Multi-objective colonial competitive algorithm for hybrid flowshop problem

This study analyses the multi-objective optimization in hybrid flowshop problem, in which two conflicting objectives, makespan and total weighted tardiness, are considered to be minimized simultaneously. The multi-objective version of Colonial Competitive Algorithm (CCA) for real world optimization problem is introduced and investigated. In contrast to multi-objective problems solved by CCA, presented in the literature, which used the combination of the objectives as single objective, the proposed algorithm is established on Pareto solutions concepts. Another novelty of this paper is estimating the power of each imperialist by a probabilistic criterion for this multi objective algorithm. Besides that, the variable neighborhood search is implemented as an assimilation strategy. Performance of the algorithm is finally compared with a famous algorithm for scheduling problem, NSGA-II, and the multi-objective form of CCA [28].     

Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems

Multi-objective optimisation problems have seen a large impulse in the last decades. Many new techniques for solving distinct variants of multi-objective problems have been proposed. Production scheduling, as with other operations management fields, is no different. The flowshop problem is among the most widely studied scheduling settings. Recently, the Iterated Greedy methodology for solving the single-objective version of the flowshop problem has produced state-of-the-art results. This paper proposes a new algorithm based on Iterated Greedy technique for solving the multi-objective permutation flowshop problem. This algorithm is characterised by an effective initialisation of the population, management of the Pareto front, and a specially tailored local search, among other things. The proposed multi-objective Iterated Greedy method is shown to outperform other recent approaches in comprehensive computational and statistical tests that comprise a large number of instances with objectives involving makespan, tardiness and flowtime. Lastly, we use a novel graphical tool to compare the performances of stochastic Pareto fronts based on Empirical Attainment Functions.     

A Pareto archive particle swarm optimization for multi-objective job shop scheduling

In this paper, we present a particle swarm optimization for multi-objective job shop scheduling problem. The objective is to simultaneously minimize makespan and total tardiness of jobs. By constructing the corresponding relation between real vector and the chromosome obtained by using priority rule-based representation method, job shop scheduling is converted into a continuous optimization problem. We then design a Pareto archive particle swarm optimization, in which the global best position selection is combined with the crowding measure-based archive maintenance. The proposed algorithm is evaluated on a set of benchmark problems and the computational results show that the proposed particle swarm optimization is capable of producing a number of high-quality Pareto optimal scheduling plans.     

Bi-objective scheduling for reentrant hybrid flow shop using Pareto genetic algorithm

This paper deals with a scheduling problem for reentrant hybrid flowshop with serial stages where each stage consists of identical parallel machines. In a reentrant flowshop, a job may revisit any stage several times. Local-search based Pareto genetic algorithms with Minkowski distance-based crossover operator is proposed to approximate the Pareto optimal solutions for the minimization of makespan and total tardiness in a reentrant hybrid flowshop. The Pareto genetic algorithms are compared with existing multi-objective genetic algorithm, NSGA-II in terms of the convergence to optimal solution, the diversity of solution and the dominance of solution. Experimental results show that the proposed crossover operator and local search are effective and the proposed algorithm outperforms NSGA-II by statistical analysis.     

A high performing metaheuristic for multi-objective flowshop scheduling problem

Genetic algorithm is a powerful procedure for finding an optimal or near optimal solution for the flowshop scheduling problem. This is a simple and efficient algorithm which is used for both single and multi-objective problems. It can easily be utilized for real life applications. The proposed algorithm makes use of the principle of Pareto solutions. It mines the Pareto archive to extract the most repetitive sequences, and constitutes artificial chromosome for generation of the next population. In order to guide the search direction, this approach coupled with variable neighborhood search. This algorithm is applied on the flowshop scheduling problem for minimizing makespan and total weighted tardiness. For the assessment of the algorithm, its performance is compared with the MOGLS [1]. The results of the experiments allow us to claim that the proposed algorithm has a considerable performance in this problem.     

