An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

基于多种群差分进化的多目标优化算法

针对差分进化算法(Differential Evolution Algorithm,DE)求解多目标优化问题时易陷入局部最优的问题,设计了一种双向搜索机制,它通过对相反进化方向产生的两个子代个体进行评价,来增强DE算法的局部搜索能力;设计了多种群机制,它可令各子群独立进化一定次数再执行全局进化,以完成子群间进化信息的交流,这一方面降低了算法陷入局部最优的风险,另一方面增强了Pareto解集的多样性,使Pareto前沿面的解集分布更为均匀。实验结果表明,相比于NSGA-II等同类算法,所提方法在搜索Pareto最优解时效率更高,并且Pareto最优解集的精度及分布程度比前者更好。     

A self-adaptive differential evolution algorithm for continuous optimization problems

This paper proposes a new self-adaptive differential evolution algorithm (DE) for continuous optimization problems. The proposed self-adaptive differential evolution algorithm extends the concept of the DE/current-to-best/1 mutation strategy to allow the adaptation of the mutation parameters. The control parameters in the mutation operation are gradually self-adapted according to the feedback from the evolutionary search. Moreover, the proposed differential evolution algorithm also consists of a new local search based on the krill herd algorithm. In this study, the proposed algorithm has been evaluated and compared with the traditional DE algorithm and two other adaptive DE algorithms. The experimental results on 21 benchmark problems show that the proposed algorithm is very effective in solving complex optimization problems.     

A HYBRID METAHEURISTIC FOR THE SINGLE-MACHINE TOTAL WEIGHTED TARDINESS PROBLEM

This article presents a new hybrid algorithm for combinatorial optimization that combines differential evolution (DE) with variable neighborhood search (VNS). DE (a population heuristic for optimization over continuous search spaces) is used as global optimizer for solution evolution guiding the search toward the optimal regions of the search space; VNS (a random local search heuristic based on the systematic change of neighborhood) is used as a local optimizer performing a sequence of local changes on individual DE solutions until a local optimum is found. The effectiveness of a DE-VNS approach is demonstrated on the solution of the single-machine total weighted tardiness scheduling problem. The concepts of Lamarckian and Baldwinian learning are also investigated and discussed. Experiments on known benchmark data sets show that DE-VNS with Lamarckian learning can produce high-quality schedules in a rather short computation time. DE-VNS uses a self-adapted mechanism for tuning the required control parameters, a critical feature rendering it applicable to real-life scheduling problems.     

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.     

混合模式搜索的分布式memetic差分进化算法

针对差分进化（DE）算法存在的早熟收敛与搜索停滞的问题,提出memetic分布式差分进化（DDE）算法。将memetic算法的思想融入到差分进化算法中,采用分布式的种群结构以及memetic算法中的混合策略,前者将初始种群分为多个子种群,子种群间根据冯·诺依曼拓扑结构周期性地实现信息交流,后者将差分进化算法作为进化的主要框架,模式搜索作为辅助手段,从而平衡算法的探索与开发能力。所提算法充分利用了模式搜索和差分进化算法的优势,建立了有效的搜索机制,增强了算法摆脱局部最优的能力,能够满足搜索过程对种群多样性及收敛速度的需求。将所提算法与几种先进的差分进化算法相比较,对标准测试函数进行优化的实验结果显示：所提算法在解的质量和收敛性能方面,均优于其他几种相比较的先进的差分进化算法。     

Nonlinear system identification using memetic differential evolution trained neural networks

Several gradient-based approaches such as back propagation (BP) and Levenberg Marquardt (LM) methods have been developed for training the neural network (NN) based systems. But, for multimodal cost functions these procedures may lead to local minima, therefore, the evolutionary algorithms (EAs) based procedures are considered as promising alternatives. In this paper we focus on a memetic algorithm based approach for training the multilayer perceptron NN applied to nonlinear system identification. The proposed memetic algorithm is an alternative to gradient search methods, such as back-propagation and back-propagation with momentum which has inherent limitations of many local optima. Here we have proposed the identification of a nonlinear system using memetic differential evolution (DE) algorithm and compared the results with other six algorithms such as Back-propagation (BP), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), Genetic Algorithm Back-propagation (GABP), Particle Swarm Optimization combined with Back-propagation (PSOBP). In the proposed system identification scheme, we have exploited DE to be hybridized with the back propagation algorithm, i.e. differential evolution back-propagation (DEBP) where the local search BP algorithm is used as an operator to DE. These algorithms have been tested on a standard benchmark problem for nonlinear system identification to prove their efficacy. First examples shows the comparison of different algorithms which proves that the proposed DEBP is having better identification capability in comparison to other. In example 2 good behavior of the identification method is tested on an one degree of freedom (1DOF) experimental aerodynamic test rig, a twin rotor multi-input-multi-output system (TRMS), finally it is applied to Box and Jenkins Gas furnace benchmark identification problem and its efficacy has been tested through correlation analysis.     

