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.     

Solving a multi-objective no-wait flow shop scheduling problem with an immune algorithm

Flow shop scheduling problems have gained wide attention both in practical and academic fields. In this paper, we consider a multi-objective no-wait flow shop scheduling problem by minimizing the weighted mean completion time and weighted mean tardiness simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in a strong sense, an effective immune algorithm (IA) is proposed for searching locally the Pareto-optimal frontier for the given problem. To validate the performance of the proposed algorithm in terms of solution quality and diversity level, various test problems are carried out and the efficiency of the proposed algorithm, based on some comparison metrics, is compared with a prominent multi-objective genetic algorithm, i.e., strength Pareto evolutionary algorithm II (SPEA-II). The computational results show that the proposed IA outperforms the above genetic algorithm, especially for large problems.     

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 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.     

Two meta-heuristics for solving a new two-machine flowshop scheduling problem with the learning effect and dynamic arrivals

This paper develops a new mathematical model and proposes two meta-heuristics for solving a two-machine flowshop scheduling problem that minimizes bi-objectives, namely the total idle time and the mean deviation from a common due data. In this paper, we assume the arrival time of jobs is dynamic, in which each job has a time window and can arrive in its time window randomly. We also assume the learning effect on the processing times considering as a position-dependent effect. Since the problem is an NP-hard one, we present a multiobjective genetic algorithm (MOGA) and a multiobjective simulated annealing (MOSA) algorithm to solve the given problems. The computational results confirm that the proposed MOGA has a better solution in comparison with the proposed MOSA, especially in large-sized problems.     

Multi-objective integrated optimization research on preventive maintenance planning and production scheduling for a single machine

Preventive maintenance (PM) planning and production scheduling are among the most important problems in the manufacturing industries. Researchers have begun to investigate the integrated optimization problem of PM and production scheduling with a single objective. However, many industries have trade-offs in their scheduling problems where multiple objectives must be considered in order to optimize the overall performance of the system. In this paper, five objectives, including minimizing maintenance cost, makespan, total weighted completion time of jobs, total weighted tardiness, and maximizing machine availability are simultaneously considered to optimize the integrated problem of PM and production scheduling introduced by Cassady and Kutanoglu. Multi-objective genetic algorithm (MOGA) is used to solve the integrated optimization problem. To illuminate the conflicting nature of the objective functions, decision-makers’ preferences of the multiple objectives are not integrated into the MOGA. The total weighted percent deviation, which represents not only the preferences of the objectives but also the deviations of the solutions, is proposed to help decision-makers select the best solution among the near-Pareto optimal solutions obtained by the MOGA. A numerical example reveals the necessity and significance of integrating optimization of PM and production scheduling considering multiple objectives.     

An effective multi-objective genetic algorithm based on immune principle and external archive for multi-objective integrated process planning and scheduling

Process planning and scheduling are two major sub-systems in a modern manufacturing system. In traditional manufacturing system, they were regarded as the separate tasks to perform sequentially. However, considering their complementarity, integrating process planning and scheduling can further improve the performance of a manufacturing system. Meanwhile, the multiple objectives are needed to be considered during the realistic decision-making process in a manufacturing system. Based on the above requirements from the real manufacturing system, developing effective methods to deal with the multi-objective integrated process planning and scheduling (MOIPPS) problem becomes more and more important. Therefore, this research proposes a multi-objective genetic algorithm based on immune principle and external archive (MOGA-IE) to solve the MOIPPS problem. In MOGA-IE, the fast non-dominated sorting approach used in NSGA-II is utilized as the fitness assignment scheme and the immune principle is exploited to maintain the diversity of the population and prevent the premature condition. Moreover, the external archive is employed to store and maintain the Pareto solutions during the evolutionary process. Effective genetic operators are also designed for MOIPPS. To test the performance of the proposed algorithm, three different scale instances have been employed. And the proposed method is also compared with other previous algorithms in literature. The results show that the proposed algorithm has achieved good improvement and outperforms the other algorithms.     

Bicriteria scheduling of a two-machine flowshop with sequence-dependent setup times

A two-machine flowshop scheduling problem is addressed to minimize setups and makespan where each job is characterized by a pair of attributes that entail setups on each machine. The setup times are sequence-dependent on both machines. It is shown that these objectives conflict, so the Pareto optimization approach is considered. The scheduling problems considering either of these objectives are $ \mathcal{N}{\wp } - {\text{hard}} $ , so exact optimization techniques are impractical for large-sized problems. We propose two multi-objective metaheurisctics based on genetic algorithms (MOGA) and simulated annealing (MOSA) to find approximations of Pareto-optimal sets. The performances of these approaches are compared with lower bounds for small problems. In larger problems, performance of the proposed algorithms are compared with each other. Experimentations revealed that both algorithms perform very similar on small problems. Moreover, it was observed that MOGA outperforms MOSA in terms of the quality of solutions on larger problems.     

基于多目标遗传算法的直升机总体参数优化设计

应用多目标优化问题中Pareto最优解集的概念,提出了一种基于多目标遗传算法的直升机总体参数优化设计方法。算法引入了个体的序和密度的概念,改进了变异操作算子,使用精英策略,确保能够搜索到具有较高贴近性、均匀性和完整性的Pareto解集。以UH-1H直升机为优化算例的计算结果表明:多目标遗传算法适用于解决多目标优化问题,能够改善Pareto解的质量和均匀性分布。     

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.     

