两输入幂激励前向神经网络权值与结构确定

基于多元函数逼近与二元幂级数展开理论,构建了一个以二元幂函数序列为隐神经元激励函数的两输入幂激励前向神经网络模型.以该网络模型为基础,基于权值直接确定法以及隐神经元数目与逼近误差的关系,提出了一种网络权值与结构确定算法.计算机仿真与数值实验结果验证了所构建的网络在逼近与去噪方面具有优越的性能,所提出的权值与结构确定算法能够快速、有效地确定网络的权值与最优结构,保证网络的最佳逼近能力.     

基于混沌和自适应搜索策略的GSO算法分析与优化

针对基本萤火虫群算法在全局优化问题求解过程中存在的求解精度偏低、易陷入局部最优、收敛速度较慢等问题，提出一种基于混沌和自适应搜索策略的萤火虫优化算法（CSAGSO）。利用混沌搜索技术对萤火虫种群进行初始化以得到分布更为均匀、合理的较优初始解；运用混沌扰动优化策略对每一代适应度较差的部分萤火虫个体进行混沌扰动以增强种群多样性和提高全局搜索能力。采用动态步长的自适应搜索策略，并对寻优过程中静止不动的萤火虫个体位置进行更新，加快了算法前期收敛速度，减少了后期震荡现象发生。仿真实验结果表明，优化后的萤火虫算法参数较少并具有较好稳定性，同时在求解精度和收敛速度上都明显优于基本萤火虫群算法。     

基于协方差矩阵自适应进化策略的机器人手眼标定算法

针对视觉传感器标定和机器人运动学求解过程中存在噪声干扰，导致传统的手眼标定算法求解误差较大的问题，提出一种基于协方差矩阵自适应进化策略（CMAES）的机器人手眼标定算法。首先，采用对偶四元数（DQ）对旋转和平移分别建立目标函数和几何约束，简化求解模型；其次，采用惩罚函数法将约束问题转化成无约束优化问题；最后，使用CMAES算法逼近手眼标定旋转和平移方程的全局最优解。搭建机器人、相机实测实验平台，将所提算法与Tsai两步法、非线性优化算法INRIA、DQ算法进行对比。实验结果表明：所提算法在旋转和平移上的求解误差和方差均小于传统算法；与Tsai算法相比，所提算法的旋转精度提升了4.58%，平移精度提升了10.54%。可见在存在噪声干扰的实际手眼标定过程中，所提算法具有更好的求解精度与稳定性。     

基于粒子群灰狼混合算法的多目标约束优化问题求解

近年来，多目标优化问题引起了广泛关注，其求解目标多、目标函数复杂，当前方法通常将所有目标加权后求解，但这些方法会造成解集缺乏准确性.针对上述情况，本文首先根据目标分解的框架：辅助目标和等价目标约束优化框架，该框架是将约束优化的问题分解为辅助目标和等价目标相结合的优化问题，同时动态调整所分解出的对应子问题的权值，使分解出的子问题求解趋向于等价目标求解.其次基于粒子群优化算法和灰狼优化算法的各自优势，提出参数自适应的粒子群灰狼混合算法，混合算法的优势集合了粒子群算法的收敛性快和灰狼算法的搜索过程多样性，从而提高粒子进化过程的准确性.通过IEEE CEC2017数据集测试的结果表明：在调参合适的情况下，获得的函数最优值个数多于乌鸦搜索、受约束的模拟退火、带约束的水循环等经典算法，在10D情况下，28个测试函数中11个测试函数表现最佳；在30D的情况下，12个测试函数表现最佳.     

基于Lagrange插值的学习猴群算法求解折扣｛0-1｝背包问题

折扣｛0-1｝背包问题（D｛0-1｝KP）的目的是在不超过背包载重的前提下，使得装入背包的所有物品价值系数之和为最大。针对已有算法在求解规模大、复杂度高的D｛0-1｝KP时的求解精度低的问题，提出了Lagrange插值的学习猴群算法（LSTMA）。首先，在基本猴群算法的望过程中重新定义了视野长度；其次，在跳过程中引入了种群中最优的个体作为第二个支点，并调整搜索机制；最后，在跳过程之后引入Lagrange插值操作来提高算法的搜索性能。对四类实例的仿真结果表明：LSTMA在求解D｛0-1｝KP时的求解精度高于对比算法，并且具有良好的鲁棒性。     

基于混沌搜索的自适应差分进化算法

提出一种基于混沌搜索的自适应差分进化算法（CADE）,该算法在计算过程中自适应地调整交叉率,在搜索初期保持种群多样性的同时增强算法的全局收敛性。具有较强局部遍历搜索性能的混沌搜索的引入使得算法具有较好的求解精度,增加搜索到全局最优解的概率。对几种典型的测试函数对CADE进行了测试,实验结果表明,该算法能有效地避免早熟收敛,具有良好的全局收敛性。     

