Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm

Most flexible job shop scheduling models assume that the machines are available all of the time. However, in most realistic situations, machines may be unavailable due to maintenances, pre-schedules and so on. In this paper, we study the flexible job shop scheduling problem with availability constraints. The availability constraints are non-fixed in that the completion time of the maintenance tasks is not fixed and has to be determined during the scheduling procedure. We then propose a hybrid genetic algorithm to solve the flexible job shop scheduling problem with non-fixed availability constraints (fJSP-nfa). The genetic algorithm uses an innovative representation method and applies genetic operations in phenotype space in order to enhance the inheritability. We also define two kinds of neighbourhood for the problem based on the concept of critical path. A local search procedure is then integrated under the framework of the genetic algorithm. Representative flexible job shop scheduling benchmark problems and fJSP-nfa problems are solved in order to test the effectiveness and efficiency of the suggested methodology. Received: June 2005 /Accepted: December 2005     

An improved PSO algorithm with genetic and neighborhood-based diversity operators for the job shop scheduling problem

The job shop scheduling problem (JSSP) is an important NP-hard practical scheduling problem that has various applications in the fields of optimization and production engineering. In this paper an effective scheduling method based on particle swarm optimization (PSO) for the minimum makespan problem of the JSSP is proposed. New variants of the standard PSO operators are introduced to adapt the velocity and position update rules to the discrete solution space of the JSSP. The proposed algorithm is improved by incorporating two neighborhood-based operators to improve population diversity and to avoid early convergence to local optima. First, the diversity enhancement operator tends to improve the population diversity by relocating neighboring particles to avoid premature clustering and to achieve broader exploration of the solution space. This is achieved by enforcing a circular neighboring area around each particle if the population diversity falls beneath the adaptable diversity threshold. The adaptive threshold is utilized to regulate the population diversity throughout the different stages of the search process. Second, the local search operator based on critical path analysis is used to perform local exploitation in the neighboring area of the best particles. Variants of the genetic well-known operators “selection” and “crossover” are incorporated to evolve stagnated particles in the swarm. The proposed method is evaluated using a collection of 123 well-studied benchmarks. Experimental results validate the effectiveness of the proposed method in producing excellent solutions that are robust and competitive to recent state-of-the-art heuristic-based algorithms reported in literature for nearly all of the tested instances.     

A hybrid genetic algorithm for the job shop scheduling problems

The Job Shop Scheduling Problem (JSSP) is one of the most general and difficult of all traditional scheduling problems. The goal of this research is to develop an efficient scheduling method based on genetic algorithm to address JSSP. We design a scheduling method based on Single Genetic Algorithm (SGA) and Parallel Genetic Algorithm (PGA). In the scheduling method, the representation, which encodes the job number, is made to be always feasible, the initial population is generated through integrating representation and G&T algorithm, the new genetic operators and selection method are designed to better transmit the temporal relationships in the chromosome, and island model PGA are proposed. The scheduling methods based on genetic algorithm are tested on five standard benchmark JSSP. The results are compared with other proposed approaches. Compared to traditional genetic algorithm, the proposed approach yields significant improvement in solution quality. The superior results indicate the successful incorporation of a method to generate initial population into the genetic operators.     

A new hybrid parallel genetic algorithm for the job‐shop scheduling problem

The job‐shop scheduling problem (JSSP) is considered one of the most difficult NP‐hard problems. Numerous studies in the past have shown that as exact methods for the problem solution are intractable, even for small problem sizes, efficient heuristic algorithms must achieve a good balance between the well‐known themes of exploitation and exploration of the vast search space. In this paper, we propose a new hybrid parallel genetic algorithm with specialized crossover and mutation operators utilizing path‐relinking concepts from combinatorial optimization approaches and tabu search in particular. The new scheme relies also on the recently introduced concepts of solution backbones for the JSSP in order to intensify the search in promising regions. We compare the resulting algorithm with a number of state‐of‐the‐art approaches for the JSSP on a number of well‐known test‐beds; the results indicate that our proposed genetic algorithm compares fairly well with some of the best‐performing genetic algorithms for the problem.     