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.     

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 distance-ranked 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.     

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。     

A Genetic Algorithm Approach to the Scheduling of FMSs with Multiple Routes

Usually, most of the typical job shop scheduling approaches deal with the processing sequence of parts in a fixed routing condition. In this paper, we suggest a genetic algorithm (GA) to solve the job-sequencing problem for a production shop that is characterized by flexible routing and flexible machines. This means that all parts, of all part types, can be processed through alternative routings. Also, there can be several machines for each machine type. To solve these general scheduling problems, a genetic algorithm approach is proposed and the concepts of virtual and real operations are introduced. Chromosome coding and genetic operators of GAs are defined during the problem solving. A minimum weighted tardiness objective function is used to define code fitness, which is used for selecting species and producing a new generation of codes. Finally, several experimental results are given.     

Optimal disc cutters plane layout design of the full-face rock tunnel boring machine (tbm) based on a multi-objective genetic algorithm

Improving of the quality of the disc cutters’ plane layout design of the full-face rock tunnel boring machine (TBM) is the most effective way to improve the global performance of a TBM. The plane layout design of disc cutters contains multiple complex engineering technical requirements and belongs to a multi-objective optimization problem with multiple nonlinear constraints. Based on analysis of the technical requirements of the plane layout problem, an optimizing mathematical model was built. To obtain a set of design schemes for engineers to choose from, a multi-objective genetic algorithm (MOGA) was applied to carry out the optimization of the mathematical model. A constraint-domination principle was utilized to handle the constraints, and a nondominated sorting method was adopted to obtain Pareto solutions. Simulation results showed that the proposed method was efficient and accurate in obtaining the Pareto layout solutions.     

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.     

A nondominated ranked genetic algorithm for bi-objective single machine preemptive scheduling in just-in-time environment

Motivated by just-in-time (JIT) manufacturing, we study the bi-objective scheduling problem of minimizing the total weighted earliness and the number of tardy jobs on a single machine, in which machine idle time and preemption are allowed. The problem is known to be NP-hard. In this paper, we propose a new mathematical model, with nonlinear terms and integer variables which cannot be solved efficiently for medium- and large-sized problems. A method combining the new ranked-based roulette wheel selection algorithm with Pareto-based population ranking algorithm, named nondominated ranking genetic algorithm (NRGA), has been presented to find nondominated solutions in a reasonable time. Various operators and parameters of the proposed algorithm are reviewed to calibrate the algorithm by means of the Taguchi method. A number of numerical examples are solved to demonstrate the effectiveness of the proposed approach. The solutions obtained via NRGA are compared against solutions obtained via ε-constraint method in small-sized problems. Experimental results show that the proposed NRGA is competitive in terms of the quality and diversity of solutions in medium- and large-sized problems.     

A multi-objective electromagnetism algorithm for a bi-objective hybrid no-wait flowshop scheduling problem

This article studies multi-objective hybrid no-wait flowshop scheduling problems to minimize both makespan and total tardiness. This article mathematically formulates the problem using an effective multi-objective mixed integer linear programming models. Since the problem is NP-hard and it is difficult to find an optimal solution in a reasonable computational time, an efficient multi-objective electromagnetism algorithm (MOEA) is presented as the solution procedure. Electromagnetism algorithm is known as a flexible and effective population-based algorithm utilizing an attraction/repulsion mechanism to move the particles towards optimality. MOEA is carefully evaluated for its performance against multi-objective immune algorithms and the adaptation of a well-known multi-objective simulated annealing in the relevant literature by means of multi-objective performance measures and statistical tools. The results show that the proposed solution method outperforms the others.     

考虑节能的改进多目标樽海鞘群算法TFT-LCD面板阵列制程调度问题

TFT-LCD面板生产的阵列制程是可重入混合流水车间调度问题,采用一种改进多目标樽海鞘群算法对其进行优化求解。构建以最大完工时间、总拖期时间和总耗能为优化目标的数学规划模型;针对该问题结构特点,对基本多目标樽海鞘群算法进行了一系列改进操作,包括基于升序排列的随机键编码、PS方法解码、基于Lévy飞行的领导者个体位置更新方式,以及外部档案中非支配个体的变邻域搜索操作,并采用田口方法进行算法参数设置;最后通过对基准算例的数值实验,将改进多目标樽海鞘群算法与基本多目标樽海鞘群算法、多目标粒子群优化算法、快速非支配排序遗传算法进行对比,实验结果表明了改进多目标樽海鞘群算法的有效性。     

A novel discrete particle swarm optimization algorithm for the manufacturing cell formation problem

The manufacturing cell formation problem, with the aim of grouping parts into families and machines into cells, is considered with the objective of maximizing grouping efficacy. A new solution approach based on the particle swarm optimization (PSO) algorithm is presented for the problem. Unlike the original PSO algorithm which works with arithmetic operators and scalars, the new algorithm uses group-based operators, in place of arithmetic operators, in the body of the updating equations analogous to those of the classical PSO equations (given the fact that the cell formation problem is essentially a grouping problem, all operators in the new algorithm work with constructed cells (groups) rather than parts/machines (objects), isolatedly). We benchmark a set of 40 test problem instances from previous researches and do comparisons between the new algorithm and existing algorithms. We also compare the performance of our algorithm when it is hybridized with a local search module. Our computations reveal that the proposed algorithm performs well on all test problems, exceeding or matching the best solution’s quality presented in the literature.