基于个体优化的自适应小生境遗传算法

针对遗传算法在处理复杂多峰函数优化问题时易于早熟和局部搜索能力差等问题,提出一种基于个体优化的自适应小生境遗传算法。在自适应小生境的基础上,利用进化过程中相邻个体的信息产生的试探点标记的算法进化方向,缩短邻域搜索的区间,提高算法的局部搜索能力。对复杂多峰问题进行的优化实验结果证明,该算法能快速可靠地收敛到全局最优解,其收敛速度和解精度均优于简单遗传算法和其他小生境算法。     

模式搜索法在最优化问题中的应用

模式搜索方法(pattenrsearch)是求解最优化问题的一种直接搜索方法,它不要求目标函数必须可微或者连续,是求解不可导或求导代价较大的最优化问题的一种有效方法。介绍了模式搜索法的原理与改进,以及Matlab模式搜索工具箱应用实例     

一种用于图象帧间主运动估计的快速线搜索方法

本文中作者提出了一种新的基于鲁棒统计的快速搜索方法,可以用于图象帧间主运动估计,能够提高提高算法速度,近年来,一种新的参数估计技术－鲁棒统计－被越来越广泛地用于主运动估计,与传统的基于最小二乘的估计方法相比较,鲁棒统计对于外点具有更好的鲁棒性,但运算复杂度较高,而主运动估计中耗时最大的部分是线搜索。因此我们针对鲁棒统计中常用的Ｍ估计函数形式,采用近似函数拟合的方法,设计了一种快速的线搜索方法,与牛     

基于混合遗传算法的聚类分析

聚类问题在一定条件下可以归结为一个带约束的最优化问题.遗传算法作为一种鲁棒性很强的优化算法,可用于解决聚类问题.本文提出一种改进的混合遗传聚类算法通过全局搜索与局部搜索相结合的方法提高收敛速度,还采用基于最近邻基因匹配的交叉算子来维持群体的多样性.实验表明,该算法的局部收敛速度和全局收敛性能均明显优于已有的几种遗传聚类算法.     

最优化问题全局寻优的PSO-BFGS混合算法

针对利用粒子群优化算法进行多极值函数优化时存在早熟收敛和搜索效率低的问题,提出混合的PSO-BFGS算法,并增强了混合算法的变异能力使算法能逃出局部极值点.通过对三种Benchmark函数的测试结果表明,PSO-BFGS算法不仅具有有效的全局收敛性能,而且还具有较快的收敛速度,是求解最优化问题的一种有效算法.     

遥感图像小型目标的识别方法

提出使用特征提取的方法来识别遥感图像中的小目标。介绍了不变矩法和高阶累积量法两种用于目标识别方法的原理和如何构造它们的不变特征集的过程。在论述了这两种不变特征集的构造方法的基础上，对遥感图像采用多元识别方法。实验结果证明：经过图像预处理后，采用不变矩法和高阶累积量法进行多元搜索有很高的准确度。     

基于模式搜索的连续函数寻优

模式搜索方法是求解最优化问题的一种直接搜索方法,它只根据函数值信息来进行求优。但模式搜索对起始点非常敏感,对好的起始点,模式搜索可以搜索到全局最优点,但对某些起始点,模式搜索只能搜索到局部极值点。本文提出基于模式搜索的一个新方法,实验证明,它能搜索到全局最优。     

建立启发式评价函数h(n)的一般方法

本文给出了在启发式图搜索策略中建立有效的启发式评价函数h(n)的两个一般方法:相似问题逼近法和函数逼近法,并对这两种方法进行了讨论。     

求解线性SVM的非精确步长搜索割平面方法

割平面方法可高效求解线性支持向量机问题,其主要思路是通过不断添加割平面并利用精确线性搜索实现算法的加速和优化.针对其中的非光滑线性搜索问题,文中提出一种基于非精确步长搜索的加速割平面方法.该方法使用较少的迭代次数就能确定最优步长所在的子区间.在此基础上,用二点二次插值的闭式解逼近最优步长,从而较精确线性搜索方法速度更快、开销更小,且保持同样的收敛边界.大量实验表明,文中方法效率优于基于精确线性搜索的优化割平面方法,在一些数据库上的收敛速度甚至提升50%.     

基于马氏距离的遥感图像高温目标识别方法研究

高温目标(森林火灾、草原火、煤层自燃、火山喷发等)具有显著区别于常温地物的波谱特性.马氏距离相当于加权的欧式距离,在多元统计分析中被用于多维数据的分类.分别采用马氏距离多元截尾法和马氏距离多类判别法对ETM+遥感图像进行高温目标识别,结果表明:两种方法具有较好的一致性.在异点识别的基础上,对所得结果的光谱特性深入分析,可明确所提异点的物理意义并提取真正的高温目标.经野外验证,两种方法的结合可有效提高高温目标识别精度,分别可达到88.01％和88.09％.     