Neural network and genetic algorithm-based hybrid approach to expanded job-shop scheduling

The expanded job-shop scheduling problem (EJSSP) is a practical production scheduling problem with processing constraints that are more restrictive and a scheduling objective that is more general than those of the standard job-shop scheduling problem (JSSP). A hybrid approach involving neural networks and genetic algorithm (GA) is presented to solve the problem in this paper. The GA is used for optimization of sequence and a neural network (NN) is used for optimization of operation start times with a fixed sequence.

After detailed analysis of an expanded job shop, new types of neurons are defined to construct a constraint neural network (CNN). The neurons can represent processing restrictions and resolve constraint conflicts. CNN with a gradient search algorithm, gradient CNN in short, is applied to the optimization of operation start times with a fixed processing sequence. It is shown that CNN is a general framework representing scheduling problems and gradient CNN can work in parallel for optimization of operation start times of the expanded job shop.

Combining gradient CNN with a GA for sequence optimization, a hybrid approach is put forward. The approach has been tested by a large number of simulation cases and practical applications. It has been shown that the hybrid approach is powerful for complex EJSSP.     

A new hybrid genetic algorithm for job shop scheduling problem

Job shop scheduling problem is a typical NP-hard problem. To solve the job shop scheduling problem more effectively, some genetic operators were designed in this paper. In order to increase the diversity of the population, a mixed selection operator based on the fitness value and the concentration value was given. To make full use of the characteristics of the problem itself, new crossover operator based on the machine and mutation operator based on the critical path were specifically designed. To find the critical path, a new algorithm to find the critical path from schedule was presented. Furthermore, a local search operator was designed, which can improve the local search ability of GA greatly. Based on all these, a hybrid genetic algorithm was proposed and its convergence was proved. The computer simulations were made on a set of benchmark problems and the results demonstrated the effectiveness of the proposed algorithm.     

求解包含复杂关联约束的JSSP 的二级嵌套混合算法

作业车间调度问题(JSSP)包含“设备分配”和“工序排序” 2 个相互耦合的子问题,目 前的研究主要集中于工序串行的小规模问题。如果工序之间还存在并行、甚至嵌套等复杂关联 约束,则可行域性状非常复杂,当规模较大时,甚至难以求得可行解。针对以上难点问题,在 分别发挥遗传算法求解“分配问题”和蚁群算法求解“排序问题”的优势基础上,提出了二级嵌套 模型及其基本思路。通过一系列改进策略,如：基于工序的整数编码策略、基于设备类型的多 节点交叉策略、设备类别区间内基因互换的变异策略、基于逆向遍历的可行路径形成策略、基 于最短加工时间的信息素播洒与更新策略等等,构造了集成遗传算法与蚁群算法于同一循环体 的二级嵌套混合算法。针对中等规模问题,分别采用遗传算法、蚁群算法、二级嵌套蚁群算法、 遗传算法与蚁群算法相结合的二级嵌套混合算法,进行了对比试验研究。结果验证了所提算法 的可靠性和优越性,为求解包含复杂关联约束的JSSP 提供了新思路和新方法。     

Total flow time minimization in no-wait job shop using a hybrid discrete group search optimizer

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances.     

加热炉优化调度模型及算法研究

加热炉是热轧生产中主要的能源消耗设备,其合理调度对于降低生产过程的能耗和生产成本都具有重要作用.根据加热炉的生产工艺和约束条件建立了加热炉优化调度数学模型,针对模型特点提出了分散搜索（scattersearch,SS）算法,设计了基于随机变量序列的投票组合算子和单点交叉组合算子.根据国内某钢铁企业加热炉生产过程的实绩随机生成40个测试案例,进行实验,分析了参考集规模及不同组合算子对SS算法性能的影响,并与遗传局域搜索（genetic local search,GLS）算法的求解结果进行了比较.结果表明所提出的模型和算法对解决本文研究的加热炉调度问题有效.     

