A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems

This paper presents a novel discrete differential evolution (DDE) algorithm for solving the no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, the individuals in the DDE algorithm are represented as discrete job permutations, and new mutation and crossover operators are developed based on this representation. Second, an elaborate one-to-one selection operator is designed by taking into account the domination status of a trial individual with its counterpart target individual as well as an archive set of the non-dominated solutions found so far. Third, a simple but effective local search algorithm is developed to incorporate into the DDE algorithm to stress the balance between global exploration and local exploitation. In addition, to improve the efficiency of the scheduling algorithm, several speed-up methods are devised to evaluate a job permutation and its whole insert neighborhood as well as to decide the domination status of a solution with the archive set. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed DDE algorithm is superior to a recently published hybrid differential evolution (HDE) algorithm [Qian B, Wang L, Huang DX, Wang WL, Wang X. An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Computers & Operations Research 2009;36(1):209–33] and the well-known multi-objective genetic local search algorithm (IMMOGLS2) [Ishibuchi H, Yoshida I, Murata T. Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Transactions on Evolutionary Computation 2003;7(2):204–23] in terms of searching quality, diversity level, robustness and efficiency. Moreover, the effectiveness of incorporating the local search into the DDE algorithm is also investigated.     

An effective hybrid discrete differential evolution algorithm for the flow shop scheduling with intermediate buffers

In this paper, an effective hybrid discrete differential evolution (HDDE) algorithm is proposed to minimize the maximum completion time (makespan) for a flow shop scheduling problem with intermediate buffers located between two consecutive machines. Different from traditional differential evolution algorithms, the proposed HDDE algorithm adopted job permutation to represent individuals and applies job-permutation-based mutation and crossover operations to generate new candidate solutions. Moreover, a one-to-one selection scheme with probabilistic jumping is used to determine whether the candidates will become members of the target population in next generation. In addition, an efficient local search algorithm based on both insert and swap neighborhood structures is presented and embedded in the HDDE algorithm to enhance the algorithm’s local searching ability. Computational simulations and comparisons based on the well-known benchmark instances are provided. It shows that the proposed HDDE algorithm is not only capable to generate better results than the existing hybrid genetic algorithm and hybrid particle swarm optimization algorithm, but outperforms two recently proposed discrete differential evolution (DDE) algorithms as well. Especially, the HDDE algorithm is able to achieve excellent results for large-scale problems with up to 500 jobs and 20 machines.     

A DE-based approach to no-wait flow-shop scheduling

This paper proposes an effective hybrid differential evolution (HDE) for the no-wait flow-shop scheduling problem (FSSP) with the makespan criterion, which is a typical NP-hard combinational optimization problem. Firstly, a largest-order-value (LOV) rule is presented to transform individuals in DE from real vectors to job permutations so that the DE can be applied for solving FSSPs. Secondly, the DE-based parallel evolution mechanism and framework is applied to perform effective exploration, and a simple but efficient local search developed according to the landscape of FSSP is applied to emphasize problem-dependent local exploitation. Thirdly, a speed-up evaluation method and a fast Insert-based neighborhood examining method are developed based on the properties of the no-wait FSSPs. Due to the hybridization of DE-based evolutionary search and problem-dependent local search as well as the utilization of the speed-up evaluation and fast neighborhood examining, the no-wait FSSPs can be solved efficiently and effectively. Simulations and comparisons based on well-known benchmarks demonstrate the efficiency, effectiveness, and robustness of the proposed HDE.     

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.     

基于混合差分进化算法的无等待流水车间总流水时间优化*

以调度的总流水时间为优化目标, 提出一种混合差分进化算法。 首先, 建立无等待流水车间调度的问题模型,并用快速方法评估总流水时间指标。 其次,采用LPV规则,实现离散问题的连续编码; 用差分进化算法对总流水时间指标执行优化;引入插入邻域和基于pairwise的局部搜索算法, 分别对差分进化算法产生的新个体和差分进化算法的最优解执行邻域搜索, 达到优化目标全局和局部的最优。 最后,通过计算标准算例, 并与其他算法比较, 验证该混合差分进化算法的有效性。     