A multi-objective electromagnetism algorithm for a bi-objective flowshop scheduling problem

This paper deals with a bi-objective flowshop scheduling problem minimizing the makespan and total weighted tardiness, in which all jobs may not be processed by all machines. Furthermore, we consider transportation times between machines. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. This paper presents a new multi-objective electromagnetism algorithm (MOEM). The motivation behind this algorithm has risen from the attraction–repulsion mechanism of electromagnetic theories. Along with MOEA, we apply simulated annealing to solve the given problem. A set of experimental instances are carried out to evaluate the algorithm by advanced multi-objective performance measures. The related results show that a variant of our proposed MOEM provides sound performance comparing with other algorithms.     

An iterated local search for the multi-objective permutation flowshop scheduling problem with sequence-dependent setup times

Due to its simplicity yet powerful search ability, iterated local search (ILS) has been widely used to tackle a variety of single-objective combinatorial optimization problems. However, applying ILS to solve multi-objective combinatorial optimization problems is scanty. In this paper we design a multi-objective ILS (MOILS) to solve the multi-objective permutation flowshop scheduling problem with sequence-dependent setup times to minimize the makespan and total weighted tardiness of all jobs. In the MOILS, we design a Pareto-based variable depth search in the multi-objective local search phase. The search depth is dynamically adjusted during the search process of the MOILS to strike a balance between exploration and exploitation. We incorporate an external archive into the MOILS to store the non-dominated solutions and provide initial search points for the MOILS to escape from local optima traps. We compare the MOILS with several multi-objective evolutionary algorithms (MOEAs) shown to be effective for treating the multi-objective permutation flowshop scheduling problem in the literature. The computational results show that the proposed MOILS outperforms the MOEAs.     

An adaptive multi-population genetic algorithm to solve the multi-objective group scheduling problem in hybrid flexible flowshop with sequence-dependent setup times

In this paper we consider a multi-objective group scheduling problem in hybrid flexible flowshop with sequence-dependent setup times by minimizing total weighted tardiness and maximum completion time simultaneously. Whereas these kinds of problems are NP-hard, thus we proposed a multi-population genetic algorithm (MPGA) to search Pareto optimal solution for it. This algorithm comprises two stages. First stage applies combined objective of mentioned objectives and second stage uses previous stage’s results as an initial solution. In the second stage sub-population will be generated by re-arrangement of solutions of first stage. To evaluate performance of the proposed MPGA, it is compared with two distinguished benchmarks, multi-objective genetic algorithm (MOGA) and non-dominated sorting genetic algorithm II (NSGA-II), in three sizes of test problems: small, medium and large. The computational results show that this algorithm performs better than them.     

变邻域遗传算法在车间物流调度中的应用

针对含有自动引导小车(Automated Guided Vehicle,AGV)的离散化车间物流调度问题,以最小化物流任务时间惩罚成本和最小化运载小车的总行驶距离为优化目标,构建离散化车间多目标物流调度优化模型,设计一种基于Pareto寻优的多目标混合变邻域搜索遗传算法(VNSGA-II).以遗传算法为基础,通过使用NSGA-II的Pareto分层和拥挤度计算方法评估种群优劣实现多目标优化,为了提高算法的寻优能力,避免算法陷入局部最优,通过添加保优记忆库对精英个体进行保护,并利用变邻域搜索算法在搜索过程中的局部寻优能力,针对本文模型特点,设计6个随机邻域结构,来达到算法求解最优值的目标.并提出了基于关键AGV小车的插入邻域和基于关键物流任务的交换邻域调整策略以进一步降低成本.最后,以某离散车间物流调度为实例,分别使用VNSGA-II、带精英策略的快速非支配排序遗传算法Ⅱ(Nondominated Sorting Genetic AlgorithmⅡ,NSGA-II)和强Pareto进化算法(Strong Pareto Evolutionary Algorithm 2,SPEA2)对问题进行求解,计算结果表明,VNSGA-II能得到更好的Pareto解集,验证了算法的有效性和可行性.     

