Differential Evolution Training Algorithm for Feed-Forward Neural Networks

An evolutionary optimization method over continuous search spaces, differential evolution, has recently been successfully applied to real world and artificial optimization problems and proposed also for neural network training. However, differential evolution has not been comprehensively studied in the context of training neural network weights, i.e., how useful is differential evolution in finding the global optimum for expense of convergence speed. In this study, differential evolution has been analyzed as a candidate global optimization method for feed-forward neural networks. In comparison to gradient based methods, differential evolution seems not to provide any distinct advantage in terms of learning rate or solution quality. Differential evolution can rather be used in validation of reached optima and in the development of regularization terms and non-conventional transfer functions that do not necessarily provide gradient information. This revised version was published online in June 2006 with corrections to the Cover Date.     

A hybrid differential evolution augmented Lagrangian method for constrained numerical and engineering optimization

We present a new hybrid method for solving constrained numerical and engineering optimization problems in this paper. The proposed hybrid method takes advantage of the differential evolution (DE) ability to find global optimum in problems with complex design spaces while directly enforcing feasibility of constraints using a modified augmented Lagrangian multiplier method. The basic steps of the proposed method are comprised of an outer iteration, in which the Lagrangian multipliers and various penalty parameters are updated using a first-order update scheme, and an inner iteration, in which a nonlinear optimization of the modified augmented Lagrangian function with simple bound constraints is implemented by a modified differential evolution algorithm. Experimental results based on several well-known constrained numerical and engineering optimization problems demonstrate that the proposed method shows better performance in comparison to the state-of-the-art algorithms.     

A novel clustering-based differential evolution with 2 multi-parent crossovers for global optimization

Differential evolution (DE) is a simple and efficient global optimization algorithm. However, DE has been shown to have certain weaknesses, especially if the global optimum should be located using a limited number of function evaluations (NFEs). Hence hybridization with other methods is a research direction for the improvement of differential evolution. In this paper, a hybrid DE based on the one-step k-means clustering and 2 multi-parent crossovers, called clustering-based differential evolution with 2 multi-parent crossovers (2-MPCs-CDE) is proposed for the unconstrained global optimization problems. In 2-MPCs-CDE, k cluster centers and several new individuals generate two search spaces. These spaces are then searched in turn. This method utilizes the information of the population effectively and improves search efficiency. Hence it can enhance the performance of DE. A comprehensive set of 35 benchmark functions is employed for experimental verification. Experimental results indicate that 2-MPCs-CDE is effective and efficient. Compared with other state-of-the-art evolutionary algorithms, 2-MPCs-CDE performs better, or at least comparably, in terms of the solution accuracy and the convergence rate.     

动态识别三维几何约束冲突的方法研究

基于装配几何特征的广义几何约束图,避免了传统几何约束图的超图性质和模糊性,为几何约束满足问题提供了一个清晰的分析模型。文中以此模型来分析产生约束冲突的原因。空间分析法定义和推导了约束满足空间约束满足条件,提出了自由空间和自由度的计算方法,并据此在动态满足三维几何约束的过程中识别约束冲突,明确指出产生约束冲突的原因。     

差分演化优化Ncut准则的彩色图像分割

针对解Ncut准则的SM算法寻优能力不足的问题,提出一种基于差分演化优化归一化准则的彩色图像分割算法。首先对彩色图像进行爬山法预分割为多类,并构造类级间的无向完全图,之后再使用二进制差分演化算法求得Ncut准则最小化的图二分,最后通过映射获得图像的二值分割。实验结果表明,在相同预处理情况下,本文的寻优算法与SM算法相比,分割效果更为精准。     

Sensor Network Structure Recognition Based on P-law

A sensor graph network is a sensor network model organized according to graph network structure. Structural unit and signal propagation of core nodes are the basic characteristics of sensor graph networks. In sensor networks, network structure recognition is the basis for accurate identification and effective prediction and control of node states. Aiming at the problems of difficult global structure identification and poor interpretability in complex sensor graph networks, based on the characteristics of sensor networks, a method is proposed to firstly unitize the graph network structure and then expand the unit based on the signal transmission path of the core node. This method which builds on unit patulousness and core node signal propagation (called p-law) can rapidly and effectively achieve the global structure identification of a sensor graph network. Different from the traditional graph network structure recognition algorithms such as modularity maximization and spectral clustering, the proposed method reveals the natural evolution process and law of graph network subgroup generation. Experimental results confirm the effectiveness, accuracy and rationality of the proposed method and suggest that our method can be a new approach for graph network global structure recognition.     

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.     