基于微粒群优化的序贯二次规划方法

文章针对约束非线性优化问题,将微粒群优化算法(PSO)和序贯二次规划(SQP)算法结合起来,提出了一种解决此类问题的有效算法。PSO可以看作是全局搜索器,而SQP则主要执行局部搜索。对于那些具有多个局部极值点的优化问题,大大增加了获得全局极值点的几率。由于PSO具有快速全局收敛的特点,同时SQP的局部搜索能力很强,所以所提算法可以快速获得全局最优值。将基于PSO的序贯二次规划算法在两个标准优化问题上进行仿真,结果证明与标准的PSO和SQP相比,算法具有明显的优越性。     

Adaptive representation for single objective optimization

A new technique called Adaptive Representation Evolutionary Algorithm (AREA) is proposed in this paper. AREA involves dynamic alphabets for encoding solutions. The proposed adaptive representation is more compact than binary representation. Genetic operators are usually more aggressive when higher alphabets are used. Therefore the proposed encoding ensures an efficient exploration of the search space. This technique may be used for single and multiobjective optimization. We treat the case of single objective optimization problems in this paper. Despite its simplicity the AREA method is able to generate a population converging towards optimal solutions. Numerical experiments indicate that the AREA technique performs better than other single objective evolutionary algorithms on the considered test functions.     

Multiple meta-models based design space differentiation method for expensive problems

Meta-models and meta-models based global optimization methods have been commonly used in design optimizations of expensive problems. In this work, a multiple meta-models based design space differentiation (MDSD) method is proposed. In the proposed method, an important region will be constructed using the expensive points inside the whole design space. Then, quadratic function (QF) will be employed in the search of the constructed important region. To avoid the local optima, kriging is employed in the search of the whole design space simultaneously. The MDSD method employs different meta-models in the different design space instead of space reduction, which preserves the advantages of high efficiency of the space reduction methods and avoids their shortcomings of removing the global optimum by mistake in theory. Through extensive test and comparison with three meta-model based algorithms, efficient global optimization (EGO), Mode-pursuing sampling method (MPS) and hybrid and adaptive meta-modeling method (HAM) using several benchmark math functions and an engineering problem involving finite element analysis (FEA), the proposed method shows excellent performance in search efficiency and accuracy.     

On the nonmonotonicity degree of nonmonotone line searches

The nonmonotone globalization technique is useful in difficult nonlinear problems, because of the fact that it may help escaping from steep sided valleys and may improve both the possibility of finding the global optimum and the rate of convergence. This paper discusses the nonmonotonicity degree of nonmonotone line searches for the unconstrained optimization. Specifically, we analyze some popular nonmonotone line search methods and explore, from a computational point of view, the relations between the efficiency of a nonmonotone line search and its nonmonotonicity degree. We attempt to answer this question how to control the degree of the nonmonotonicity of line search rules in order to reach a more efficient algorithm. Hence in an attempt to control the nonmonotonicity degree, two adaptive nonmonotone rules based on the morphology of the objective function are proposed. The global convergence and the convergence rate of the proposed methods are analysed under mild assumptions. Numerical experiments are made on a set of unconstrained optimization test problems of the CUTEr (Gould et al. in ACM Trans Math Softw 29:373–394, 2003) collection. The performance data are first analysed through the performance profile of Dolan and Moré (Math Program 91:201–213, 2002). In the second kind of analyse, the performance data are analysed in terms of increasing dimension of the test problems.     

Global optimization using a multipoint type quasi-chaotic optimization method

This paper proposes a new global optimization method called the multipoint type quasi-chaotic optimization method. In the proposed method, the simultaneous perturbation gradient approximation is introduced into a multipoint type chaotic optimization method in order to carry out optimization without gradient information. The multipoint type chaotic optimization method, which has been proposed recently, is a global optimization method for solving unconstrained optimization problems in which multiple search points which implement global searches driven by a chaotic gradient dynamic model are advected to their elite search points (best search points among the current search histories). The chaotic optimization method uses a gradient to drive search points. Hence, its application is restricted to a class of problems in which the gradient of the objective function can be computed. In this paper, the simultaneous perturbation gradient approximation is introduced into the multipoint type chaotic optimization method in order to approximate gradients so that the chaotic optimization method can be applied to a class of problems for which only the objective function values can be computed. Then, the effectiveness of the proposed method is confirmed through application to several unconstrained multi-peaked, noisy, or discontinuous optimization problems with 100 or more variables, comparing to other major meta-heuristics.     