动态子和声算法求解无等待批量流水线问题

针对无等待批量流水线调度问题,根据和声算法的机理,提出了一种改进的和声算法对其进行求解。利用NEH和混沌序列相结合的方法产生初始解,并实现了和声向量与工序之间的转换;充分利用最优解,设计新的更新算子,为了避免陷入局部最优,引入了变异策略;结合蛙跳算法分组的特点,将和声库随机动态的分成了几个子和声;为平衡算法的全局开发和局部搜索的能力,对子和声中的最优解执行了局部搜索。通过仿真实验与其他几种算法进行比较,证明了算法的有效性。     

混合离散人工蜂群算法求解含不相关并行机的分布式柔性流水线调度

研究每阶段含不相关并行机的分布式柔性流水线调度问题.考虑顺序相关准备时间和工件动态到达时间,以最小化总加权提前/拖期惩罚为目标建立整数规划模型,提出一种融合离散差分进化算法、变邻域下降算法和局域搜索的混合离散人工蜂群算法以获取近优解.该算法采用基于工厂-工件号的编码以及基于机器最早空闲时间的动态解码机制,通过随机规则和均衡分派策略生成初始工厂-工件序列群,在引领蜂阶段引入离散差分进化算法产生优质工厂-工件序列,在跟随蜂阶段利用变邻域下降算法在被选择序列附近继续搜索以得到邻域序列,在侦察蜂阶段设计基于关键/非关键工厂间插入的局域搜索提高算法搜索能力.通过仿真实验测试不同规模的算例,实验结果表明,所提出的混合离散人工蜂群算法表现出较好的求解性能.     

融入概率学习的混合差分进化算法求解绿色分布式可重入作业车间调度

本文针对绿色分布式可重入作业车间调度问题(GDRJSSP), 提出一种融入概率学习的混合差分进化算法 (HDE PL), 以实现最大完工时间和总能耗最小. 根据GDRJSSP的问题特点, 设计编码和解码规则, 并采用差分进化 算法执行全局搜索来发现优质解区域. 为能更明确地引导全局搜索方向, 设计基于贝叶斯网络结构的多维概率模型 合理学习和积累优质解(即当前种群中的较优解)的模式信息. 结合问题解的结构特征, 提出基于关键路径的4种邻 域结构来构造局部搜索, 并设计基于非关键路径的节能策略来提升算法获取低能耗非劣解的能力. 仿真实验和算 法对比验证了HDE PL可有效求解GDRJSSP.     

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.     

Flexible job shop scheduling using hybrid differential evolution algorithms

This paper proposes hybrid differential evolution (HDE) algorithms for solving the flexible job shop scheduling problem (FJSP) with the criterion to minimize the makespan. Firstly, a novel conversion mechanism is developed to make the differential evolution (DE) algorithm that works on the continuous domain adaptive to explore the problem space of the discrete FJSP. Secondly, a local search algorithm based on the critical path is embedded in the DE framework to balance the exploration and exploitation by enhancing the local searching ability. In addition, in the local search phase, the speed-up method to find an acceptable schedule within the neighborhood structure is presented to improve the efficiency of whole algorithms. Extensive computational results and comparisons show that the proposed algorithms are very competitive with the state of the art, some new best known solutions for well known benchmark instances have even been found.     

Inventory based two-objective job shop scheduling model and its hybrid genetic algorithm

Job shop scheduling problem is a typical NP-hard problem. An inventory based two-objective job shop scheduling model was proposed in this paper, in which both the make-span (the total completion time) and the inventory capacity were as objectives and were optimized simultaneously. To solve the proposed model more effectively, some tailor made genetic operators were designed by making full use of the characteristics of the problem. Concretely, a new crossover operator based on the critical path was specifically designed. 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. The computer simulations were made on a set of benchmark problems and the results demonstrated the effectiveness of the proposed algorithm.     

Local Search Genetic Algorithms for the Job Shop Scheduling Problem

In previous work, we developed three deadlock removal strategies for the job shop scheduling problem (JSSP) and proposed a hybridized genetic algorithm for it. While the genetic algorithm (GA) gave promising results, its performance depended greatly on the choice of deadlock removal strategies employed. This paper introduces a genetic algorithm based scheduling scheme that is deadlock free. This is achieved through the choice of chromosome representation and genetic operators. We propose an efficient solution representation for the JSSP in which the job task ordering constraints are easily encoded. Furthermore, a problem specific crossover operator that ensures solutions generated through genetic evolution are all feasible is also proposed. Hence, both checking of the constraints and repair mechanism can be avoided, thus resulting in increased efficiency. A mutation-like operator geared towards local search is also proposed which further improves the solution quality. Lastly, a hybrid strategy using the genetic algorithm reinforced with a tabu search is developed. An empirical study is carried out to test the proposed strategies.     