基于差分进化算法多处理机任务调度研究

本文主要基于现代启发式差分算法讨论多处理机调度,多处理机调度是NP组合优化问题,目前多采用启发算法。差分进化算法是最近提出的进化算法,主要根据父代个体之间矢量差构造下一代,是一种全局优化搜索方式。本文考虑采用差分进化矢量优先级模型描述调度顺序进行调度,与模拟退火算法比较得到较好调度结果。     

A parallel algorithm for graph matching and its MasParimplementation

Search of discrete spaces is important in combinatorial optimization. Such problems arise in artificial intelligence, computer vision, operations research, and other areas. For realistic problems, the search spaces to be processed are usually huge, necessitating long computation times, pruning heuristics, or massively parallel processing. We present an algorithm that reduces the computation time for graph matching by employing both branch-and-bound pruning of the search tree and massively-parallel search of the as-yet-unpruned portions of the space. Most research on parallel search has assumed that a multiple-instruction-stream/multiple-data-stream (MIMD) parallel computer is available. Since massively parallel stream (SIMD) computers are much less expensive than MIMD systems with equal numbers of processors, the question arises as to whether SIMD systems can efficiently handle state-space search problems. We demonstrate that the answer is yes, and in particular, that graph matching has a natural and efficient implementation on SIMD machines     

A Graphical Tool for Describing the Temporal Evolution of Clusters in Financial Stock Markets

We propose a methodology for clustering financial time series of stocks’ returns, and a graphical set-up to quantify and visualise the evolution of these clusters through time. The proposed graphical representation allows for the application of well known algorithms for solving classical combinatorial graph problems, which can be interpreted as problems relevant to portfolio design and investment strategies. We illustrate this graph representation of the evolution of clusters in time and its use on real data from the Madrid Stock Exchange market.     

Advances in swift analysis of structures: Near-regular structures,and optimal analysis and design

In this paper a review of optimal analysis of structures is presented. Different methods of swift analyses are employed for various problem formulations. Depending on the problem at hand, a proper combination of graph products, sub-structuring methods, finite difference method and manipulating the stiffness matrix manipulation is selected to achieve the most efficient design. Design problems can be classified as three types. The first type includes the solution of near-regular structures using graph products and sub-structuring methods. These structures consist of two groups. In the first group, the main structure contains some additional members with respect to its corresponding regular structure while the structures in the second group contain some additional nodes with respect to the corresponding regular structures. The second type of problems includes the simultaneous optimal analysis and optimal design of structures. The presented method is applicable to an arbitrary structure and the optimal solution is obtained by manipulating the stiffness matrices and taking advantages of the iterations during design process. The third type of problems includes the efficient modal analysis of structures using a combined finite difference method and graph products. Boundary-value and initial-value differential equations are solved using finite difference method and graph products, and then the method is applied to the dynamic equations of modal analysis.     

Two hybrid differential evolution algorithms for engineering design optimization

This paper presents two hybrid differential evolution algorithms for optimizing engineering design problems. One hybrid algorithm enhances a basic differential evolution algorithm with a local search operator, i.e., random walk with direction exploitation, to strengthen the exploitation ability, while the other adding a second metaheuristic, i.e., harmony search, to cooperate with the differential evolution algorithm so as to produce the desirable synergetic effect. For comparison, the differential evolution algorithm that the two hybrids are based on is also implemented. All algorithms incorporate a generalized method to handle discrete variables and Deb's parameterless penalty method for handling constraints. Fourteen engineering design problems selected from different engineering fields are used for testing. The test results show that: (i) both hybrid algorithms overall outperform the differential evolution algorithms; (ii) among the two hybrid algorithms, the cooperative hybrid overall outperforms the other hybrid with local search; and (iii) the performance of proposed hybrid algorithms can be further improved with some effort of tuning the relevant parameters.     

针对动态目标的多无人机协同组合差分进化搜索方法

针对多无人机动态目标协同搜索问题,提出一种组合差分进化无人机协同搜索航迹规划方法.建立动态目标协同搜索环境信息图模型及无人机运动模型.基于改进差分蝙蝠算法和自适应差分进化算法,设计基于种群数量自适应分配的组合框架,将差分进化算法中的变异、交叉和选择机制引入蝙蝠算法,构建组合差分进化算法的协同搜索算法,并对无人机动态目标协同搜索的航迹进行优化.针对待搜索目标轨迹随机多变且具有规避侦察特性的现实场景,建立可回访数字信息图和自适应目标搜索增益函数,从而提高无人机对动态目标的捕获能力.最后,通过仿真结果验证所提出的无人机动态目标协同搜索算法的有效性.     