Improved differential evolution algorithms for solving generalized assignment problem

This paper presents algorithms based on differential evolution (DE) to solve the generalized assignment problem (GAP) with the objective to minimize the assignment cost under the limitation of the agent capacity. Three local search techniques: shifting, exchange, and k-variable move algorithms are added to the DE algorithm in order to improve the solutions. Eight DE-based algorithms are presented, each of which uses DE with a different combination of local search techniques. The experiments are carried out using published standard instances from the literature. The best proposed algorithm using shifting and k-variable move as the local search (DE-SK) techniques was used to compare its performance with those of Bee algorithm (BEE) and Tabu search algorithm (TABU). The computational results revealed that the BEE and DE-SK are not significantly different while the DE-SK outperforms the TABU algorithm. However, even though the statistical test shows that DE-SK is not significantly different compared with the BEE algorithm, the DE-SK is able to obtain more optimal solutions (87.5%) compared to the BEE algorithm that can obtain only 12.5% optimal solutions. This is because the DE-SK is designed to enhance the search capability by improving the diversification using the DE's operators and the k-variable moves added to the DE can improve the intensification. Hence, the proposed algorithms, especially the DE-SK, can be used to solve various practical cases of GAP and other combinatorial optimization problems by enhancing the solution quality, while still maintaining fast computational time.     

Accelerating Differential Evolution Using an Adaptive Local Search

We propose a crossover-based adaptive local search (LS) operation for enhancing the performance of standard differential evolution (DE) algorithm. Incorporating LS heuristics is often very useful in designing an effective evolutionary algorithm for global optimization. However, determining a single LS length that can serve for a wide range of problems is a critical issue. We present a LS technique to solve this problem by adaptively adjusting the length of the search, using a hill-climbing heuristic. The emphasis of this paper is to demonstrate how this LS scheme can improve the performance of DE. Experimenting with a wide range of benchmark functions, we show that the proposed new version of DE, with the adaptive LS, performs better, or at least comparably, to classic DE algorithm. Performance comparisons with other LS heuristics and with some other well-known evolutionary algorithms from literature are also presented.     

A Review on Swarm Intelligence and Evolutionary Algorithms for Solving Flexible Job Shop Scheduling Problems

Flexible job shop scheduling problems (FJSP) have received much attention from academia and industry for many years. Due to their exponential complexity, swarm intelligence (SI) and evolutionary algorithms (EA) are developed, employed and improved for solving them. More than 60% of the publications are related to SI and EA. This paper intents to give a comprehensive literature review of SI and EA for solving FJSP. First, the mathematical model of FJSP is presented and the constraints in applications are summarized. Then, the encoding and decoding strategies for connecting the problem and algorithms are reviewed. The strategies for initializing algorithms? population and local search operators for improving convergence performance are summarized. Next, one classical hybrid genetic algorithm (GA) and one newest imperialist competitive algorithm (ICA) with variables neighborhood search (VNS) for solving FJSP are presented. Finally, we summarize, discus and analyze the status of SI and EA for solving FJSP and give insight into future research directions.      

改进的离散型萤火虫优化算法求解柔性作业车间调度问题

针对传统的群智能优化算法在求解柔性作业车间调度问题(FJSP)时,存在寻优能力不足且易陷入局部最优等缺点,本文以最小化最大完工时间为目标,将萤火虫算法(FA)用于求解柔性作业车间调度问题,提出一种改进的离散型萤火虫算法(DFA)。首先,通过两段式编码建立FA连续优化问题与FJSP离散优化问题之间的联系;其次,设计一种群初始化方法,以确保初始解的质量以及多样性;然后,提出改进离散型萤火虫优化算法并引入局部搜索算法,加强算法的全局搜索能力和局部搜索能力;最后,对标准算例进行仿真,验证DFA算法求解FJSP的有效性。通过与遗传算法和粒子群优化算法进行仿真对比,表明了DFA求解FJSP的优越性。     

一种改进的微分进化算法

相对于其他优化算法来说,微分进化算法具有控制参数少、易于使用以及鲁棒性强等特点,但在搜索过程中存在着局部搜索能力弱的缺点。针对微分进化算法局部搜索能力弱的缺点,提出了一种基于局部变异的微分进化算法,该算法使个体具有良好快速收敛能力。使用典型优化函数对比较算法进行了测试,算法分析和仿真结果表明,改进以后的算法具有寻优能力...     

