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.     

Approximation algorithms for shop scheduling problems with minsum objective: A correction

We present a correction to the paper, “Approximation algorithms for shop scheduling problems with minsum objective” (Journal of Scheduling 2002; 5:287–305) by Queyranne and Sviridenko. This correction provides a correct derivation of its 2eρ approximation result. Wenhua Li and Jinjiang Yuan: Project supported by NNSFC (Grant 10371112) and NSFHN (Grant 0411011200). Maurice Queyranne: Supported by research grants from NSERC, the Natural Sciences and Engineering Research Council of Canada.     

A simulated annealing algorithm based on block properties for the job shop scheduling problem with total weighted tardinessobjective

In modern manufacturing systems, due date related performance is becoming increasingly important in maintaining a high service reputation. However, compared with the extensive research on makespan minimization, research on the total weighted tardiness objective is comparatively scarce, partly because this objective function is more difficult and complex to optimize. In this paper, we focus on the job shop scheduling problem with the objective of minimizing total weighted tardiness. First, we discuss the mathematical programming model and its duality when the processing orders for each machine are fixed. Then, a block-based neighborhood structure is defined and its important properties are shown. Finally, a simulated annealing algorithm is designed which directly utilizes the features of this neighborhood. According to the computational results, the new neighborhood considerably promotes the searching capability of simulated annealing and helps it converge to high-quality solutions.     

A hybrid immune simulated annealing algorithm for the job shop scheduling problem

A hybrid simulated annealing algorithm based on a novel immune mechanism is proposed for the job shop scheduling problem with the objective of minimizing total weighted tardiness. The proposed immune procedure is built on the following fundamental idea: the bottleneck jobs existing in each scheduling instance generally constitute the key factors in the attempt to improve the quality of final schedules, and thus, the sequencing of these jobs needs more intensive optimization. To quantitatively describe the bottleneck job distribution, we design a fuzzy inference system for evaluating the bottleneck level (i.e. the criticality) of each job. By combining the immune procedure with a simulated annealing algorithm, we design a hybrid optimization algorithm which is subsequently tested on a number of job shop instances. Computational results for different-sized instances show that the proposed hybrid algorithm performs effectively and converges fast to satisfactory solutions.     

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.     

Integrating simulation and genetic algorithm to schedule a dynamic flexible job shop

Much of the research on operations scheduling problems has ignored dynamic events in real-world environments where there are complex constraints and a variety of unexpected disruptions. Besides, while most scheduling problems which have been discussed in the literature assume that machines are incessantly available, in most real life industries a machine can be unavailable for many reasons, such as unanticipated breakdowns (stochastic unavailability), or due to a scheduled preventive maintenance where the periods of unavailability are determined in advance (deterministic unavailability). This paper describes how we can integrate simulation into genetic algorithm to the dynamic scheduling of a flexible job shop with machines that suffer stochastic breakdowns. The objectives are the minimization of two criteria, expected makespan and expected mean tardiness. An overview of the flexible job shops and scheduling under the stochastic unavailability of machines are presented. Subsequently, the details of integrating simulation into genetic algorithm are described and implemented. Consequently, problems of various sizes are used to test the performance of the proposed algorithm. The results obtained reveal that the relative performance of the algorithm for both abovementioned objectives can be affected by changing the levels of the breakdown parameters.     

A two-stage-priority-rule-based algorithm for robust resource-constrained project scheduling

Traditionally, the resource-constrained project scheduling problem (RCPSP) is modeled as a static and deterministic problem and is solved with the objective of makespan minimization. However, many uncertainties, such as unpredictable increases in processing times caused by rework or supplier delays, random transportation and/or setup, may render the proposed solution obsolete. In this paper, we present a two-stage algorithm for robust resource-constrained project scheduling. The first stage of the algorithm solves the RCPSP for minimizing the makespan only using a priority-rule-based heuristic, namely an enhanced multi-pass random-biased serial schedule generation scheme. The problem is then similarly solved for maximizing the schedule robustness while considering the makespan obtained in the first stage as an acceptance threshold. Selection of the best schedule in this phase is based on one out of 12 alternative robustness predictive indicators formulated for the maximization purpose. Extensive simulation testing of the generated schedules provides strong evidence of the benefits of considering robustness of the schedules in addition to their makespans. For illustration purposes, for 10 problems from the well-known standard set J30, both robust and non-robust schedules are executed with a 10% duration increase that is applied to the same randomly picked 20% of the project activities. Over 1000 iterations per instance problem, the robust schedules display a shorter makespan in 55% of the times while the non-robust schedules are shown to be the best performing ones in only 6% of the times.     

Scheduling a dynamic job shop production system with sequence-dependent setups: An experimental study

This paper presents the salient aspects of a simulation-based experimental study of scheduling rules for scheduling a dynamic job shop in which the setup times are sequence dependent. A discrete event simulation model of the job shop system is developed for the purpose of experimentation. Seven scheduling rules from the literature are incorporated in the simulation model. Five new setup-oriented scheduling rules are proposed and implemented. Simulation experiments have been conducted under various experimental conditions characterized by factors such as shop load, setup time ratios and due date tightness. The results indicate that setup-oriented rules provide better performance than ordinary rules. The difference in performance between these two groups of rules increases with increase in shop load and setup time ratio. One of the proposed rules performs better for mean flow time and mean tardiness measures.     

A hybrid genetic and variable neighborhood descent algorithm for flexible job shop scheduling problems

This paper addresses the flexible job shop scheduling problem (fJSP) with three objectives: min makespan, min maximal machine workload and min total workload. We developed a hybrid genetic algorithm (GA) for the problem. The GA uses two vectors to represent solutions. Advanced crossover and mutation operators are used to adapt to the special chromosome structure and the characteristics of the problem. In order to strengthen the search ability, individuals of GA are first improved by a variable neighborhood descent (VND), which involves two local search procedures: local search of moving one operation and local search of moving two operations. Moving an operation is to delete the operation, find an assignable time interval for it, and allocate it in the assignable interval. We developed an efficient method to find assignable time intervals for the deleted operations based on the concept of earliest and latest event time. The local optima of moving one operation are further improved by moving two operations simultaneously. An extensive computational study on 181 benchmark problems shows the performance of our approach.     

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.     

Two-stage hybrid flow shop scheduling with dynamic job arrivals

Motivated by applications in semiconductor manufacturing industry, we consider a two-stage hybrid flow shop where a discrete machine is followed by a batching machine. In this paper, we analyze the computational complexity of a class of two-machine problems with dynamic job arrivals. For the problems belonging to P we present polynomial algorithms. For the NP-complete problems we propose the heuristics, and then establish the upper bounds on the worst case performance ratios of the heuristics. In addition, we give the improved heuristics that can achieve better performances.     

An efficient memetic algorithm for solving the job shop scheduling problem

The job shop scheduling problem (JSP) is well known as one of the most complicated combinatorial optimization problems, and it is a NP-hard problem. Memetic algorithm (MA) which combines the global search and local search is a hybrid evolutionary algorithm. In this paper, an efficient MA with a novel local search is proposed to solve the JSP. Within the local search, a systematic change of the neighborhood is carried out to avoid trapping into local optimal. And two neighborhood structures are designed by exchanging and inserting based on the critical path. The objective of minimizing makespan is considered while satisfying a number of hard constraints. The computational results obtained in experiments demonstrate that the efficiency of the proposed MA is significantly superior to the other reported approaches in the literature.     

动态零等待流水线调度问题的滚动策略及优化算法

针对工件动态到达的零等待流水线调度问题,提出一种基于工件的滚动策略.证明了在该策略下全局调度性能随着局部调度的逐步滚动可得到不断改善.将该策略与基于差分进化的混合算法有机结合,能有效处理动态零等待流水线调度问题.最后通过实验验证了所提出策略和算法的有效性.     

基于杂合机制的免疫遗传算法在动态问题中的应用

针对遗传算法在求解动态问题时存在多样性缺失,无法快速响应环境变化的问题,提出一种基于杂合子机制的免疫遗传算法．该算法借鉴免疫系统中多样性与记忆机理,从保持等位基因多样性出发,在免疫变异中引入杂合映射机制,使种群能够探索更大的解空间．同时,通过引入记忆策略,使算法迅速跟踪最优解变化轨迹．该方法在动态０-１优化问题的求解中取得了较好的效果．     

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     

Simulation-based optimization vs. mathematical programming: A hybrid approach for optimizing scheduling problems

With the increasing computing power of modern processors, exact solution methods (solvers) for the optimization of scheduling problems become more and more important. Based on the mixed integer programming (MIP) formulation of a scheduling problem, it will be analyzed how powerful the present solvers of this problem class are and up to which complexity real scheduling problems are manageable. For this, initially some common benchmark problems are investigated to find out the boundaries for practical application. Then, the acquired results will be compared with the results of a conventional simulation-based optimization approach under comparable time restrictions. As a next step, the general advantages and disadvantages of both approaches were analyzed. As the result, a coupling of the discrete event simulation system and an MIP solver is presented. This coupling automatically generates an MIP-formulation for the present simulation model which can be solved externally by an MIP solver. After the external optimization process follows a backward transformation of the results into the simulation system. All features of the simulation system (like Gantt-Charts, etc.) could be used to check or to illustrate these results. To perform the coupling for a wide range of simulation models, it has to be defined which general constraints the model has to satisfy.     

A two-stage genetic algorithm for multi-objective job shop scheduling problems

This paper presents a two-stage genetic algorithm (2S-GA) for multi-objective Job Shop scheduling problems. The 2S-GA is proposed with three criteria: Minimize makespan, Minimize total weighted earliness, and Minimize total weighted tardiness. The proposed algorithm is composed of two Stages: Stage 1 applies parallel GA to find the best solution of each individual objective function with migration among populations. In Stage 2 the populations are combined. The evolution process of Stage 2 is based on Steady-State GA using the weighted aggregating objective function. The algorithm developed can be used with one or two objectives without modification. The genetic algorithm is designed and implemented with the GALIB object library. The random keys representation is applied to the problem. The schedules are constructed using a permutation with m-repetitions of job numbers. Performance of the proposed algorithm is tested on published benchmark instances and compared with results from other published approaches for both the single objective and multi-objective cases. The experimental results show that 2S-GA is effective and efficient to solve job shop scheduling problem in term of solution quality.     

A hybrid genetic algorithm for no-wait job shop scheduling problems

A no-wait job shop (NWJS) describes a situation where every job has its own processing sequence with the constraint that no waiting time is allowed between operations within any job. A NWJS problem with the objective of minimizing total completion time is a NP-hard problem and this paper proposes a hybrid genetic algorithm (HGA) to solve this complex problem. A genetic operation is defined by cutting out a section of genes from a chromosome and treated as a subproblem. This subproblem is then transformed into an asymmetric traveling salesman problem (ATSP) and solved with a heuristic algorithm. Subsequently, this section with new sequence is put back to replace the original section of chromosome. The incorporation of this problem-specific genetic operator is responsible for the hybrid adjective. By doing so, the course of the search of the proposed genetic algorithm is set to more profitable regions in the solution space. The experimental results show that this hybrid genetic algorithm can accelerate the convergence and improve solution quality as well.     

基于信息素调整的蚁群算法求解JSP问题

为更好的求解作业车间调度问题,针对基本蚁群算法求解作业车间调度问题容易进入局部最优问题的情况,提出了一种基于信息素调整的蚁群算法.该算法通过判断信息素矩阵中最大值与最小值之间的比值,当该比值达到算法设定的阀值时,根据相应策略时信息素矩阵进行调整,有效地缩小了信息素之间的差距,有利于跳出局部最优状态;给出了该算法实施的具体步骤.用该算法求解作业车间调度问题,仿真实验结果表明,该算法与基本蚁群算法相比在收敛速度和计算最优解方面都有了改进.     

A genetic algorithm with tabu search procedure for flexible job shop scheduling with transportation constraints and bounded processing times

In this paper, we propose a model for Flexible Job Shop Scheduling Problem (FJSSP) with transportation constraints and bounded processing times. This is a NP hard problem. Objectives are to minimize the makespan and the storage of solutions. A genetic algorithm with tabu search procedure is proposed to solve both assignment of resources and sequencing problems on each resource. In order to evaluate the proposed algorithm's efficiency, five types of instances are tested. Three of them consider sequencing problems with or without assignment of processing or/and transport resources. The fourth and fifth ones introduce bounded processing times which mainly characterize Surface Treatment Facilities (STFs). Computational results show that our model and method are efficient for solving both assignment and scheduling problems in various kinds of systems.