噪声环境下基于蒲丰距离的依概率多峰优化算法

针对噪声环境下求解多个极值点的问题, 本文提出了噪声环境下基于蒲丰距离的依概率多峰优化算法(Probabilistic multimodal optimization algorithm based on the Button distance, PMB). 算法依据蒲丰投针原理提出噪声下的蒲丰距离和极值分辨度概念, 理论推导证明了二者与算法峰值检测率符合依概率关系. 在全局范围内依据蒲丰距离划分搜索空间, 可以使PMB算法保持较好的搜索多样性. 在局部范围内利用改进的斐波那契法进行探索, 减少了算法陷入噪声引起的局部最优的概率. 基于34个测试函数, 从依概率特性验证、寻优结果影响因素分析、多极值点寻优和多维函数寻优四个角度进行实验. 证明了蒲丰距离与算法的峰值检测率符合所推导的依概率关系. 对比噪声环境下的改进蝙蝠算法和粒子群算法, PMB算法在噪声环境中可以依定概率更精确地定位多峰函数的更多极值点, 从而证明了PMB算法原理的正确性和噪声条件下全局寻优的依概率性能, 具有理论意义和实用价值.     

改进型PSO算法在VRP中的应用

运用罚函数法将约束优化问题转化为无约束优化问题,同时采用实数编码方案,将离散的车辆路径问题转化成准连续优化问题,在此基础上,用改进的粒子群优化算法求解最优值.改进的粒子群算法引入了杂交PSO模型和变异算子.仿真实验结果表明,该算法在保持粒子种群多样性、提高收敛速度和搜索精度、扩大搜索范围、避免过早收敛于局部极值点等方面...     

Variable-fidelity expected improvement method for efficient global optimization of expensive functions

The efficient global optimization method (EGO) based on kriging surrogate model and expected improvement (EI) has received much attention for optimization of high-fidelity, expensive functions. However, when the standard EI method is directly applied to a variable-fidelity optimization (VFO) introducing assistance from cheap, low-fidelity functions via hierarchical kriging (HK) or cokriging, only high-fidelity samples can be chosen to update the variable-fidelity surrogate model. The theory of infilling low-fidelity samples towards the improvement of high-fidelity function is still a blank area. This article proposes a variable-fidelity EI (VF-EI) method that can adaptively select new samples of both low and high fidelity. Based on the theory of HK model, the EI of the high-fidelity function associated with adding low- and high-fidelity sample points are analytically derived, and the resulting VF-EI is a function of both the design variables x and the fidelity level l. Through maximizing the VF-EI, both the sample location and fidelity level of next numerical evaluation are determined, which in turn drives the optimization converging to the global optimum of high-fidelity function. The proposed VF-EI is verified by six analytical test cases and demonstrated by two engineering problems, including aerodynamic shape optimizations of RAE 2822 airfoil and ONERA M6 wing. The results show that it can remarkably improve the optimization efficiency and compares favorably to the existing methods.     

A new spectral conjugate gradient method for large-scale unconstrained optimization

The spectral conjugate gradient methods, with simple construction and nice numerical performance, are a kind of effective methods for solving large-scale unconstrained optimization problems. In this paper, based on quasi-Newton direction and quasi-Newton condition, and motivated by the idea of spectral conjugate gradient method as well as Dai-Kou's selecting technique for conjugate parameter [SIAM J. Optim. 23 (2013), pp. 296–320], a new approach for generating spectral parameters is presented, where a new double-truncating technique, which can ensure both the sufficient descent property of the search directions and the bounded property of the sequence of spectral parameters, is introduced. Then a new associated spectral conjugate gradient method for large-scale unconstrained optimization is proposed. Under either the strong Wolfe line search or the generalized Wolfe line search, the proposed method is always globally convergent. Finally, a large number of comparison numerical experiments on large-scale instances from one thousand to two million variables are reported. The numerical results show that the proposed method is more promising.     

A Non-monotone Line Search Algorithm for?Unconstrained Optimization

The monotone line search schemes have been extensively used in the iterative methods for solving various optimization problems. It is well known that the non-monotone line search technique can improve the likelihood of finding a global optimal solution and the numerical performance of the methods, especially for some difficult nonlinear problems. The traditional non-monotone line search approach requires that a maximum of recent function values decreases. In this paper, we propose a new line search scheme which requires that a convex combination of recent function values decreases. We apply the new line search technique to solve unconstrained optimization problems, and show the proposed algorithm possesses global convergence and R-linear convergence under suitable assumptions. We also report the numerical results of the proposed algorithm for solving almost all the unconstrained testing problems given in CUTEr, and give numerical comparisons of the proposed algorithm with two famous non-monotone methods.