一种求解多模态复杂问题的混合和声差分算法

针对多模态复杂优化问题,提出了一种基于和声搜索和差分进化的混合优化算法:HHSDE算法。在不同的进化阶段,HHSDE算法依据累积加权更新成功率来自适应地选择和声算法或差分算法作为更新下一代种群的方式,并改进了差分算法的变异策略来平衡差分算法的全局与局部搜索能力。通过对10个多模态Benchmark函数进行测试,利用Wilcoxon秩和检验对不同算法的计算结果进行比较,结果表明HHSDE算法具有收敛速度快,求解精度高,稳定性好等优势。     

求解高维多模优化问题的自适应差分进化算法

在基变量选择方差理论分析的基础上,提出一种自适应差分进化算法(ADE).ADE算法通过设计自适应收敛因子构建自调整的权重质心变异策略,同时在交叉策略中引入发射、收缩两种单纯形操作算子,保证算法全局搜索能力的同时,能钉效提高算法后期的局部增强能力.30个优化问题的数值研究结果表明ADE算法具有比DE、DERL以及DERB三种算法更快的收敛速度和可靠性,尤其适合于高维多模优化问题的求解.     

Modified differential evolution approach for optimization of planar parallel manipulators force capabilities

The global optimization problem is not easy to solve and is still an open challenge for researchers since an analytical optimal solution is difficult to obtain even for relatively simple application problems. Conventional deterministic numerical algorithms tend to stop the search in local minimum nearest to the input starting point, mainly when the optimization problem presents nonlinear, non-convex and non-differential functions, multimodal and nonlinear. Nowadays, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. The primary advantage of EAs over other numerical methods is that they just require the objective function values, while properties such as differentiability and continuity are not necessary. In this context, the differential evolution (DE), a paradigm of the evolutionary computation, has been widely used for solving numerical global optimization problems in continuous search space. DE is a powerful population-based stochastic direct search method. DE simulates natural evolution combined with a mechanism to generate multiple search directions based on the distribution of solutions in the current population. Among DE advantages are its simple structure, ease of use, speed, and robustness, which allows its application on several continuous nonlinear optimization problems. However, the performance of DE greatly depends on its control parameters, such as crossover rate, mutation factor, and population size and it often suffers from being trapped in local optima. Conventionally, users have to determine the parameters for problem at hand empirically. Recently, several adaptive variants of DE have been proposed. In this paper, a modified differential evolution (MDE) approach using generation-varying control parameters (mutation factor and crossover rate) is proposed and evaluated. The proposed MDE presents an efficient strategy to improve the search performance in preventing of premature convergence to local minima. The efficiency and feasibility of the proposed MDE approach is demonstrated on a force optimization problem in Robotics, where the force capabilities of a planar 3-RRR parallel manipulator are evaluated considering actuation limits and different assembly modes. Furthermore, some comparison results of MDE approach with classical DE to the mentioned force optimization problem are presented and discussed.     

A novel hybrid DE–random search approach for unit commitment problem

Differential evolution (DE) is a population-based stochastic search algorithm, whose simple yet powerful and straightforward features make it very attractive for numerical optimization. DE uses a rather greedy and less stochastic approach to problem-solving than other evolutionary algorithms. DE combines simple arithmetic operators with the classical operators of recombination, mutation and selection to evolve from a randomly generated starting population to a final solution. Although global exploration ability of DE algorithm is adequate, its local exploitation ability is feeble and convergence velocity is too low and it suffers from the problem of untime convergence for multimodal objective function, in which search process may be trapped in local optima and it loses its diversity. Also, it suffers from the stagnation problem, where the search process may infrequently stop proceeding toward the global optimum even though the population has not converged to a local optimum or any other point. To improve the exploitation ability and global performance of DE algorithm, a novel and hybrid version of DE algorithm is presented in the proposed research. This research paper presents a hybrid version of DE algorithm combined with random search for the solution of single-area unit commitment problem. The hybrid DE–random search algorithm is tested with IEEE benchmark systems consisting of 4, 10, 20 and 40 generating units. The effectiveness of proposed hybrid algorithm is compared with other well-known evolutionary, heuristics and meta-heuristics search algorithms, and by experimental analysis, it has been found that proposed algorithm yields global results for the solution of unit commitment problem.