Multi-elite guide hybrid differential evolution with simulated annealing technique for dynamic economic emission dispatch

This paper proposes an improved multi-objective differential evolutionary algorithm named multi-objective hybrid differential evolution with simulated annealing technique (MOHDE-SAT) to solve dynamic economic emission dispatch (DEED) problem. The proposed MOHDE-SAT integrates the orthogonal initialization method into the differential evolution, which enlarges the population diversity at the beginning of population evolution. In addition, modified mutation operator and archive retention mechanisms are used to control convergence rate, and simulated annealing technique and entropy diversity method are utilized to adaptively monitor the population diversity as the evolution proceeds, which can properly avoid the premature convergence problem. Furthermore, the MOHDE-SAT is applied on the thermal system with a heuristic constraint handling method, and obtains more desirable results in comparison to those alternatives established recently. The obtained results also reveal that the proposed MOHDE-SAT can provide a viable way for solving DEED problems.     

一种维持种群多样性的多目标差分演化算法

差分演化算法是一种简单而有效的全局优化算法。本文将差分演化算法用于求解多目标优化问题,给出了一种维持种群多样性的多目标差分演化算法。该算法采用正交设计法初始化种群,改进差分演化算子,从而有利于维持种群多样性,提高演化算法的搜索性能。初步实验表明,新算法能有效地求解多目标优化问题。     

基于混沌差分进化FCM算法的舵回路故障诊断

为了提高故障分类的准确性,提出了一种混沌差分进化模糊C-均值故障识别方法(CDEFCM,chaotic differential evolution fuzzy C-mean).该方法利用差分进化算法高效的全局搜索能力以及混沌序列的均匀遍历特性,克服了模糊C-均值算法(FCM,fuzzy C-mean)对初始值敏感的缺点及遗传算法易收敛到局部极值点的缺陷,用该方法进行故障聚类分析,可以准确地识别故障.以某飞控系统舵回路常见故障为例进行了仿真验证,结果表明该方法能有效地识别出故障.     

量子协同的二分图最大权完美匹配求解方法

信息科学中许多组合优化问题可抽象为二分图最大权完美匹配问题.由于数据量的增长,经典算法难以平衡匹配问题求解效率和求解精度的矛盾.基于此,提出一种适用于求解通用最大权完美匹配的智能优化方法.该方法将原始的矩阵形式的匹配候选解转换成可被智能优化算法处理的演化基结构,通过子代选择和量子策略协同过程,自适应地从改进的离散粒子群策略以及模拟退火策略中选择适用于当前演化过程的有效策略,并在保持种群稳定进化的同时促使种群快速收敛.通过不同类型检验函数以及不同维度匹配矩阵的实验,结果表明：与其他方法相比,该方法在有限迭代次数内具有较高的收敛精度以及较快的收敛速度,体现出对经典问题以及高维匹配问题的适应能力.     

A Fuzzy Adaptive Differential Evolution Algorithm

The differential evolution algorithm is a floating-point encoded evolutionary algorithm for global optimization over continuous spaces. The algorithm has so far used empirically chosen values for its search parameters that are kept fixed through an optimization process. The objective of this paper is to introduce a new version of the Differential Evolution algorithm with adaptive control parameters – the fuzzy adaptive differential evolution algorithm, which uses fuzzy logic controllers to adapt the search parameters for the mutation operation and crossover operation. The control inputs incorporate the relative objective function values and individuals of the successive generations. The emphasis of this paper is analysis of the dynamics and behavior of the algorithm. Experimental results, provided by the proposed algorithm for a set of standard test functions, outperformed those of the standard differential evolution algorithm for optimization problems with higher dimensionality.     

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems (LSMOPs) pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces. While evolutionary algorithms are good at solving small-scale multi-objective optimization problems, they are criticized for low efficiency in converging to the optimums of LSMOPs. By contrast, mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems, but they have difficulties in finding diverse solutions for LSMOPs. Currently, how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored. In this paper, a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method. On the one hand, conjugate gradients and differential evolution are used to update different decision variables of a set of solutions, where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front. On the other hand, objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions, and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent. In comparison with state-of-the-art evolutionary algorithms, mathematical programming methods, and hybrid algorithms, the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.      

ICPN的时间自动机构造方法

为克服Petri网行为演变分析技术的局限性,利用时间自动机技术分析区间速率连续Petri网(ICPN)特性。根据区间速率连续Petri网模型语义提出基于冲突消解的区间速率连续Petri网状态演变图构造算法,给出状态演变图的时间自动机构造方法。对某化工生产过程的分析表明了该方法的必要性和有效性。