求解二重积分问题的差分进化算法

传统计算二重积分方法大都是等距分割方法,但是在在被积函数区间变化快慢相差较大时,计算精度大为降低。为此,提出一种不等距点分割的差分进化算法用于求解复杂函数的二重积分问题。在积分区域x向与y向上选取一些节点,将积分区域分割成很多小的子矩形域,并通过差分进化算法对其进行优化,使函数变化较快的区域分得小一些,函数变化较慢的区域分得大一些,从而得到较准确的二重积分。仿真结果表明,提出的算法收敛速度快,计算精度高,能计算较复杂的二重积分。     

基于进化策略方法求任意函数的数值积分

提出了两种基于进化策略求任意函数数值积分的新方法,其中方法一是基于混合基函数进化策略的数值积分算法;方法二是基于不等距点分割的进化策略数值积分算法.两种算法都采用适用于高维优化问题的单基因突变进化策略,使得该算法不但能计算通常意义下任意函数的定积分,而且能计算奇异函数积分和振荡函数积分.最后给出几个数值积分算例,并与传统数值积分方法作了比较,仿真结果分析表明,两种算法十分有效,能够快速有效地获得任意函数的数值积分值.     

改进的蝙蝠算法在数值积分中的应用研究

蝙蝠算法具有收敛速度快、潜在分布式和并行性等特点,但也存在着寻优精度不高、后期收敛速度慢、易陷入局部最优等问题。针对蝙蝠算法和目前数值积分方法的不足,把具有很强的全局寻优能力和局部搜索能力的差分进化算法融合到蝙蝠算法中,提出了一种基于差分进化算法的改进蝙蝠算法求任意函数数值积分的新方法,该算法不仅能求解通常意义下任意函数的定积分,而且能计算振荡积分和奇异积分。通过6个不同算例与当前数值积分方法比较,实验仿真结果表明,该算法是有效的和可行的,能够快速有效地获取任意函数的数值积分值。同时,扩展了蝙蝠算法的应用领域。     

基于遗传算法求任意函数的数值积分

针对复杂函数的数值积分问题,给出了若干个任意分割积分区间的数值积分的误差结果,并提出一种基于遗传算法的不等距节点分割的数值积分方法。该方法初始时在积分区间内任意选取一定的节点,通过遗传算法优化这些节点,在相邻节点间利用Simpson公式近似计算积分,最后得到较准确的积分结果。数值计算结果表明,该方法计算精度高,而且可以计算奇异函数及震荡函数的积分。     

基于进化策略的广义积分计算方法研究

提出了一种基于进化策略算法的广义积分计算新方法,该方法根据被积函数的变量区间任意选取分割点,作为进化策略的初始的群体,通过进化策略算法来优化这些分割点,最终可得到一些最优的分割点,然后再求和,再根据和函数定义适应度函数,在给定的终止条件下,可获的精度较高的积分值.最后,以广义积分(无穷积分),二重广义积分(瑕积分)为例,仿真结果表明,该算法相比传统的一些方法,具有计算精度高,自适应性强等特点.     

基于粒子群算法的二重积分方法研究

提出了一种基于粒子群算法的不等距节点数值积分方法,该方法初始时在矩形积分区域两个方向的区间内各自任意选取一定的节点,通过粒子群算法优化这些节点,以优化后的节点为分割点求数值积分的值,最后得到比较精确的积分结果.数值积分算例表明,该算法得到的积分值精度高,自适应强,是一种有效的数值积分方法,在数值计算和工程实际应用中具有一定的参考和应用价值.     

基于幂基函数变步长神经网络求解数值积分

提出一种基于幂基函数变步长神经网络算法求解数值积分的新方法,证明了该算法的收敛性以及数值积分的求解定理及推论。通过典型数值积分算例,计算机仿真实验表明,提出的基于幂基函数变步长神经网络积分算法相比传统的数值积分方法,具有计算精度高、收敛速度快、算法稳定等特点。     

分形变异因子修正的差分进化算法?

为提高差分进化算法的求解精度,其变异策略应适应目标函数整体变化趋势和随机变化部分。文中提出利用不同的Hurst指数的分形布朗运动改进差分进化算法变异策略,进而构建分形变异因子修正的差分进化算法。针对该算法应用CEC2005进化计算国际会议提出的25个标准测试函数进行测试,至少有10个测试函数的计算结果优于其他差分进化算法,其余测试结果大部分相近,因此文中算法能提高优化问题的求解精度和适应性。     

基于GPU的并行协同差分进化算法研究

针对大规模高维数复杂非线性函数优化的问题,提出一种新的基于GPU的协同差分进化算法。该方法将协同进化的思想引入启发式差分进化算法,随机分解大规模计算问题,利用GPU处理数据的并行性,同步计算分解后的子问题,加快算法的精度和收敛速度。实验对比结果表明,所提出的基于GPU的协同差分进化算法对大规模非线性函数优化具有更高的精度和效率。     

量子差分进化算法及在函数极值优化中的应用研究

本文提出一种基于量子差分进化算法的识别方法.首先根据样本数据建立非线性回归模型,然后采用差分进化算法优化模型参数.方法简单直观,物理概念清楚.以函数极值优化为例进行仿真,结果表明该方法计算效率有所降低,但寻优能力明显提高,整体优化性能优于原算法.     

