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.     

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.     

基于二元分布估计算法的置换流水车间调度方法

针对最大完工时间最小的置换流水车间调度问题,提出了一种结合二元分布估计算法与生物地理学算法的混合优化算法（HB-EDA）。算法以分布估计算法为架构,以二元概率模型为进化依据,针对优秀染色体和劣势染色体分别通过概率模型挖掘出具有优势信息和劣势信息的链接基因区块组成区块库1和区块库2,借鉴生物地理学算法中的群体迁移思想,用两个区块库分别对优势和劣势染色体以指定比例进行更新操作产生子群体,并对染色体进行切段与重组,以进一步筛选高适应度的解。最后通过对Reeves和Taillard标准测试集的仿真结果和算法比较验证了所提出算法的有效性。     

[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。     

An ant colony algorithm for scheduling in flowshops with sequence-dependent setup times of jobs

The problem of scheduling in flowshops with sequence-dependent setup times of jobs is considered and solved by making use of ant colony optimization (ACO) algorithms. ACO is an algorithmic approach, inspired by the foraging behavior of real ants, that can be applied to the solution of combinatorial optimization problems. A new ant colony algorithm has been developed in this paper to solve the flowshop scheduling problem with the consideration of sequence-dependent setup times of jobs. The objective is to minimize the makespan. Artificial ants are used to construct solutions for flowshop scheduling problems, and the solutions are subsequently improved by a local search procedure. An existing ant colony algorithm and the proposed ant colony algorithm were compared with two existing heuristics. It was found after extensive computational investigation that the proposed ant colony algorithm gives promising and better results, as compared to those solutions given by the existing ant colony algorithm and the existing heuristics, for the flowshop scheduling problem under study.     

A Modi ed Iterated Greedy Algorithm for Flexible Job Shop Scheduling Problem

The flexible job shop scheduling problem(FJSP) is considered as an important problem in the modern manufacturing system. It is known to be an NP-hard problem. Most of the algorithms used in solving FJSP problem are categorized as metaheuristic methods. Some of these methods normally consume more CPU time and some other methods are more complicated which make them di cult to code and not easy to reproduce. This paper proposes a modified iterated greedy(IG) algorithm to deal with FJSP problem in order to provide a simpler metaheuristic, which is easier to code and to reproduce than some other much more complex methods. This is done by separating the classical IG into two phases. Each phase is used to solve a sub-problem of the FJSP: sequencing and routing sub-problems. A set of dispatching rules are employed in the proposed algorithm for the sequencing and machine selection in the construction phase of the solution. To evaluate the performance of proposed algorithm, some experiments including some famous FJSP benchmarks have been conducted. By compared with other algorithms, the experimental results show that the presented algorithm is competitive and able to find global optimum for most instances. The simplicity of the proposed IG provides an e ective method that is also easy to apply and consumes less CPU time in solving the FJSP problem.     

考虑批量装配的柔性作业车间调度问题研究

柔性作业车间调度是生产调度领域中的一个重要组合优化问题,由于取消了工序与加工设备的唯一性对应关系,因而相较于作业车间调度问题,具有更高的复杂度。针对该问题在批量装配方面的不足,考虑将批量因素与装配环节同时集成到柔性作业车间调度问题当中。以成品件的完工时间为优化目标,对该批量装配柔性作业车间调度问题进行了数学建模。针对该模型,提出一种多层编码结构的粒子群算法,并对该算法的各个模块进行了设计。最后,以实例验证了该数学模型的正确性及算法的有效性。     

Scheduling flowshops with condition-based maintenance constraint to minimize expected makespan

Flexible job-shop scheduling problem (FJSP) is an extended traditional job-shop scheduling problem, which more approximates to practical scheduling problems. This paper presents a multi-objective genetic algorithm (MOGA) based on immune and entropy principle to solve the multi-objective FJSP. In this improved MOGA, the fitness scheme based on Pareto-optimality is applied, and the immune and entropy principle is used to keep the diversity of individuals and overcome the problem of premature convergence. Efficient crossover and mutation operators are proposed to adapt to the special chromosome structure. The proposed algorithm is evaluated on some representative instances, and the comparison with other approaches in the latest papers validates the effectiveness of the proposed algorithm.     