A hybrid Jaya algorithm for solving flexible job shop scheduling problem considering multiple critical paths

As an extension of the classical job shop scheduling problem, flexible job shop scheduling problem (FJSP) is considered as a challenge in manufacturing systems for its complexity and flexibility. Meta-heuristic algorithms are shown effective in solving FJSP. However, the multiple critical paths issue, which has not been formally discussed in the existing literature, is discovered to be a primary obstacle for further optimization by meta-heuristics. In this paper, a hybrid Jaya algorithm integrated with Tabu search is proposed to solve FJSP for makespan minimization. Two Jaya operators are designed to improve solutions under a two-vector encoding scheme. During the local search phase, three approaches are proposed to deal with multiple critical paths and have been evaluated by experimental study and qualitative analyses. An incremental parameter setting strategy and a makespan estimation method are employed to speed up the searching process. The proposed algorithm is compared with several state-of-the-art algorithms on three well-known FJSP benchmark sets. Extensive experimental results suggest its superiority in both optimality and stability. Additionally, a real world scheduling problem, including six instances with different scales, is applied to further prove its ability in handling large-scale scheduling problems.     

基于改进教学算法的车间作业调度问题

为求解车间作业调度问题,提出一种基于个体差异化自学习的改进教学算法.针对教学算法局部搜索能力不高的缺陷, 提出学生不仅应向能力好的学习者学习,亦应进行有差异的自我学习.通过学习者的完工时间评估学生的学习能力,提出学习次数概念,并设计自学习算子,完善学生阶段的更新,提高算法的局部搜索能力.最后,对OR-Library中的标准仿真实例进行实验,结果表明改进教学算法是有效的,其在收敛精度和鲁棒性能上均有较好的提高.     

An improved iterated greedy algorithm with a Tabu-based reconstruction strategy for the no-wait flowshop scheduling problem

This paper proposes a Tabu-mechanism improved iterated greedy (TMIIG) algorithm to solve the no-wait flowshop scheduling problem with a makespan criterion. The idea of seeking further improvement in the iterated greedy (IG) algorithm framework is based on the observation that the construction phase of the original IG algorithm may not achieve good performance in escaping from local minima when incorporating the insertion neighborhood search. To overcome this limitation, we have modified the IG algorithm by utilizing a Tabu-based reconstruction strategy to enhance its exploration ability. A powerful neighborhood search method that involves insert, swap, and double-insert moves is then applied to obtain better solutions from the reconstructed solution in the previous step. Empirical results on several benchmark problem instances and those generated randomly confirm the advantages of utilizing the new reconstruction scheme. In addition, our results also show that the proposed TMIIG algorithm is relatively more effective in minimizing the makespan than other existing well-performing heuristic algorithms.     

一种具有混合编码的二进制差分演化算法

差分演化(DE)是Storn和Price于1997年提出的一种基于个体差异重组思想的演化算法,非常适用于求解连续域上的最优化问题.首先引入"差异算子"等概念,给出DE的一种简洁算法描述,并分析了它所具有的特性.然后,为了使DE能够求解离散域上的最优化问题,基于数学变换思想引入"辅助搜索空间"和"个体混合编码"等概念,通过定义一个特殊的满射变换,在辅助搜索空间的作用下将连续域上的高效差分演化搜索变换为离散域上的同步演化搜索,由此提出了第1个二进制差分演化算法:具有混合编码的二进制差分演化算法(HBDE).接着,给出了HBDE的依概率收敛和完全收敛的定义,并利用离散Markov随机理论证明了HBDE是完全收敛的. HBDE不仅完全具有DE的各种特性和所有优点,而且非常适用于求解离散域上的最优化问题,对随机生成的大规模3-SAT问题实例和典型0/1背包问题实例的数值计算表明:该算法具有很好的全局收敛性和稳定性,其性能远远超过二进制粒子群优化算法和遗传算法.     