Algorithm 36 SNIFF: Efficient self-tuning algorithm for numerical integration

A new adaptive algorithm for the integration of analytic functions is presented. The algorithm processes the integration interval by generating local subintervals whose length is controlled through a feedback loop. Control is performed by means of a relation derived on an analytical basis and valid for an arbitrary integration rule: two different estimates of an integral are used to compute the interval length necessary to obtain an integral estimate with accuracy within the assigned error bounds. The implied method for local generation of subintervals and an effective assumption of error partition among subintervals give rise to an adaptive algorithm provided with an accurate and very efficient integration process. The particular algorithm obtained by choosing the 6-point Gauß-Legendre integration rule is considered and extensive comparisons are made with other outstanding integration algorithms.     

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.     

改进DE/EDA算法在求解难约束优化问题中的应用研究*

针对约束优化问题13个Benchmark函数中最难求解的Bump函数,利用简单罚函数算子对DE/EDA算法进行改进,提出了改进DE/EDA算法。仿真实验结果表明,求解Bump函数最优解时,改进DE/EDA算法优于其他文献的算法,且比DE算法收敛速度更快,求解效果更好。     

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.

     

Modeling of oxygen mass transfer in the presence of oxygen-vectors using neural networks developed by differential evolution algorithm

The search capabilities of the Differential Evolution (DE) algorithm – a global optimization technique – make it suitable for finding both the architecture and the best internal parameters of a neural network, usually determined by the training phase. In this paper, two variants of the DE algorithm (classical DE and self-adaptive mechanism) were used to obtain the best neural networks in two distinct cases: for prediction and classification problems. Oxygen mass transfer in stirred bioreactors is modeled with neural networks developed with the DE algorithm, based on the consideration that the oxygen constitutes one of the decisive factors of cultivated microorganism growth and can play an important role in the scale-up and economy of aerobic biosynthesis systems. The coefficient of mass transfer oxygen is related to the viscosity, superficial speed of air, specific power, and oxygen-vector volumetric fraction (being predicted as function of these parameters) using stacked neural networks. On the other hand, simple neural networks are designed with DE in order to classify the values of the mass transfer coefficient oxygen into different classes. Satisfactory results are obtained in both cases, proving that the neural network based modeling is an appropriate technique and the DE algorithm is able to lead to the near-optimal neural network topology.     

Orthogonal Algorithm of Logic Probability and Syndrome-Testable Analysis

A new method,orthogonal algoritm,is presented to compute the logic probabilities(i.e.signal probabilities)accurately,The transfer properties of logic probabilities are studied first,which are useful for the calculation of logic probability of the circuit with random independent inputs.Then the orthogonal algoritm is described to compute the logic probability of Boolean function realized by a combinational circuit.This algorithm can make Boolean function “ORTHOGONAL”so that the logic probabilities can be easily calculated by summing up the logic probabilities of all orthogonal terms of the Booleam function.     

有理曲面的区间隐式化

利用一个低阶多项式区间隐式曲面来包围所给的参数式有理曲面,并构造了一些关于区间隐式曲面厚度和微分张量的目标函数.在最小化这些目标函数的条件下,该区间隐式曲面的中心曲面可以近似地逼近有理曲面,其逼近的误差可以利用区间隐式曲面的区间宽度进行估计.最后提供了具体的算法和一些实例.     

一种基于正交设计的快速差分演化算法及其应用研究

为了进一步加快差分演化算法的速度和增强算法的鲁棒性,提出了一种基于正交设计的快速差分演化算法,并把它应用于函数优化问题的求解中.新算法在保持传统差分演化算法的简单、有效等特性的同时,具有以下特征：1）采用基于正交设计的杂交算子,并结合直观统计法产生最优子个体;2）采用决策变量分块策略,以减少正交实验次数,加快算法收敛速度;3）提出一种基于非凸理论的多父体混合自适应杂交变异算子,以增强算法的非凸搜索能力和自适应能力;4）简化基本差分演化算法的缩放因子,尽量减少算法的控制参数,方便工程人员的使用.通过对12个标准测试函数进行实验,并与其他演化算法的结果相比较,其结果表明,新算法在解的精度、稳定性和收敛性上表现出很好的性能.