基于改进BBO算法的二维交叉熵多阈值图像分割

为了提高生物地理学优化(BBO)算法在多阈值图像分割中的全局搜索能力,提出一种基于改进的BBO算法的多阈值图像分割.在运用BBO算法进行优化阈值时,首先,采用精英选择算子保留出最优的几组解.其次,引入一种基于优秀解和待迁出解融合的迁移策略,以减少传统迁移操作的过早收敛以及无效迁移等行为.再次,为了减少传统变异操作的盲目性,创建一种通过二进制计算的变异操作.然后将其应用到二维交叉熵的多阈值图像分割中.最后,使用该方法对典型图像进行分割实验,并与粒子群算法的二维多阈值分割,以及基于标准的BBO算法的二维多阈值图像分割进行比较,实验结果表明:该方法具有良好的收敛稳定性,可以有效缩短迭代的时间,并且优化性能优于标准的BBO算法.     

APPLYING PARTICLE SWARM OPTIMIZATION TO JOB-SHOPSCHEDULING PROBLEM

A new heuristic algorithm is proposed for the problem of finding the minimum makespan in the job-shop scheduling problem. The new algorithm is based on the principles of particle swarm optimization (PSO). PSO employs a collaborative population-based search, which is inspired by the social behavior of bird flocking. It combines local search (by self experience) and global search (by neighboring experience), possessing high search efficiency. Simulated annealing (SA) employs certain probability to avoid becoming trapped in a local optimum and the search process can be controlled by the cooling schedule. By reasonably combining these two different search algorithms, a general, fast and easily implemented hybrid optimization algorithm, named HPSO, is developed. The effectiveness and efficiency of the proposed PSO-based algorithm are demonstrated by applying it to some benchmark job-shop scheduling problems and comparing results with other algorithms in literature. Comparing results indicate that PSO-based a     

柔性作业车间调度问题的两级遗传算法

研究不同性能指标柔性作业车间调度问题的优化.针对柔性作业车间调度问题的特点,设计基于工序编码和基于机器分配编码的两种交叉和变异算子,并提出一种双层子代产生模式的改进遗传算法应用于该调度问题,以使子代更好地继承父代的优良特征.使用实例测试改进的遗传算法,并与其他遗传算法的测试结果进行比较,所提出算法的有效性得到证实.     

多目标柔性作业车间调度优化研究

提出了一种集成权重系数变化法和小生境技术的混合遗传算法,建立了包括时间、成本、交货期满意度和设备利用率在内的多目标优化模型。采用基于工序的编码方式和“间隙挤压法”活动化解码方法;遗传算子包括选择、交叉、变异3种类型;选择操作采用轮盘赌选择方式。为了保证解的收敛性和多样性,采用了精英保留策略和小生境技术。交叉操作采用线性次序交叉方式;变异操作采用互换操作变异方法。染色体的适应度是各个目标函数的随机加权和。仿真实验证明,提出的混合遗传算法可以有效解决柔性作业车间多目标调度优化问题。     

不确定信息条件下Job-shop调度的混合智能算法

目前大多数生产调度的研究往往聚焦于经典调度问题的优化算法而忽略了车间中大量存在的不确定性，因而难以应用于实际车间调度。采用随机变量来描述真实车间中存在的一些不确定信息，在基于不确定规划理论的基础上建立了相应的不确定性调度模型，并研究了解决此类问题的混合智能算法。开发了混合智能优化原型系统，并结合仿真工具对该调度模型和混合智能算法进行了验证。     

Optimization of multi-objective integrated process planning and scheduling problem using a priority based optimization algorithm

For increasing the overall performance of modern manufacturing systems, effective integration of process planning and scheduling functions has been an important area of consideration among researchers. Owing to the complexity of handling process planning and scheduling simultaneously, most of the research work has been limited to solving the integrated process planning and scheduling (IPPS) problem for a single objective function. As there are many conflicting objectives when dealing with process planning and scheduling, real world problems cannot be fully captured considering only a single objective for optimization. Therefore considering multi-objective IPPS (MOIPPS) problem is inevitable. Unfortunately, only a handful of research papers are available on solving MOIPPS problem. In this paper, an optimization algorithm for solving MOIPPS problem is presented. The proposed algorithm uses a set of dispatching rules coupled with priority assignment to optimize the IPPS problem for various objectives like makespan, total machine load, total tardiness, etc. A fixed sized external archive coupled with a crowding distance mechanism is used to store and maintain the non-dominated solutions. To compare the results with other algorithms, a C-matric based method has been used. Instances from four recent papers have been solved to demonstrate the effectiveness of the proposed algorithm. The experimental results show that the proposed method is an efficient approach for solving the MOIPPS problem.     