A discrete differential evolution algorithm for the single machine total weighted tardiness problem with sequence dependent setup times

This paper is concerned with solving the single machine total weighted tardiness problem with sequence dependent setup times by a discrete differential evolution algorithm developed by the authors recently. Its performance is enhanced by employing different population initialization schemes based on some constructive heuristics such as the well-known NEH and the greedy randomized adaptive search procedure (GRASP) as well as some priority rules such as the earliest weighted due date (EWDD) and the apparent tardiness cost with setups (ATCS). Additional performance enhancement is further achieved by the inclusion of a referenced local search (RLS) in the algorithm together with the use of destruction and construction (DC) procedure when obtaining the mutant population. Furthermore, to facilitate the greedy job insertion into a partial solution which will be employed in the NEH, GRASP, DC heuristics as well as in the RLS local search, some newly designed speed-up methods are presented for the insertion move for the first time in the literature. They are novel contributions of this paper to the single machine tardiness related scheduling problems with sequence dependent setup times. To evaluate its performance, the discrete differential evolution algorithm is tested on a set of benchmark instances from the literature. Through the analyses of experimental results, its highly effective performance with substantial margins both in solution quality and CPU time is shown against the best performing algorithms from the literature, in particular, against the very recent newly designed particle swarm and ant colony optimization algorithms of Anghinolfi and Paolucci [A new discrete particle swarm optimization approach for the single machine total weighted tardiness scheduling problem with sequence dependent setup times. European Journal of Operational Research 2007; doi:10.1016/j.ejor.2007.10.044] and Anghinolfi and Paolucci [A new ant colony optimization approach for the single machine total weighted tardiness scheduling problem. http://www.discovery.dist.unige.it/papers/Anghinolfi_Paolucci_ACO.pdf, respectively. Ultimately, 51 out of 120 overall aggregated best known solutions so far in the literature are further improved while other 50 instances are solved equally.     

Multi-objective no-wait flow-shop scheduling with a memetic algorithm based on differential evolution

In this paper, a memetic algorithm (MA) based on differential evolution (DE), namely MADE, is proposed for the multi-objective no-wait flow-shop scheduling problems (MNFSSPs). Firstly, a largest-order-value rule is presented to convert individuals in DE from real vectors to job permutations so that the DE can be applied for solving flow-shop scheduling problems (FSSPs). Secondly, the DE-based parallel evolution mechanism is applied to perform effective exploration, and several local searchers developed according to the landscape of multi-objective FSSPs are applied to emphasize local exploitation. Thirdly, a speed-up computing method is developed based on the property of the no-wait FSSPs. In addition, the concept of Pareto dominance is used to handle the updating of solutions in sense of multi-objective optimization. Due to the well balance between DE-based global search and problem-dependent local search as well as the utilization of the speed-up evaluation, the MNFSSPs can be solved effectively and efficiently. Simulation results and comparisons demonstrate the effectiveness and efficiency of the proposed MADE.     

A hybrid harmony search algorithm for the flexible job shop scheduling problem

In this paper, a novel hybrid harmony search (HHS) algorithm based on the integrated approach, is proposed for solving the flexible job shop scheduling problem (FJSP) with the criterion to minimize makespan. First of all, to make the harmony search (HS) algorithm adaptive to the FJSP, the converting techniques are developed to convert the continuous harmony vector to a kind of discrete two-vector code for the FJSP. Secondly, the harmony vector is mapped into a feasible active schedule through effectively decoding the transformed two-vector code, which could largely reduce the search space. Thirdly, a resultful initialization scheme combining heuristic and random strategies is introduced to make the initial harmony memory (HM) occur with certain quality and diversity. Furthermore, a local search procedure is embedded in the HS algorithm to enhance the local exploitation ability, whereas HS is employed to perform exploration by evolving harmony vectors in the HM. To speed up the local search process, the improved neighborhood structure based on common critical operations is presented in detail. Empirical results on various benchmark instances validate the effectiveness and efficiency of our proposed algorithm. Our work also indicates that a well designed HS-based method is a competitive alternative for addressing the FJSP.     

An efficient simple metaheuristic for minimizing the makespan in two-machine no-wait job shops

This paper examines the problem of scheduling two-machine no-wait job shops to minimize makespan. The problem is known to be strongly NP-hard. A two-phase heuristic is developed to solve the problem. Phase 1 of the heuristic transforms the problem into a no-wait flow shop problem and solves it using the well known Gilmore and Gomory algorithm. Phase 2 of the heuristic improves the solution obtained in phase 1 using a simple tabu search algorithm. Computational results show that the proposed heuristic performs extremely well in terms of both solution quality and computation time. It finds an optimal solution to about 90% of the problem instances and the average deviation from the lower bond for the other problem instances is infinitesimal.