. However, the problem with fixed number of machines and servers in the case of minimizing maximum lateness is proven to be unary NP-hard. In addition, recent algorithms for some parallel machine scheduling problems with constant precessing times are generalized to the corresponding server problems for the case of constant setup times. Moreover, we perform a worst case analysis of two list scheduling algorithms for makespan minimization.     

Makespan minimization subject to flowtime optimality on identical parallel machines

We consider the identical parallel machine problem with makespan minimization subject to minimum total flowtime. First, we develop an optimal algorithm to the identical parallel machine problem with the objective of minimizing makespan. To improve the computational efficiency, two implementation techniques, the lower bound calculation and the job replacement rule, are applied. Based on the algorithm, an optimal algorithm, using new lower bounds, to the considered problem is developed. The result of this study can also be used to solve the bicriteria problem of minimizing the weighted sum of makespan and mean flowtime. Computational experiments are conducted up to six machines and 1000 jobs. Although the proposed algorithm has an exponential time complexity, the computational results show that it is efficient to find the optimal solution.     

Non-identical parallel machine scheduling using genetic algorithm

Most of the scheduling problems are NP-hard. In the literature, several heuristics and dispatching rules are proposed to solve such hard combinatorial optimization problems and genetic algorithm (GA) ranks among the most preferred ones in view of its characteristics such as high adaptability, near optimization and easy realization. But, even though it is a common problem in the industry, only a small number of studies deal with non-identical parallel machines. In this paper, the authors propose a new “crossover operator” and a new “optimality criterion” in order to adapt the GA to non-identical parallel machine scheduling problem. New algorithm is tested on a numerical example by implementing it in a simulation software and computational results are compared to those obtained with LPT (Longest Processing Time) dispatching rule; results were promising. Findings show that, in addition to its high computational speed for larger scale problem, the GA proposed here fits the non-identical parallel machine scheduling problem of minimizing the maximum completion time (makespan).     

复杂并行机调度问题基于分解的优化算法

针对纺织生产过程中广泛存在的带特殊工艺约束的大规模并行机调度问题，提出了一种基于分解的优化算法。首先将原调度问题分解为机台选择和工件排序两个子问题，然后针对机台选择子问题提出一种进化规划算法，并采用一种具有多项式时间复杂度的最优算法求解工件排序子问题，以得到问题特征信息（即每台机器对应拖期工件数的最小值），该问题特征信息用以指导进化规划算法的迭代过程。不同规模并行机调度问题的数值计算结果及实际制造企业应用效果表明，本文提出的算法是有效的。     

解并行多机提前/拖后调度问题的并行遗传算法

为有效地解决带有公共交货期的非等同并行多机提前/拖后调度问题,设计了一种分段扩展排列编码的混合遗传算法,使遗传编码能同时反映调度方案和公共交货期,并对其初始种群产生、交叉和变异方法也进行了研究。同时为了更好地适应调度实时性和解大规模此类问题的需要,基于遗传算法自然并行性特点的基础上,实现了主从式控制网络模式下并行混合遗传算法。计算结果表明,此算法是有效的,优于启发式算法和遗传算法,有着较高的并行性,并能适用于大规模非等同并行多机提前/拖后调度问题。     

An improved particle swarm optimization algorithm for flowshop scheduling problem

The flowshop scheduling problem has been widely studied and many techniques have been applied to it, but few algorithms based on particle swarm optimization (PSO) have been proposed to solve it. In this paper, an improved PSO algorithm (IPSO) based on the “alldifferent” constraint is proposed to solve the flow shop scheduling problem with the objective of minimizing makespan. It combines the particle swarm optimization algorithm with genetic operators together effectively. When a particle is going to stagnate, the mutation operator is used to search its neighborhood. The proposed algorithm is tested on different scale benchmarks and compared with the recently proposed efficient algorithms. The results show that the proposed IPSO algorithm is more effective and better than the other compared algorithms. It can be used to solve large scale flow shop scheduling problem effectively.