A genetic algorithm for energy-efficiency in job-shop scheduling

Many real-world scheduling problems are solved to obtain optimal solutions in term of processing time, cost, and quality as optimization objectives. Currently, energy-efficiency is also taken into consideration in these problems. However, this problem is NP-hard, so many search techniques are not able to obtain a solution in a reasonable time. In this paper, a genetic algorithm is developed to solve an extended version of the Job-shop Scheduling Problem in which machines can consume different amounts of energy to process tasks at different rates (speed scaling). This problem represents an extension of the classical job-shop scheduling problem, where each operation has to be executed by one machine and this machine can work at different speeds. The evaluation section shows that a powerful commercial tool for solving scheduling problems was not able to solve large instances in a reasonable time, meanwhile our genetic algorithm was able to solve all instances with a good solution quality.     

基于遗传-粒子群混合算法的柔性作业车间多资源调度问题

在传统柔性作业车间调度问题(FJSP)中加入运输和装配环节,提出一种柔性作业车间多资源调度问题(MRFJSP),以完工时间最短为目标建立了包含加工、运输和装配的柔性作业车间调度模型。为了提高传统遗传算法(GA)在车间调度问题中的寻优能力,将粒子群算法(PSO)的寻优过程进行改进并与遗传算法进行结合,提出一种带保优策略的遗传-粒子群混合算法,利用单层编码对模型进行求解。通过算例验证了模型的可行性,并将提出的混合算法与遗传算法和粒子群算法进行比较,证明了混合算法的优越性。     

A New Cyclic Scheduling Algorithm for Flexible Manufacturing Systems

Flexible manufacturing system control is an NP-hard problem. A cyclic approach has been demonstrated to be adequate for an infinite scheduling problem because of maximal throughput reachability. However, it is not the only optimization criterion in general. In this article we consider the minimization of the work in process (WIP) as an economical and productivity factor. We propose a new cyclic scheduling algorithm giving the maximal throughput (a hard constraint) while minimizing WIP. This algorithm is based on progressive operations placing. A controlled beam search approach has been developed to determine at each step the schedule of the next operations. After presenting the main principles of the algorithm, we compare our approach to several most known cyclic scheduling algorithms using a significant existing example from the literature.     

基于Pareto优化的离散自由搜索算法求解多目标柔性作业车间调度问题

针对多目标柔性作业车间调度问题搜索空间的离散性和求解算法的收敛性,提出一种基于Pareto优化的离散自由搜索算法来求解多目标柔性作业车间调度问题。在建立基于Markov链数学模型的基础上,证明了算法以概率1收敛;引入首达最优解期望时间来分析算法收敛速度,并分析了算法时间复杂度。采用基于工序排序和机器分配的个体表达方式,在多目标柔性作业车间离散域,利用自由搜索算法在邻域小步幅精确搜索和在全局空间大步幅勘测进行寻优;通过自由搜索算法自适应赋予个体各异辨别能力和Pareto优化概念来比较个体优劣性,不仅保留优化个体,而且使个体寻优方向沿多目标柔性作业车间调度问题Pareto前沿逼近。通过对搜索过程中产生的伪调度方案进行可行性判定,以确保调度方案可行。采用10×10FJSP和8×8FJSP问题的实例进行寻优测试,验证了所提算法的可行性和有效性。     

利用有限制稳定配对策略求解双目标柔性作业车间调度问题

实际生产中,以最小完工时间和最低成本为目标的调度是柔性作业车间最常见的问题。提出了一种有限制稳定配对策略的双目标柔性作业车间调度问题的求解方法。该方法将双目标优化问题分解为一系列的标量优化子问题,并利用多目标进化算法对子问题进行优化求解;同时,将有限制稳定配对策略用于进化过程中各子问题解的协调选择,以保证解的收敛性和分布性。仿真数据和应用实例表明：该方法可以获得收敛和分布性能更优的调度方案。