     

基于模拟退火的混合差分进化算法及其在联合补货-配送集成优化中的应用

针对差分进化 (Differential evolution, DE)算法搜索效率较低和容易陷入局部最优的缺点,设计了基于SA的混合差分进化算法(SA-based Hybrid DE, SAHDE),以提高DE算法的全局寻优能力。该算法采用自适应变异算子和交叉算子,并结合模拟退火(Simulated Annealing, SA)算法的Metropolis 准则。首先通过标准测试函数对改进的SAHDE进行性能测试,证明了该算法比DE、自适应混合DE (Adaptive Hybrid DE, AHDE)和遗传算法(Genetic Algorithm, GA)更有效。进而将该算法运用到联合补货-配送集成优化(典型NP-hard)问题的求解中,通过大规模的算例分析,证实SAHDE在解决联合补货-配送优化问题比DE、AHDE和GA更有效。     

An integrated search heuristic for large-scale flexible job shop scheduling problems

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop scheduling problem (JSP), where each operation is allowed to be processed by any machine from a given set, rather than one specified machine. In this paper, two algorithm modules, namely hybrid harmony search (HHS) and large neighborhood search (LNS), are developed for the FJSP with makespan criterion. The HHS is an evolutionary-based algorithm with the memetic paradigm, while the LNS is typical of constraint-based approaches. To form a stronger search mechanism, an integrated search heuristic, denoted as HHS/LNS, is proposed for the FJSP based on the two algorithms, which starts with the HHS, and then the solution is further improved by the LNS. Computational simulations and comparisons demonstrate that the proposed HHS/LNS shows competitive performance with state-of-the-art algorithms on large-scale FJSP problems, and some new upper bounds among the unsolved benchmark instances have even been found.     

Remote sensing image subpixel mapping based on adaptive differential evolution

In this paper, a novel subpixel mapping algorithm based on an adaptive differential evolution (DE) algorithm, namely, adaptive-DE subpixel mapping (ADESM), is developed to perform the subpixel mapping task for remote sensing images. Subpixel mapping may provide a fine-resolution map of class labels from coarser spectral unmixing fraction images, with the assumption of spatial dependence. In ADESM, to utilize DE, the subpixel mapping problem is transformed into an optimization problem by maximizing the spatial dependence index. The traditional DE algorithm is an efficient and powerful population-based stochastic global optimizer in continuous optimization problems, but it cannot be applied to the subpixel mapping problem in a discrete search space. In addition, it is not an easy task to properly set control parameters in DE. To avoid these problems, this paper utilizes an adaptive strategy without user-defined parameters, and a reversible-conversion strategy between continuous space and discrete space, to improve the classical DE algorithm. During the process of evolution, they are further improved by enhanced evolution operators, e.g., mutation, crossover, repair, exchange, insertion, and an effective local search to generate new candidate solutions. Experimental results using different types of remote images show that the ADESM algorithm consistently outperforms the previous subpixel mapping algorithms in all the experiments. Based on sensitivity analysis, ADESM, with its self-adaptive control parameter setting, is better than, or at least comparable to, the standard DE algorithm, when considering the accuracy of subpixel mapping, and hence provides an effective new approach to subpixel mapping for remote sensing imagery.     

基于改进量子差分进化的含分布式电源的配电网无功优化

差分进化算法（DE）已被证明为解决无功优化问题的有效方法.随着越来越多的分布式电源并网,对配电网潮流、电压均有一定改变,同时也影响了DE的鲁棒性和性能.本文在研究DE基础上,针对其收敛过早、局部搜索能力较差的缺陷,分析了量子计算思想和人工蜂群算法的优势,提出改进量子差分进化混合算法（IQDE）.通过量子编码思想提高了种群个体的多样性,人工蜂群算法的观察蜂加速进化操作和侦查蜂随机搜索操作分别提高了算法的局部搜索和全局搜索性能.建立以有功网损最小为目标的数学模型,将IQDE算法和DE算法分别用于14节点和30节点标准数据集进行大量仿真实验.实验结果表明,IQDE算法用更少的收敛时间、更小的种群规模便可以获得与DE算法相同甚至更佳的优化效果,并且可以很好的应用于解决难分布式电源的配电网无功优化问题.