Hybrid whale optimization algorithm enhanced with Lévy flight and differential evolution for job shop scheduling problems

The job shop scheduling problem (JSSP) has been a hot issue in manufacturing. For the past few decades, scholars have been attracted to research JSSP and proposed many novel meta-heuristic algorithms to solve it. Whale optimization algorithm (WOA) is such a novel meta-heuristic algorithm and has been proven to be efficient in solving real-world optimization problems in the literature. This paper proposes a hybrid WOA enhanced with Lévy flight and differential evolution (WOA-LFDE) to solve JSSP. By changing the expression of Lévy flight and DE search strategy, Lévy flight enhances the abilities of global search and convergence of WOA in iteration, while DE algorithm improves the exploitation and local search capabilities of WOA and keeps the diversity of solutions to escape local optima. It is then applied to solve 88 JSSP benchmark instances and compared with other state-of-art algorithms. The experimental results and statistical analysis show that the proposed algorithm has superior performance over contesting algorithms.     

求解工件车间调度问题的一种新的邻域搜索算法

该文提出了一种新的求解工件车间调度(job shop scheduling)问题的邻域搜索算法．问题的目标是：在满足约束条件的前提下使得调度的makespan尽可能地小．定义了一种新的优先分配规则以生成初始解;定义了一种新的邻域结构;将邻域搜索跟单机调度结合在一起;提出了跳坑策略以跳出局部最优解并且将搜索引向有希望的方向．计算了当前国际文献中的一组共58个benchmark问题实例,算法的优度高于当前国外学者提出的两种著名的先进算法．其中对18个10工件10机器的实例,包括最著名的难解实例ft10,在可接受的时间内都找到了最优解．这些实例是当前文献中报导的所有规模为10工件10机器的实例．     

A genetic algorithm for multiprocessor scheduling

The problem of multiprocessor scheduling can be stated as finding a schedule for a general task graph to be executed on a multiprocessor system so that the schedule length can be minimized. This scheduling problem is known to be NP-hard, and methods based on heuristic search have been proposed to obtain optimal and suboptimal solutions. Genetic algorithms have recently received much attention as a class of robust stochastic search algorithms for various optimization problems. In this paper, an efficient method based on genetic algorithms is developed to solve the multiprocessor scheduling problem. The representation of the search node is based on the order of the tasks being executed in each individual processor. The genetic operator proposed is based on the precedence relations between the tasks in the task graph. Simulation results comparing the proposed genetic algorithm, the list scheduling algorithm, and the optimal schedule using random task graphs, and a robot inverse dynamics computational task graph are presented     

求解流水线调度问题的万有引力搜索算法

研究了以最大完工时间为目标的流水线调度问题,使用万有引力算法求解调度问题,提出了一种最大排序规则,利用物体间各个位置分量值存在的大小次序关系,并结合随机键编码的方法产生,将物体的连续位置转变成了一个可行的调度方案;提出了一种边界变异的策略使得越界的物体不再聚集在边界上,而是分布在边界附近的可行空间内,从而增加种群的多样性;结合交换算子和插入算子提出了一种新的局部搜索算法,有效地避免了算法陷入局部最优值,进一步提高了解的质量.最后证明了算法的收敛性,并且计算了算法的时间复杂度和空间复杂度,仿真实验说明了所得算法的有效性.     

A taboo search approach for deadlock-free scheduling of automated manufacturing systems

This paper addresses the scheduling problem of a class of automated manufacturing systems. A new manufacturing system model is proposed. In this model, a set of jobs is to be processed and each job requires a sequence of operations. Each operation may need more than one resource. Upon the completion of an operation, resources needed in the next operation of the same job cannot be released and the remaining resources cannot be released until the start of the next operation. The scheduling problem consists in sequencing the operations on the resources in order to avoid deadlocks and to minimize the makespan. The classical disjunctive graph representation is extended to model the scheduling problem. A taboo search algorithm is then proposed using an original neighborhood structure defined by two basic moves: the permutation of disjunctive arcs of critical paths and a deadlock recovery move if the former fails. Numerical results presented in the paper show the efficiency of the proposed algorithm.     

Tardiness minimization in a flexible job shop: A tabu search approach

This paper addresses the problem of scheduling jobs in a flexible job shop with the objective of minimizing total tardiness. The flexible job shop differs from the classical job shop in that each of the operations associated with a job can be processed on any of a set of alternative machines. Two heuristics based on tabu search are developed for this problem: a hierarchical procedure and a multiple start procedure. The procedures use dispatching rules to obtain an initial solution and then search for improved solutions in neighborhoods generated by the critical paths of the jobs in a disjunctive graph representation. Diversification strategies are also implemented and tested. The outcomes of extensive computational results are reported.     

