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 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.     

A GRASP heuristic for the multi-objective permutation flowshop scheduling problem

This paper presents a multi-objective greedy randomized adaptive search procedure (GRASP)-based heuristic for solving the permutation flowshop scheduling problem in order to minimize two and three objectives simultaneously: (1) makespan and maximum tardiness; (2) makespan, maximum tardiness, and total flowtime. GRASP is a competitive metaheuristic for solving combinatorial optimization problems. We have customized the basic concepts of GRASP algorithm to solve a multi-objective problem and a new algorithm named multi-objective GRASP algorithm is proposed. In order to find a variety of non-dominated solutions, the heuristic blends two typical approaches used in multi-objective optimization: scalarizing functions and Pareto dominance. For instances involving two machines, the heuristic is compared with a bi-objective branch-and-bound algorithm proposed in the literature. For instances involving up to 80 jobs and 20 machines, the non-dominated solutions obtained by the heuristic are compared with solutions obtained by multi-objective genetic algorithms from the literature. Computational results indicate that GRASP is a promising approach for multi-objective optimization.     

基于DNA遗传算法求解机床加工调度问题

研究了机床加工的多目标调度问题,提出一种基于DNA计算的混合遗传算法,结合Pareto非支配排序法来求解。为保证最优解集的多样性,采用四进制编码方式,将DNA序列分成中性和有害两部分,交叉操作只在中性部分进行;由动态变化的变异概率决定是否执行变异操作,并比较设计的算法与常规遗传算法获得的结果。试验结果表明,可以有效地解决机床加工中的多目标调度问题。     

考虑多目标的工艺规划与调度集成问题研究

针对工艺规划与调度集成问题在多目标优化方面的不足,考虑将多目标优化集成到工艺规划与调度集成问题中。以最长完工时间、加工成本及设备最大负载为优化目标,对该多目标工艺规划与调度集成问题进行建模,并提出了一种非支配排序遗传算法,鉴于加工信息的多样性,使用多层结构表示可行解,对该算法的选择及遗传操作等步骤进行了设计。最后,以实例验证了上述模型的正确性及算法的有效性。     

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.     

Solving a multi-objective job shop scheduling problem with sequence-dependent setup times by a Pareto archive PSO combined with genetic operators and VNS

In this paper, we present a combination of particle swarm optimization (PSO) and genetic operators for a multi-objective job shop scheduling problem that minimizes the mean weighted completion time and the sum of the weighted tardiness/earliness costs, simultaneously. At first, we propose a new integer linear programming for the given problem. Then, we redefine and modify PSO by introducing genetic operators, such as crossover and mutation operators, to update particles and improve particles by variable neighborhood search. Furthermore, we consider sequence-dependent setup times. We then design a Pareto archive PSO, where the global best position selection is combined with the crowding measure-based archive updating method. To prove the efficiency of our proposed PSO, a number of test problems are solved. Its reliability based on some comparison metrics is compared with a prominent multi-objective genetic algorithm (MOGA), namely non-dominated sorting genetic algorithm II (NSGA-II). The computational results show that the proposed PSO outperforms the above MOGA, 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.     

基于混合的多目标遗传算法的多目标流水车间逆调度问题求解方法*

将逆优化理论与方法引入车间调度领域,探讨近年来车间调度领域出现的一种新方法“逆调度”。研究多目标流水车间逆调度问题,建立考虑调度效率和调度稳定性的数学模型,综合考虑了加工参数改变量、系统改变量以及完工时间和等目标。提出一种基于混合的多目标遗传算法(Hybrid multi-objective genetic algorithm, HMGA)的求解方法,将多种策略进行混合以提高算法性能,主要包括快速非支配排序遗传算法(Non-dominated sorting genetic algorithm II, NSGAII)中的快速非支配排序方法、两种多样性保持策略、混合的精英保留策略,以及改进的局部搜索策略等。通过实例测试与方差分析(Analysis of variance, ANOVA),验证了该算法的有效性。     

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。     

分时电价下多目标绿色可重入混合流水车间调度

针对多目标绿色可重入混合流水车间调度问题（RHFSP）的特点,在机器分配和工序排序的基础上引入分时电价机制,构建了以最小化最大完工时间、总能耗成本和碳排放为目标的绿色调度优化模型,提出了一种改进的多目标文化基因算法（MOMA）来求解该问题,通过数值实验验证了所设计的MOMA算法的可行性。实验结果表明MOMA算法在非劣解的收敛性、多样性和支配性指标方面都显著优于多目标蚁狮优化算法(MOALO)、多目标粒子群优化算法（MOPSO）和带精英策略的非支配排序遗传算法（NSGA-Ⅱ）,四种算法的分布性指标无显著差异。所提出的模型能够使企业有效避开高电价时段作业,合理转移用电负荷,达到降低总用电成本和碳排放的目的。     

A particle swarm optimization for multi-objective flowshop scheduling

The academic approach of single-objective flowshop scheduling has been extended to multiple objectives to meet the requirements of realistic manufacturing systems. Many algorithms have been developed to search for optimal or near-optimal solutions due to the computational cost of determining exact solutions. This paper provides a particle swarm optimization-based multi-objective algorithm for flowshop scheduling. The proposed evolutionary algorithm searches the Pareto optimal solution for objectives by considering the makespan, mean flow time, and machine idle time. The algorithm was tested on benchmark problems to evaluate its performance. The results show that the modified particle swarm optimization algorithm performed better in terms of searching quality and efficiency than other traditional heuristics.     