A multi-phase covering Pareto-optimal front method to multi-objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic

This paper considers the problem of sequence-dependent setup time hybrid flowshop scheduling with the objectives of minimizing the makespan and sum of the earliness and tardiness of jobs, and present a multi-phase method. In initial phase, the population will be decomposed into several subpopulations. In this phase we develop a random key genetic algorithm and the goal is to obtain a good approximation of the Pareto-front. In the second phase, for improvement the Pareto-front, non-dominant solutions will be unified as one big population. In this phase, based on the local search in Pareto space concept, we propose multi-objective hybrid metaheuristic. Finally in phase 3, we propose a novel method using e-constraint covering hybrid metaheuristic to cover the gaps between the non-dominated solutions and improve Pareto-front. Generally in three phases, we consider appropriate combinations of multi-objective methods to improve the total performance. The hybrid algorithm used in phases 2 and 3 combines elements from both simulated annealing and a variable neighborhood search. The aim of using a hybrid metaheuristic is to raise the level of generality so as to be able to apply the same solution method to several problems. Furthermore, in this study to evaluate non-dominated solution sets, we suggest several new approaches. The non-dominated sets obtained from each phase and global archive sub-population genetic algorithm presented previously in the literature are compared. The results obtained from the computational study have shown that the multi-phase algorithm is a viable and effective approach.     

多目标协同正弦优化算法求解分布式流水车间调度问题

针对最小化最大完工时间(makespan)、总拖期以及平均空闲时间的多目标序列相关准备时间分布式流水车间调度问题, 本文提出一种多目标协同正弦优化算法(MCSOA). 算法主要包括4个核心阶段: 在多邻域搜索阶段,提出了基于关键工厂的搜索策略, 并通过正弦优化算法控制搜索范围; 在破坏重构阶段, 设计了一种迭代搜索策略引导个体的进化方向, 同时使用正弦优化算法平衡全局开发与局部搜索; 在选择阶段, 使用非支配排序与参考点的方法筛选优质解, 外部档案集用于存储所有非支配解; 在协同阶段, 设计种群间共享与竞争机制, 平衡3个目标的优化. 本文通过多目标优化的均匀性、反世代距离和覆盖率3项性能指标验证算法的有效性, 并使用非参数检验证明所提出的算法具有显著性优势.     

基于联姻遗传算法的混合FloWshop提前/拖期调度问题

混合流水车间(Flowshop)提前／拖期调度问题的目标是4~_r-件的提前／拖期惩罚成本最小，这是一个NP完全问题，很难用一般的方法解决。文中首先给出了问题的数学模型，然后采用联姻遗传算法求解该问题。仿真结果表明此算法能有效地解决该类复杂调度问题。     

Multi-objective fuzzy multiprocessor flowshop scheduling

This paper considers a bi-objective hybrid flowshop scheduling problems with fuzzy tasks’ operation times, due dates and sequence-dependent setup times. To solve this problem, we propose a bi-level algorithm to minimize two criteria, namely makespan, and sum of the earliness and tardiness, simultaneously. In the first level, the population will be decomposed into several sub-populations in parallel and each sub-population is designed for a scalar bi-objective. In the second level, non-dominant solutions obtained from sub-population bi-objective random key genetic algorithm (SBG) in the first level will be unified as one big population. In the second level, for improving the Pareto-front obtained by SBG, based on the search in Pareto space concept, a particle swarm optimization (PSO) is proposed. We use a defuzzification function to rank the Bell-shaped fuzzy numbers. The non-dominated sets obtained from each of levels and an algorithm presented previously in literature are compared. The computational results showed that PSO performs better than others and obtained superior results.     

Genetic algorithms in integrated process planning and scheduling

Process planning and scheduling are actually interrelated and should be solved simultaneously. Most integrated process planning and scheduling methods only consider the time aspects of the alternative machines when constructing schedules. The initial part of this paper describes a genetic algorithm (GA) based algorithm that only considers the time aspect of the alternative machines. The scope of consideration is then further extended to include the processing capabilities of alternative machines, with different tolerance limits and processing costs. In the proposed method based on GAs, the processing capabilities of the machines, including processing costs as well as number of rejects produced in alternative machine are considered simultaneously with the scheduling of jobs. The formulation is based on multi-objective weighted-sums optimization, which are to minimize makespan, to minimize total rejects produced and to minimize the total cost of production. A comparison is done w ith the traditional sequential method and the multi-objective genetic algorithm (MOGA) approach, based on the Pareto optimal concept.     