Co-evolutionary genetic algorithm for fuzzy flexible job shop scheduling

Fuzzy flexible job shop scheduling problem (FfJSP) is the combination of fuzzy scheduling and flexible scheduling in job shop environment, which is seldom investigated for its high complexity. We developed an effective co-evolutionary genetic algorithm (CGA) for the minimization of fuzzy makespan. In CGA, the chromosome of a novel representation consists of ordered operation list and machine assignment string, a new crossover operator and a modified tournament selection are proposed, and the population of job sequencing and the population of machine assignment independently evolve and cooperate for converging to the best solutions of the problem. CGA is finally applied and compared with other algorithms. Computational results show that CGA outperforms those algorithms compared.     

Deadlock-free genetic scheduling algorithm for automated manufacturing systems based on deadlock control policy

Deadlock-free control and scheduling are vital for optimizing the performance of automated manufacturing systems (AMSs) with shared resources and route flexibility. Based on the Petri net models of AMSs, this paper embeds the optimal deadlock avoidance policy into the genetic algorithm and develops a novel deadlock-free genetic scheduling algorithm for AMSs. A possible solution of the scheduling problem is coded as a chromosome representation that is a permutation with repetition of parts. By using the one-step look-ahead method in the optimal deadlock control policy, the feasibility of a chromosome is checked, and infeasible chromosomes are amended into feasible ones, which can be easily decoded into a feasible deadlock-free schedule. The chromosome representation and polynomial complexity of checking and amending procedures together support the cooperative aspect of genetic search for scheduling problems strongly.     

柔性作业调度的串并行模型对比与求解

作业处理中的柔性使得作业调度更为灵活,作业中操作的执行顺序满足拓扑排序是作业调度的前提。是否允许没有优先关系的操作在不同的机器上同时执行是区分串行和并行调度的条件。文中以共生进化算法求解一个复杂的作业调度模型为例,给出了算法实现串行调度和并行调度的具体区别,并给出了串行和并行调度的结果。结果表明,并行相对于串行对算法效率的提高与柔性大小相关,与作业的规模成反比。     

基于GPGP协同机制的多Agent车间调度方法研究

车间调度作为车间制造系统的重要组成部分,影响着整个车间制造系统的敏捷性和智能性.但是,由于资源和工艺约束的并存,使得车间调度成为一类NP-hard问题.基于静态的智能算法与动态的多Agent思想,提出了一种结合通用部分全局规划(generalized partial global planning,GPGP)机制与多种智能算法的多Agent车间调度模型,设计了从"初始宏观调度"到"微观再调度"的大规模复杂问题的调度步骤,并构建了一个柔性强且Agent可自我动态调度的仿真系统.同时,从理论上总结了GPGP基本协同机制的策略,实现了二级多目标优化调度.最后使用DECAF仿真Agent软件模拟了车间调度的GPGP协同机制,并与CNP,NONE机制进行了比较.结果表明,所提出的模型不仅提高了调度的效率,而且降低了资源的损耗.     

Hybrid heuristic search approach for deadlock-free scheduling of flexible manufacturing systems using Petri nets

Based on the Petri net models of flexible manufacturing systems (FMSs), this paper focuses on deadlock-free scheduling problem with the objective of minimizing the makespan. Two hybrid heuristic search algorithms for solving such scheduling problems of FMSs are proposed. To avoid deadlocks, the deadlock control policy is embedded into heuristic search strategies. The proposed algorithms combine the heuristic best-first strategy with the controlled backtracking strategy based on the execution of the Petri nets. The scheduling problem is transformed into a heuristic search problem in the reachability graph of the Petri net, and a schedule is a transition sequence from the initial marking to the final marking in the reachability graph. By using the one-step look-ahead method in the deadlock control policy, the safety of a state in the reachability graph is checked, and hence, deadlock is avoided. Experimental results are provided and indicate the effectiveness of the proposed hybrid heuristic search algorithms in solving deadlock-free scheduling problems of FMSs. Especially, the comparison against previous work shows that both new algorithms are promising in terms of solution quality and computing times.