基于混合策略改进的鲸鱼优化算法

针对原始鲸鱼优化算法（WOA）收敛速度慢、全局搜索能力弱、求解精度低且易陷入局部最优等问题,提出一种混合策略来改进的鲸鱼优化算法（LGWOA）。首先将莱维飞行引入鲸鱼全局搜索的公式中,通过莱维飞行加大全局搜索步长,扩大搜索空间、提高全局搜索能力;其次,在鲸鱼螺旋上升阶段,加入一个自适应权重参数来提高算法的局部搜索能力和求解精度;最后结合遗传算法的交叉变异思想平衡算法的全局搜索和局部搜索能力,维持种群的多样性,规避陷入局部最优。通过对12个基准测试函数从2个角度进行实验对比分析,结果表明,基于混合策略改进的鲸鱼优化算法在收敛速度和求解精度上均有明显提升。     

基于混合搜索的多种群人工蜂群算法

针对经典人工蜂群（ABC）算法搜索策略存在搜索机制单一、群体全局搜索与局部搜索运算耦合性较高的问题,提出一种基于混合搜索的多种群人工蜂群（MPABC） 算法。首先,将种群按照适应度值进行排序,得到一个有序队列,进而将其划分为随机子群、核心子群和平衡子群三类有序子群;其次,针对不同子群结合相应的个体选择机制与搜索策略,构建出不同的差异向量;最后,在群体的搜索过程中,通过三类子群实现对具有不同适应度函数值个体的有效控制,来增强群体全局搜索和局部搜索的平衡能力。通过对16个标准测试函数进行仿真实验并与具有可变搜索策略的人工蜂群（ABCVSS）算法、基于选择概率的改进人工蜂群（MABC）算法、基于粒子群策略的多精英人工蜂群（PS-MEABC）算法、基于符号函数的多搜索策略人工蜂群（MSSABC）算法和优化高维复杂函数的改进人工蜂群（IABC）算法共五种典型的蜂群算法进行了对比,实验结果显示MPABC具有较好的优化效果;与ABC算法相比,MPABC在求解高维（100维）复杂问题上的收敛速度提高了约23%,且求解精度更优。     

幂激励前向神经网络最优结构确定算法

针对一种以幂函数序列为各隐神经元激励函数的前向神经网络,提出了一种基于权值直接确定方法的网络最优结构确定算法。计算机仿真与验证结果表明,该算法能自动、快速、有效地确定网络的最优隐神经元数,达到网络的最佳逼近能力,从而实现网络结构的最优化。     

基于IA-BP优化算法的物料含水率测量技术

为了对微波谐振腔含水率测量结果进行校正，提出一种基于IA-BP优化算法的进化神经网络模型。模型首先利用IA算法，对解群分布多样性的特性进行全局搜索；同时结合BP算法中基于梯度信息指导权值调整的性能，进行局部搜索，进而避免在最优解或次优解附近震荡，并迅速收敛到最优值。结果表明：该优化算法预测精度高，且收敛速度快，具有寻优的全局性和精确性，提高了测量精度。     

Adaptive radial basis function networks with kernel shape parameters

Radial basis function network (RBFN), commonly used in the classification applications, has two parameters, kernel center and radius that can be determined by unsupervised or supervised learning. But it has a disadvantage that it considers that all the independent variables have the equal weights. In that case, the contour lines of the kernel function are circular, but in fact, the influence of each independent variable on the model is so different that it is more reasonable if the contour lines are oval. To overcome this disadvantage, this paper presents an adaptive radial basis function network (ARBFN) with kernel shape parameters and derives the learning rules from supervised learning. To verify that this architecture is superior to that of the traditional RBFN, we make a comparison between three artificial and fifteen real examples in this study. The results show that ARBFN is much more accurate than the traditional RBFN, illustrating that the shape parameters can actually improve the accuracy of RBFN.     

On the Kernel Widths in Radial-Basis Function Networks

RBFN (Radial-Basis Function Networks) represent an attractive alternative to other neural network models. Their learning is usually split into an unsupervised part, where center and widths of the basis functions are set, and a linear supervised part for weight computation. Although available literature on RBFN learning widely covers how basis function centers and weights must be set, little effort has been devoted to the learning of basis function widths. This paper addresses this topic: it shows the importance of a proper choice of basis function widths, and how inadequate values can dramatically influence the approximation performances of the RBFN. It also suggests a one-dimensional searching procedure as a compromise between an exhaustive search on all basis function widths, and a non-optimal a priori choice.     

AGENT-BASED APPROACH TO THE DESIGN OF RBF NETWORKS

This article proposes a novel approach to the radial basis function network (RBFN) design. Its main idea is to apply the agent-based population learning algorithm to the task of initialization and training RBFNs. The approach allows for an effective network initialization and estimation of its output weights. The initialization involves two stages, where in the first one initial clusters are produced using the similarity-based procedure and next, in the second stage, prototypes (centroids) from the thus-obtained clusters are selected. The agent-based population learning algorithm is used to select prototypes. In the proposed implementation of the algorithm, both tasks—RBFN initialization and RBFN training—are carried out by a team of agents executing various local search procedures and cooperating with a view to determine the solution to the RBFN design problem at hand. The performance of the RBFN constructed using the proposed agent-based approach is analyzed and evaluated. The proposed approach is also compared with different RBFN initialization and training procedures in the literature.     

带变异算子的双种群粒子群优化算法

提出一种带变异算子的双种群粒子群算法,搜索在两个不同的子群中并行运行,分别使用不同的惯性权值,使得种群在全局和局部都有较好的搜索能力.通过子群重组实现种群间的信息交换.在算法中引入变异算子,产生局部最优解的邻域点,帮助惰性粒子逃离束缚,寻得更优解.对经典函数的测试结果表明,改进的算法在收敛速度和精度上有更好的性能.     

Solving a category of two-dimensional fractional optimal control problems using discrete Legendre polynomials

In this paper, we formulate a numerical method to approximate the solution of two-dimensional optimal control problem with a fractional parabolic partial differential equation (PDE) constraint in the Caputo type. First, the optimal conditions of the optimal control problems are derived. Then, we discretize the spatial derivatives and time derivatives terms in the optimal conditions by using shifted discrete Legendre polynomials and collocations method. The main idea is simplifying the optimal conditions to a system of algebraic equations. In fact, the main privilege of this new type of discretization is that the numerical solution is directly and globally obtained by solving one efficient algebraic system rather than step-by-step process which avoids accumulation and propagation of error. Several examples are tested and numerical results show a good agreement between exact and approximate solutions.     

确定RBF神经网络参数的新方法

提出一种确定RBF网络隐含层神经元和权值的有效方法。该方法将自动聚类算法与对称距离相结合优化每个隐含层神经元的中心向量；利用伪逆方法确定隐层神经元到输出神经元的权值。实验结果表明：该方法比自动聚类算法有更好的分类能力。     

A new structure adaptation algorithm for RBF networks and its application

An adaptation algorithm is developed for radial basis function network (RBFN) in this paper. The RBFN is adapted on-line for both model structure and parameters with measurement data. When the RBFN is used to model a non-linear dynamic system, the structure is adapted to model abrupt change of system operating region, while the weights are adapted to model the incipient time varying parameters. Two new algorithms are proposed for adding new centres while the redundant centres are pruned, which is particularly useful for model-based control. The developed algorithm is evaluated by modelling a numerical example and a chemical reactor rig. The performance is compared with a non-adaptive model.     

Optimal control problem via neural networks

This paper attempts to propose a new method based on capabilities of artificial neural networks, in function approximation, to attain the solution of optimal control problems. To do so, we try to approximate the solution of Hamiltonian conditions based on the Pontryagin minimum principle (PMP). For this purpose, we introduce an error function that contains all PMP conditions. In the proposed error function, we used trial solutions for the trajectory function, control function and the Lagrange multipliers. These trial solutions are constructed by using neurons. Then, we minimize the error function that contains just the weights of the trial solutions. Substituting the optimal values of the weights in the trial solutions, we obtain the optimal trajectory function, optimal control function and the optimal Lagrange multipliers.     

A new hybrid methodology for cooperative-coevolutionary optimization of radial basis function networks

This paper presents a new multiobjective cooperative–coevolutive hybrid algorithm for the design of a Radial Basis Function Network (RBFN). This approach codifies a population of Radial Basis Functions (RBFs) (hidden neurons), which evolve by means of cooperation and competition to obtain a compact and accurate RBFN. To evaluate the significance of a given RBF in the whole network, three factors have been proposed: the basis function’s contribution to the network’s output, the error produced in the basis function radius, and the overlapping among RBFs. To achieve an RBFN composed of RBFs with proper values for these quality factors our algorithm follows a multiobjective approach in the selection process. In the design process, a Fuzzy Rule Based System (FRBS) is used to determine the possibility of applying operators to a certain RBF. As the time required by our evolutionary algorithm to converge is relatively small, it is possible to get a further improvement of the solution found by using a local minimization algorithm (for example, the Levenberg–Marquardt method). In this paper the results of applying our methodology to function approximation and time series prediction problems are also presented and compared with other alternatives proposed in the bibliography.     

Performance Prediction in Symbolic Scheduling of Partitioned Programs with Weight Variation

In this paper we consider the symbolic scheduling of partitioned loop programs which are modeled as iterative task graphs (ITGs). Each task in such a graph is coarse grained and contains a large chunk of computations. The weights of computation and communication vary from one iteration to another depending on the index value of the loop. The goal of scheduling such graphs is to incorporate the symbolic variables in weight functions and loop bounds and provide an asymptotically optimal schedule and predict its performance accurately. We provide a lower bound for optimal scheduling when weights of iterative task graphs change monotonically in the course of iterations and there is a sufficient number of processors. We present a technique that devises a valid symbolic schedule without searching all task instances and examine the asymptotic performance of this schedule compared to an optimal solution. Finally, we present case studies and experimental results on nCUBE-2 to verify our solutions.