Modelling and scheduling multi-objective flow shop problems with interfering jobs

This paper studies multi-objective flow shop scheduling problems with interfering jobs. That is, there are two sets of jobs and each of which has its own objective. Some jobs are scheduled so as to minimize makespan while the others are to minimize total tardiness. In this case, the problem was mathematically modeled by a mixed integer linear program. Then, a novel biogeography-based optimization was developed to solve the problem. To evaluate the algorithm, its performance was compared with three well-known algorithms in the literature. The results of the present study show that the proposed algorithm outperforms the other tested algorithms.     

求解多目标流水车间调度Pareto最优解的遗传强化算法

针对多目标流水车间调度Pareto最优问题, 本文建立了以最大完工时间和最大拖延时间为优化目标的多目标流水车间调度问题模型, 并设计了一种基于Q-learning的遗传强化学习算法求解该问题的Pareto最优解. 该算法引入状态变量和动作变量, 通过Q-learning算法获得初始种群, 以提高初始解质量. 在算法进化过程中, 利用Q表指导变异操作, 扩大局部搜索范围. 采用Pareto快速非支配排序以及拥挤度计算提高解的质量以及多样性, 逐步获得Pareto最优解. 通过与遗传算法、NSGA-II算法和Q-learning算法进行对比实验, 验证了改进后的遗传强化算法在求解多目标流水车间调度问题Pareto最优解的有效性.     

Solving a bi-objective flowshop scheduling problem by a Multi-objective Immune System and comparing with SPEA2+ and SPGA

This paper presents a bi-objective flowshop scheduling problem with sequence-dependent setup times. The objective functions are to minimize the total completion time and the total earliness/tardiness for all jobs. An integer programming model is developed for the given problem that belongs to an NP-hard class. Thus, an algorithm based on a Multi-objective Immune System (MOIS) is proposed to find a locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed MOIS, different test problems are solved. Based on some comparison metrics, the computational results of the proposed MOIS is compared with the results obtained using two well-established multi-objective genetic algorithms, namely SPEA2+ and SPGA. The related results show that the proposed MOIS outperforms genetic algorithms, especially for the large-sized problems.     

Ant colony optimization algorithm for a Bi-criteria 2-stage hybrid flowshop scheduling problem

We consider the problem of scheduling jobs in a hybrid flowshop with two stages. Our objective is to minimize both the makespan and the total completion time of jobs. This problem has been little studied in the literature. To solve the problem, we propose an ant colony optimization procedure. Computational experiments are conducted using random-generated instances from the literature. In comparison against other well-known heuristics from the literature, experimental results show that our algorithm outperforms such heuristics.     

基于模糊物元模型的高维多目标FJSP研究*

为解决高维多目标柔性作业车间调度问题,提出了一种基于模糊物元模型与粒子群算法的模糊粒子群算法（Fuzzy Particle Swarm Optimization,FPSO）。该算法以模糊物元分析理论为依据,采用复合模糊物元与基准模糊物元之间的欧式贴近度作为适应度值引导粒子群算法的进化,并引入具有容量限制的外部存储器保留较优的Pareto非支配解以供决策者选择。此外,构建了优化目标为最大完工时间、设备总负荷、加工成本、最大设备负荷与加工质量的高维多目标优化模型,并以Kacem基准问题与实际生产数据为例进行仿真模拟与对比分析。结果表明,该算法具有良好的收敛性且搜索到的非支配解分布性较好,能够有效地应用于求解高维多目标柔性作业车间调度问题。     

A novel hybrid meta-heuristic algorithm for solving multi objective flexible job shop scheduling

Finding feasible scheduling that optimize all objective functions for flexible job shop scheduling problem (FJSP) is considered by many researchers. In this paper, the novel hybrid genetic algorithm and simulated annealing (NHGASA) is introduced to solve FJSP. The NHGASA is a combination of genetic algorithm and simulated annealing to propose the algorithm that is more efficient than others. The three objective functions in this paper are: minimize the maximum completion time of all the operations (makespan), minimize the workload of the most loaded machine and minimize the total workload of all machines. Pareto optimal solution approach is used in NHGASA for solving FJSP. Contrary to the other methods that assign weights to all objective functions to reduce them to one objective function, in the NHGASA and during all steps, problems are solved by three objectives. Experimental results prove that the NHGASA that uses Pareto optimal solutions for solving multi-objective FJSP overcome previous methods for solving the same benchmarks in the shorter computational time and higher quality.