多峰值全局优化的混合算法

根据遗传算法在较小的可行区域内一般有较好的求解结果这一事实,提出了一种混合算法。该算法先利用区间算法求解全局优化问题来得到包含所有最优解的小区间,随后运用遗传算法进行后续过程。算法能够有效缩小一个较大的可行区域空间,提供高适应值的初始种群,求出多峰值问题的全部最优解,提高算法的求解精度同时避免陷入局部最优。最后数值实验说明了算法的有效性。     

基于网格模式搜索的支持向量机模型选择

支持向量机的模型选择问题就是对于一个给定的核函数,调节核参数和惩罚因子C。分析了网格搜索算法和模式搜索算法,通过结合上述两种算法的优点提出了网格模式搜索算法。其核心原理是先用网格算法在全局范围内进行快速搜索,找到最优解的最小区间,再在这个最小区间内用模式搜索算法找到最优解。实验证明,网格模式搜索具有学习精度高和速度快的优点。     

改进的菌群算法研究

为了提高菌群寻优算法（Bacterial Foraging Optimization,BFO）的搜索能力和解决多峰值复杂适应度函数模型避免过早收敛的问题,文中对原始菌群算法进行改进,提出多峰值菌群算法。将寻优过程分成两个时期,前期和原始菌群算法相同,在菌群收敛的后期,加入峰值数目和区间的判断,将区间编号,保证区间内部单峰值;然后在区间内部迭代运行菌群搜索,独立寻优,在多峰值和较复杂模型的情况下进行研究和评估。实验表明,在收敛速度、收敛稳定性和寻找全局最优方面均优于原始菌群算法。     

改进的菌群算法研究

为了提高菌群寻优算法（ Bacterial Foraging Optimization, BFO）的搜索能力和解决多峰值复杂适应度函数模型避免过早收敛的问题,文中对原始菌群算法进行改进,提出多峰值菌群算法。将寻优过程分成两个时期,前期和原始菌群算法相同,在菌群收敛的后期,加入峰值数目和区间的判断,将区间编号,保证区间内部单峰值;然后在区间内部迭代运行菌群搜索,独立寻优,在多峰值和较复杂模型的情况下进行研究和评估。实验表明,在收敛速度、收敛稳定性和寻找全局最优方面均优于原始菌群算法。     

改进的小生境遗传算法

本文针对多峰值函数的优化提出了一种改进的小生境遗传算法.本算法可以自动检测波峰的存在,加强了遗传算法的局部搜索能力又避免其收敛于局部最优解,适用于多峰值函数的优化.     

用于多峰值函数优化的对数自适应排挤遗传算法

排挤遗传算法能够比较稳定地获取多个峰值,但其求解效率不高,在有限的遗传代数下无法获得较高的求解精度,需要较多的迭代次数。为了快速求出多峰函数的所有最优解,提出了一种基于对数自适应的排挤遗传算法。该算法结合小生境排挤遗传和爬山算子,根据遗传代数对爬山算子的距离值进行对数自适应计算,使种群在遗传过程中保持多样性。通过对多个一维和二维多峰函数的实验和比较分析,测试结果表明,该算法在有限的遗传代数下既能保证求解精度又能提高收敛速度,能够比较稳定地求得所有最优解,是求解多峰函数问题的有效算法。     

基于群智能的连续优化算法研究

在对蚁群优化算法(ACO)和粒子群优化算法(PSO)进行分析的基础上,提出一种解决函数连续优化的群智能混合策略-CA-PSO.在求解过程中,首先对解空间进行区域划分,进而利用ACO在优化初期具备的快速收敛性能,在整个解空间内搜索最优解的敏感区域.然后利用蚁群的搜索结果初始化PSO粒子,利用PSO快速和全局收敛性进行所在小区域内的搜索.种群更新时根据蚁群的拓扑结构和小区域间的阶跃规则,蚁群不断向最优解敏感区域聚集,使得敏感区域内粒子数增加,则局部的PSO搜索策略可以更细密的搜索最优.实例结果表明,CA-PSO既能保证解的分布性与多样性,又避免了在多峰值函数寻优过程中陷入局部最优解而停止运算,最终将收敛到全局最优解.     

一种基于云模型的改进型粒子群算法

针对经典粒子群算法在函数优化中易陷入局部最优和早熟收敛等缺点,结合云模型在定性与定量之间相互转换的优良特性,提出一种基于云模型的改进型粒子群算法。其思想是通过反向学习机制初始化种群,再通过正态云算子求解粒子群中的全局最优个体和自身最优个体周围的更优值,最后利用混沌理论对个别粒子进行变异来跳出局部最优解。典型复杂函数测试表明,该算法能有效找出全局最优解,特别适宜于多峰值函数寻优。     

求解昂贵区间多目标优化问题的高斯代理模型

本文将数据挖掘(高斯过程回归建模)和智能进化算法(GA,NSGA-Ⅱ)进行结合,用于解决优化函数未知的昂贵区间多目标优化问题.首先利用高斯过程对采用中点和不确定度表示的未知目标函数和约束函数进行建模,由于相关性和准确性是区间函数模型的两个必备条件,故提出一种融合多属性决策的双层种群筛选策略,并将其嵌入到遗传算法求解高斯模型参数的过程中,第1层根据相关性属性排除候选解集中部分劣解,第2层根据准确性属性排除候选解集中其余超出种群规模的劣解,两属性的权重系数决定两层排除劣解的比例.然后将所建模型作为优化对象的代理模型引导区间NSGA-II算法优化求解,从而获得所需的Pareto前沿.     

基于免疫量子遗传算法的多峰函数寻优

针对多峰函数优化中的全局及局部寻优问题,提出了一种结合免疫克隆算子的量子遗传算法,给出了实现流程。该算法集量子遗传算法的快速性和免疫克隆算法全局搜索性于一身。它不仅有效克服了量子遗传算法容易陷于局部最优的缺点,也避免了普通免疫克隆算法计算缓慢的缺点。用多峰值函数进行了全局寻优的仿真实验,并与基本遗传算法,量子遗传算法的计算结果进行了比较,结果表明所提算法能以较快的速度搜索到全局最优解,并且其鲁棒性远高于普通量子遗传算法和遗传算法。     

Multimodal optimization by artificial weed colonies enhanced with localized group search optimizers

Multimodal optimization aims at finding multiple global and local optima (as opposed to a single solution) of a function, so that the user can have a better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable one while still maintaining the optimal system performance. Evolutionary Algorithms (EAs) due to their population-based approach are able to detect multiple solutions within a population in a single simulation run and have a clear advantage over the classical optimization techniques, which need multiple restarts and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. This article proposes a hybrid two-stage optimization technique that firstly employs Invasive Weed Optimization (IWO), an ecologically inspired algorithm to find the promising Euclidean sub-regions surrounding multiple global and local optima. IWO is run for 80% of the total budget of function evaluations (FEs), and consecutively the search is intensified by using a modified Group Search Optimizer (GSO), in each detected sub-region. GSO, invoked in each sub-region discovered with IWO, is continued for 20% of the total budget of FEs. Both IWO and GSO have been modified from their original forms to meet the demands of the multimodal problems used in this work. Performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark-suite comprising of 21 basic multimodal problems and 7 composite multimodal problems. A practical multimodal optimization problem concerning the design of dielectric composites has also been used to test the performance of the algorithm. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.     

Numerical construction of LISS Lyapunov functions under a small-gain condition

In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. The set of such decay points plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system, and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone operator. For this purpose we use a fixed-point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. The advantage over an earlier algorithm is demonstrated. Furthermore, an example is given which shows how to analyze a given perturbed interconnected system.     

A theoretical extension on the operational law for monotone functions of uncertain variables

The classical operational law of uncertain variables proposed by Liu makes an important contribution to the development of the uncertainty theory in both theories and applications. It provides a powerful and practical approach for calculating the uncertainty distribution of strictly monotone function of uncertain variables. However, the restriction on strictly monotone functions of the operational law limits its applications since many practical problems cannot be modeled by strictly monotone functions but general monotone functions. Therefore, an extension of the original operational law is needed. For this purpose, some properties concerning the uncertainty distributions of monotone functions of uncertain variables as well as the generalized inverse uncertainty distributions are presented first in this paper. On the basis of these discussions, a generalized operational law is proposed as a natural extension of the original operational law. Then the uncertainty distribution of a general monotone function of independent regular uncertain variables can be derived, which is analogous to the way that suggested by the original operational law for dealing with strictly monotone functions. Furthermore, as an application of the generalized operational law, a theorem for calculating the expected values of general monotone functions of uncertain variables is presented as well.     

一种基于免疫和Hopfield神经网络的多峰值优化算法

分析了免疫算法和Hopfield神经网络的优缺点，提出了一种解决多峰值函数优化问题的混合算法。Hopfield神经网络易于硬件实现，具有简单、快速的优点，但是对初始值具有依赖性以及容易陷入局部极值。免疫算法具有识别多样性的特点，但搜索效率和精度不高。将两算法结合起来，优势互补。首先用免疫算法寻优，然后对所得具有全局多样性的解进行聚类分析，所得聚类中心作为Hopfield神经网络的初始搜索点，最后利用Hopfield神经网络逐个寻优。实验表明，该算法是一种有效的求解多峰函数优化问题的方法，与免疫算法相比，搜索效率和精度都较高。     

一种新的神经网络逼近函数算法

针对地震数据等大数据多属性集处理一直是科学研究的重点和难点,本文提出一种多参数的单调性函数的拟合方法。利用主成分分析法来进行简化处理,从而获得较少的属性集合,并在此基础上,提出一种新的数据预处理方法,以较好地解决数据单调性所带来的归一化误差,并构造一个与之相匹配的神经网络模型,用它的学习算法来训练网络,从而实现函数拟合。最后通过仿真验证了该方法的有效性。     

Multimodal function optimization using minimal representation size clustering and its application to planning multipaths

A novel genetic algorithm (GA) using minimal representation size cluster (MRSC) analysis is designed and implemented for solving multimodal function optimization problems. The problem of multimodal function optimization is framed within a hypothesize-and-test paradigm using minimal representation size (minimal complexity) for species formation and a GA. A multiple-population GA is developed to identify different species. The number of populations, thus the number of different species, is determined by the minimal representation size criterion. Therefore, the proposed algorithm reveals the unknown structure of the multimodal function when a priori knowledge about the function is unknown. The effectiveness of the algorithm is demonstrated on a number of multimodal test functions. The proposed scheme results in a highly parallel algorithm for finding multiple local minima. In this paper, a path-planning algorithm is also developed based on the MRSC_GA algorithm. The algorithm utilizes MRSC_GA for planning paths for mobile robots, piano-mover problems, and N-link manipulators. The MRSC_GA is used for generating multipaths to provide alternative solutions to the path-planning problem. The generation of alternative solutions is especially important for planning paths in dynamic environments. A novel iterative multiresolution path representation is used as a basis for the GA coding. The effectiveness of the algorithm is demonstrated on a number of two-dimensional path-planning problems.     

软时间窗多式联运4PL路径问题的改进乌鸦算法

针对机械故障、天气状况等随机因素在运输过程中易对各种运输方式造成影响,研究更具有实际意义的带软时间窗的多式联运4PL路径问题。在软时间窗约束下,以总运输费用最小为目标,建立带有软时间窗的多式联运4PL路径优化模型。设计基于天牛须搜索思想和莱维飞行机制的乌鸦搜索算法对模型进行求解,采用田口方法确定算法最优参数组合,与其他算法进行对比分析,实验结果表明改进算法具有更好的求解效果和稳定性。通过数据分析,采用多式联运的运输组织形式,相比单一3PL服务商的单一运输方式,能够有效降低总运输费用;对于客户不同的软时间窗要求,4PL集成商会确定不同的最优运送方案,并证实软时间窗的研究更具有实际意义。     

广义AND／OR图的自底向上的启发式搜索算法BHAO

本文首先根据三角模概念，定义了一类新的更具普遍意义的广义ＡＮＤ／ＯＲ图．根据新定义的启发式函数ｈ（ｎ，ｘ）以及广义ＡＮＤ／ＯＲ图的最佳解树之所有子树亦是最佳子解树的原理，提出了广义ＡＮＤ／ＯＲ图的自底向上的启发式搜索算法ＢＨＡＯ．文中证明了算法ＢＨＡＯ的可采纳性．本文还提出了两类新的启发式函数的单调限制概念，并据此研究了算法ＢＨＡＯ的单调限制性质，研究了两个ＢＨＡＯ算法间的比较性质．     

Multimodal genetic algorithms-based algorithm for automatic point correspondence

In this paper, the problem of automatic determination of point correspondence between two images is formulated as a multimodal function optimization and the usefulness of genetic algorithms (GAs) as a multimodal optimizer is explored. Initially, a number of variations of GAs, capable of simultaneously discovering multiple extremes of an objective function are evaluated on a mathematical benchmark objective function with multiple unequal maxima. The variation of the GAs that performs best on the benchmark function, in terms of the number of maxima discovered, is selected for the determination of automatic point correspondence between two images. The selected variation of the GAs involves an iterative procedure for the formation of a genetic population of individuals (or chromosomes). Each individual encodes the position of a point of interest on one of the available images as well as parameters of a local transformation that generates the position of the corresponding point on the other image. The proposed algorithm aims to discover individuals that corresponds to local maxima of an objective function that measures the similarity between patches of the two images. When the GAs-based multimodal optimization algorithm terminates, pairs of corresponding points between the two images are obtained that can be used for the generation of a dense deformation field by means of the thin plate splines model.The proposed algorithm is applied to 2D medical images (dental and retinal images) under known transformations (similarity and elastic transformation) and is also assessed on medical images with unknown transformations (computer tomography transverse slices). The proposed algorithm is compared against the iterative closest point (ICP) algorithm, and a well-known non-rigid registration algorithm, based on free-form deformations (FFD) using various quantitative criteria. The obtained results indicate that in case of known similarity transformations, the proposed multimodal GAs-based algorithm and the ICP algorithm present equivalent performance, whereas the FFD algorithm is clearly outperformed. In the case of known sinousoidal deformations, the proposed multimodal GAs-based and the FFD algorithm achieve equivalent performance and clearly outperform the ICP algorithm. Finally, in the case of unknown elastic deformations, the proposed GAs-based algorithm appears to perform marginally better than the FFD algorithm, whereas it clearly outperforms the ICP algorithm.