[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。     

Multi-objective optimization of electric-discharge machining process using controlled elitist NSGA-II

Parametric optimization of electric discharge machining (EDM) process is a multi-objective optimization task. In general, no single combination of input parameters can provide the best cutting speed and the best surface finish simultaneously. Genetic algorithm has been proven as one of the most popular multi-objective optimization techniques for the parametric optimization of EDM process. In this work, controlled elitist non-dominated sorting genetic algorithm has been used to optimize the process. Experiments have been carried out on die-sinking EDM by taking Inconel 718 as work piece and copper as tool electrode. Artificial neural network (ANN) with back propagation algorithm has been used to model EDM process. ANN has been trained with the experimental data set. Controlled elitist non-dominated sorting genetic algorithm has been employed in the trained network and a set of pareto-optimal solutions is obtained.

     

Multi-objective optimization and evaluation method of modular product configuration design scheme

Product configuration is one of the key technologies for mass customization. Traditional product configuration optimization targets are mostly single. In this paper, an approach based on multi-objective genetic optimization algorithm and fuzzy-based select mechanism is proposed to solve the multi-objective configuration optimization problem. Firstly, the multi-objective optimization mathematical model of product configuration is constructed, the objective functions are performance, cost, and time. Then, a method based on improved non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the configuration design optimization problem. As a result, the Pareto-optimal set is acquired by NSGA-II. Due to the imprecise nature of human decision, a fuzzy-based configuration scheme evaluation and select mechanism is proposed consequently, which helps extract the best compromise solution from the Pareto-optimal set. The proposed multi-objective genetic algorithm is compared with two other established multi-objective optimization algorithms, and the results reveal that the proposed genetic algorithm outperforms the others in terms of product configuration optimization problem. At last, an example of air compressor multi-objective configuration optimization is used to demonstrate the feasibility and validity of the proposed method.     

The two-stage assembly flowshop scheduling problem with bicriteria of makespan and mean completion time

In this paper, we address the two-stage assembly flowshop scheduling problem with a weighted sum of makespan and mean completion time criteria, known as bicriteria. Since the problem is NP-hard, we propose heuristics to solve the problem. Specifically, we propose three heuristics; simulated annealing (SA), ant colony optimization (ACO), and self-adaptive differential evolution (SDE). We have conducted computational experiments to compare the performance of the proposed heuristics. It is statistically shown that both SA and SDE perform better than ACO. Moreover, the experiments reveal that SA, in general, performs better than SDE, while SA consumes less CPU time than both SDE and ACO. Therefore, SA is shown to be the best heuristic for the problem.     

考虑外包的平行机调度问题的多目标遗传算法

研究了一类考虑外包的平行机调度问题,目标是使作业外包总成本与最大完工时间同时最小化。通过对该类问题进行形式化描述与分析,设计了一种数字串形式的解的表示方法,其中每位数字表示固定作业对应的机器编号,该方法能够有效缩小解空间,从而提高搜索效率。进而构建了一种带精英策略的非支配遗传算法PD-NSGA-Ⅱ,为该类多目标调度问题提供Pareto最优解集。大量数据实验结果表明,所构造的PD-NSGA-Ⅱ算法能够在合理的时间内有效求解该类调度问题,其解的质量与计算效率均优于SPEA算法。     

基于粒子群算法的电网检修计划编制

在电网检修计划编制的基本原则和工作流程下,根据粒子群基本算法原理对电网检修计划编制进行数学建模。考虑检修时间作为自变量矢量,考虑期望缺供电量和检修成本作为其目标函数,考虑检修时间、检修资源和安全性等多个因素作为约束。结合粒子群算法原理和多目标优化理论,全局搜索非支配解集,形成帕累托前沿。最后依据管理者不同的偏好,通过加权计算的方式量化评估各优化目标,从而遴选出最优解,也即最符合决策人员预期的检修计划。通过与非劣排序多目标遗传算法和多目标粒子群算法进行对比,证明本文算法具有较高的实用性,提升了电网运行维护的自动化水平。     

A Memetic Algorithm for the <Emphasis Type="SmallCaps">n</Emphasis>/2/Flowshop/α<Emphasis Type="SmallCaps">F </Emphasis>+ β<Emphasis Type="SmallCaps">C</Emphasis><Subscript>max</Subscript> Scheduling Problem

Machine scheduling has been a popular area of research during the past four decades. Its object is to determine the sequence for processing jobs on a given set of machines. The need for scheduling arises from the limited resources available to the decision-maker. In this study, a special situation involving a computationally difficult n/2/Flowshop/ αF + βCmax flowshop scheduling problem is discussed. We develop a memetic algorithm (MA, a hybrid genetic algorithm) by combining a genetic algorithm and the greedy heuristic using the pairwise exchange method and the insert method, to solve the n/2/Flowshop/ αF + βCmax flowshop scheduling problem. Preliminary computational experiments demonstrate the efficiency and performance of the proposed memetic algorithm. Our results compare favourably with the best-known branch-and-bound algorithm, the traditional genetic algorithm and the best-known heuristic algorithm.     

Multi-objective dynamic optimal trajectory planning of robot manipulators in the presence of obstacles

In this paper, a real-world test problem is presented and made available for the use of evolutionary multi-objective community. The generation of manipulator trajectories by considering multiple objectives and obstacle avoidance is a non-trivial optimisation problem. In this paper two multi-objective evolutionary algorithms viz., elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) algorithm are proposed to address this problem. Multiple criteria are optimised to two simultaneous objectives. Simulations results are presented for industrial robots with two degrees of freedom (Cartesian robot (PP) with two prismatic joints) and six degrees of freedom (PUMA 560 robot), by considering two objectives optimisation. Two methods (normalized weighting objective functions and average fuzzy membership function) are used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find computational effort of NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed.