Multi-objective flexible job shop scheduling problem using variable neighborhood evolutionary algorithm

This paper presents a hybrid Pareto-based local search (PLS) algorithm for solving the multi-objective flexible job shop scheduling problem. Three minimization objectives-the maximum completion time (makespan), the total workload of all machines, and the workload of the critical machine are considered simultaneously. In this study, several well-designed local search approaches are proposed, which consider the problem characteristics and thus can hold fast convergence ability while keep rich population diversity. Then, an external Pareto archive is developed to memory the Pareto optimal solutions found so far. In addition, to improve the efficiency of the scheduling algorithm, a speed-up method is devised to decide the domination status of a solution with the archive set. Experimental results on two well-known benchmarks show the efficiency of the proposed hybrid algorithm. It is concluded that the PLS algorithm is superior to the very recent algorithms in term of both search quality and computational efficiency.

Flexible job-shop scheduling problem (FJSP) is very important in both fields of production management and combinatorial optimization. This paper focuses on the multiobjective flexible job shop scheduling problem (MO-FJSP) with three objectives which minimizing make span, total workload and maximal workload, respectively, with Pareto manner. In addition, Monte-Carlo Tree Search (MCTS) is successful in computer Go and many other games. Hence, solving FJSP by MCTS is a new attempt. In this paper, we propose an MCTS algorithm for FJSP, by incorporating Variable Neighborhood Descent Algorithm and other techniques like Rapid Action Value Estimates Heuristic and Transposition Table. Our algorithm finds Pareto solutions of the benchmark problems proposed by Kacem et al. within 116 seconds: 4 solutions in 4×5, 3 in 10×7, 4 in 8×8, 4 in 10×10 and 2 in 15×10. These solutions are the same as the best found to date. Although one article claimed to have an extra 8×8 solution, that article did not find some of the above solutions.

Flexible job shop scheduling problem is a key factor of using efficiently in production systems. This paper attempts to simultaneously optimize three objectives including minimization of the make span, total workload and maximum workload of jobs. Since the multi objective flexible job shop scheduling problem is strongly NP-Hard, an integrated heuristic approach has been used to solve it. The proposed approach was based on a floating search procedure that has used some heuristic algorithms. Within floating search procedure utilize local heuristic algorithms; it makes the considered problem into two sections including assigning and sequencing sub problem. First of all search is done upon assignment space achieving an acceptable solution and then search would continue on sequencing space based on a heuristic algorithm. This paper has used a multi-objective approach for producing Pareto solution. Thus proposed approach was adapted on NSGA II algorithm and evaluated Pareto-archives. The elements and parameters of the proposed algorithms were adjusted upon preliminary experiments. Finally, computational results were used to analyze efficiency of the proposed algorithm and this results showed that the proposed algorithm capable to produce efficient solutions.

Due to intense competition in the market place, effective scheduling has now become an important issue for the growth and survival of manufacturing firms. To sustain in the current competitive environment, it is essential for the manufacturing firms to improve the schedule based on simultaneous optimization of performance measures such as makespan, flow time, and tardiness. The current paper presents a novel particle swarm optimization (PSO) algorithm for solving multi-objective flexible job shop scheduling problem with the goal of finding approximations of the optimal Pareto front. The Pareto-optimal solutions obtained through multi-objective particle swarm optimization (MOPSO) have been ranked by the composite scores obtained through maximum deviation theory (MDT) to avoid subjectiveness and impreciseness in the decision-making. The results are compared with non-dominated sorting genetic algorithm-II (NSGA-II) and multi-objective evolutionary algorithm (MOEA) in terms of four performance metrics. Twenty-eight benchmark instances from literature are solved by the proposed algorithm. It is observed that MOPSO outperforms NSGA-II and MOEA in four performance metrics in most of the instances.

This paper presents a hybrid Pareto-based local search (PLS) algorithm for solving the multi-objective flexible job shop scheduling problem. Three minimisation objectives are considered simultaneously, i.e. the maximum completion time (makespan), the total workload of all machines, and the workload of the critical machine. In this study, several well-designed neighbouring approaches are proposed, which consider the problem characteristics and thus can hold fast convergence ability while keep the population with a certain level of quality and diversity. Moreover, a variable neighbourhood search (VNS) based self-adaptive strategy is embedded in the hybrid algorithm to utilise the neighbouring approaches efficiently. Then, an external Pareto archive is developed to record the non-dominated solutions found so far. In addition, a speed-up method is devised to update the Pareto archive set. Experimental results on several well-known benchmarks show the efficiency of the proposed hybrid algorithm. It is concluded that the PLS algorithm is superior to the very recent algorithms, in term of both search quality and computational efficiency.

In modern manufacturing industry, not only production efficiency, but also fairness in wages should be emphasized so as to motivate the staff. To this end, this paper addresses the multi-objective flexible job shop scheduling problem (MOFJSP) aiming at minimizing the makespan and maximum wage gap among workers simultaneously. An improved nondominated sorting genetic algorithm-II (INSGAII) is developed. The novelties are mainly presented as follows. First, a probability-based extended precedence preservative crossover operator (PEPPX) is designed for accelerating the convergence rate. Second, in order to solve the multi-modal problem, a “pruning-regenerating” mechanism (PRM) is developed to remove the redundant solutions in objective space and reinsert new solutions. Specifically, a novel metric called “encoding distance” is proposed to measure the diversity of solutions with exactly the same objective function values in chromosome encoding. Meanwhile, a critical path based variable neighborhood search (VNS) is designed to regenerate new solutions replacing the removed ones. Numerical experiments on a wide set of well-known benchmarks have confirmed the effectiveness and efficiency of the proposed INSGA-II.

Flexible job shop scheduling problem (FJSP) is very complex to be controlled, and it is a problem which inherits job shop scheduling problem (JSP) characteristics. FJSP has two sub-problems: routing sub-problem and scheduling sub-problem. In this paper, improved differential evolution (DE) algorithm is presented for multi-objective FJSP. Minimization of three objective functions includes maximum completion time, workload of the most loaded machine and total workload of all machines. The improved algorithm has a well-designed mutation and crossover operator, and uses a Pareto non-dominated sorting method. Computational simulations and comparisons demonstrate the effectiveness of the proposed improved DE algorithm.

A linguistic-based meta-heuristic modeling and solution approach for solving the flexible job shop scheduling problem (FJSSP) is presented in this study. FJSSP is an extension of the classical job-shop scheduling problem. The problem definition is to assign each operation to a machine out of a set of capable machines (the routing problem) and to order the operations on the machines (the sequencing problem), such that predefined performance measures are optimized. In this research, the scope of the problem is widened by taking into account the alternative process plans for each part (process plan selection problem). Probabilistic selection of alternative process plans and machines are also considered. The FJSSP is presented as a grammar and the productions in the grammar are defined as controls (Baykasoglu, 2002). Using these controls and Giffler and Thompson's (1960) priority rule-based heuristic along with the multiple objective tabu search algorithm of Baykasoglu et al. (1999) FJSSP is solved. This novel approach simplifies the modeling process of the FJSSP and enables usage of existing job shop scheduling algorithms for its fast solution. Instead of scheduling job shops with inflexible algorithms that cannot take into account the flexibility which is available in the job shop, the present algorithm is developed which can take into account the flexibility during scheduling. Such an approach will considerably increase the responsiveness of the job shops.

An efficient evolutionary grey wolf optimizer for multi-objective flexible job shop scheduling problem with hierarchical job precedence constraints

In this paper, a modified invasive weed optimization (IWO) algorithm is presented for optimization of multiobjective flexible job shop scheduling problems (FJSSPs) with the criteria to minimize the maximum completion time (makespan), the total workload of machines and the workload of the critical machine. IWO is a bio-inspired metaheuristic that mimics the ecological behaviour of weeds in colonizing and finding suitable place for growth and reproduction. IWO is developed to solve continuous optimization problems that’s why the heuristic rule the Smallest Position Value (SPV) is used to convert the continuous position values to the discrete job sequences. The computational experiments show that the proposed algorithm is highly competitive to the state-of-the-art methods in the literature since it is able to find the optimal and best-known solutions on the instances studied.

在实际工业生产中, 调度环境的复杂性与不确定性使得调度问题求解难度大大提高. 针对加工时间不确定的柔性作业车间调度问题, 采用不确定参数描述随机工时波动程度和约束条件允许违背程度, 构建工时波动服从指数分布的机会约束规划模型, 将不确定调度问题模型转化为加工时间确定的柔性作业车间调度问题, 求解得到一定程度上具有鲁棒性能的调度方案. 并在执行过程中对工时扰动驱动下采用工序移动调整和重调度方法对作业排产方案进行动态调整. 基于双链式编码以及贪婪插入法解码规则, 提出了基于变邻域搜索的混合NSGA-II算法. 针对车间调度问题的多约束性和计算复杂度高等特点, 设计了基于机器选择的复合启发式规则以获取分布均匀且更加接近pareto前沿的初始种群, 包括依概率应用机器累计负载最小、工序加工时间最短规则, 采用改进工序和设备交叉策略以提高算法的全局搜索能力, 研究基于关键工序和机器选择的多种邻域结构设计变邻域搜索策略, 以进一步提高算法的局部搜索能力. 通过Kacem和Brandimarte标准算例的数值仿真以及与多种代表算法的统计比较, 验证了所提算法的有效性, 并为不确定柔性作业车间调度问题提供更优的调度方案.

This paper investigates the application of particle swarm optimization (PSO) to the multi-objective flexible job shop scheduling problem with sequence-dependent set-up times, auxiliary resources and machine down time. To achieve this goal, alternative particle representations and problem mapping mechanisms were implemented within the PSO paradigm. This resulted in the development of four PSO-based heuristics. Benchmarking on real customer data indicated that using the priority-based representation resulted in a significant performance improvement over the existing rule-based algorithms commonly used to solve this problem. Additional investigation into algorithm scalability led to the development of a priority-based differential evolution algorithm. Apart from the academic significance of the paper, the benefit of an improved production schedule can be generalized to include cost reduction, customer satisfaction, improved profitability, and overall competitive advantage.

In this paper, a hybrid discrete particle swarm algorithm based on maximum fitness function is proposed for a dual-resources constrained flexible job shop scheduling problem with multiple optimisation objectives. An improved position updating mechanism of particles is used to effectively avoid the occurrence of infeasible solution. Additionally, a novel dynamic search strategy is designed to enhance the local exploiting search ability of discrete particle swarms. Finally, simulation results demonstrate that the proposed algorithm effectively decreases both the production time and production cost.

In this paper, an improved ant colony algorithm is proposed to solve solving multi-objective flexible shop scheduling problem. Limitations of the traditional ant colony algorithm weighting coefficient method will result in a greater impact on the results because the determination of the weighting factor has greater subjective factors. Proposed algorithm adds a set of BPs to save all the Pareto set ant appear after iteration, the algorithm improves the search capabilities of the ant colony. The convergence speed is improved on ameliorating the pheromone update rule based on the global optimal experience to guide the optimization way. Thus, multi-objective Flexible Job Shop Scheduling Problems Pareto optimal solution was conducted. Finally, the proposed theory in this paper is proved to solve the multi-objective flexible job shop scheduling optimization problems by examples.

This paper focuses on multi-objective dynamic flexible job shop scheduling problem (MODFJSP) with machine breakdown. First, a multi-objective dynamic scheduling model is established, with objectives to minimize makespan and total machine workload. Second, according to the processing status of faulty machine, a hybrid rescheduling strategy including transfer rescheduling strategy and complete rescheduling strategy is proposed to react to stochastic machine breakdown. The performance of two rescheduling strategies is analyzed in terms of the scheduling efficiency and its stability, from the delay extent and initial scheduling deviation, respectively. Besides, the optimal adaptation conditions of both scheduling strategies are obtained. Furthermore, the non-dominated sorting genetic algorithm (NSGA-II) is employed to solve the constructed model. Experimental results demonstrate the effectiveness of the proposed strategies on reducing the impact of machine breakdown in real scheduling.