求解非线性互补问题的熵函数认知优化算法

提出了一个求解非线性互补问题的熵函数社会认知优化算法。首先将非线性互补问题转化为非线性方程组来求解,然后利用熵函数法将非线性方程组求解转化为一个光滑的无约束优化问题,最后应用社会认知优化算法求解此优化问题。实验结果表明,该算法收敛速度快,稳定性好,是求解非线性互补问题的一种有效算法。     

求解非线性方程组的智能优化算法综述

非线性方程组的求解是优化领域的一个重要研究课题.近年来,利用智能优化算法求解非线性方程组已成为一个重要方向.首先介绍非线性方程组的定义;其次,根据智能优化算法求解非线性方程组问题的基本框架,从转化方法和智能优化算法两方面入手,对求解非线性方程组的算法的研究进展进行归纳总结;再次,对非线性方程组的测试函数及评价指标进行描述,对比了5个具有代表性算法的性能,分析了目前利用智能优化算法求解非线性方程组亟待解决的问题;最后,指出值得进一步研究的方向.     

竞选优化算法求解非线性方程组的应用研究

针对非线性方程组的求解在工程上具有广泛的实际意义,经典的数值求解方法存在其收敛性依赖于初值而实际计算中初值难确定的问题,将复杂非线性方程组的求解问题转化为函数优化问题,引入竞选优化算法进行求解。同时竞选优化算法求解时无需关心方程组的具体形式,可方便求解几何约束问题。通过对典型非线性测试方程组和几何约束问题实例的求解,结果表明了竞选优化算法具有较高的精确性和收敛性,是应用于非线性方程组求解的一种可行和有效的算法。     

求解非线性方程组的蚁群算法

研究非线性方程组的求解问题,提高有效性。针对非线性方程数与变量数一致的非线性方程组问题,当方程组是一些强非线性方程组时,传统方法易导致失败,有效率低。为了提高求解强非线性方程组的求解效率,提出一种蚁群算法的求解方法。首先将方程组问题转化为函数优化问题,然后用全局搜索速度快的蚁群算法对函数进行求解,找到最优解,最后通过具体实例进行仿真研究,结果表明蚁群算法的有效性。     

烟花算法求解非线性方程组

烟花算法是最近提出的一种效率较高的优化算法,已被用于求解众多的优化问题.给出利用烟花算法求解非线性方程组的方法.实验表明,所提出的算法对于求解变量耦合的非线性方程组比其他算法占有优势,进一步分析存在优势的原因.     

基于极大熵差分进化混合算法求解非线性方程组*

针对非线性方程组,给出了一种新的算法——极大熵差分进化混合算法。首先把非线性方程组转换为一个不可微优化问题;然后用一个称之为凝聚函数的光滑函数直接代替不可微的极大值函数,从而可把非线性方程组的求解转换为无约束优化问题,利用差分进化算法对其进行求解。计算结果表明,该算法在求解的准确性和有效性均优于其他算法。     

非线性约束优化的算法分析

针对非线性约束优化问题,运用了一种新的智能优化算法——社会认知优化算法。社会认知优化算法是一种基于社会认知理论的集群智能优化算法,它对目标函数的解析性质没有要求,适合于大规模约束问题处理的优点,使搜索不容易陷入局部最优。将该算法引入非线性约束问题,解决优化问题。通过实例和其他算法进行比较,对比数值实验结果表明,即使只有一个学习主体,该算法能够高效、稳定地得到解决方案,便于求解非线性约束优化问题。     

求解互补问题的极大熵社会认知算法

针对传统算法无法获得互补问题的多个最优解的困难,提出了求解互补问题的社会认知优化算法.通过利用NCP函数,将互补问题的求解转化为一个非光滑方程组问题,然后用凝聚函数对其进行光滑化,进而把互补问题的求解转化为无约束优化问题,利用社会认知算法对其进行求解.该算法是基于社会认知理论,通过一系列的学习代理来模拟人类的社会性以及智能性从而完成对目标的优化.该算法对目标函数的解析性质没有要求且容易实现,数值实验结果表明了该方法是有效的.     

求解非线性方程组的蛙跳和 BFGS 混合算法

混合蛙跳算法具有算法简单、控制参数少、易于实现等优点,但缺乏良好的局部细化搜索能力,使得求解精度不高。借鉴BFGS算法强的局部搜索能力,将BFGS算法与混合蛙跳算法有机融合,形成性能更优的混合优化算法,并用来求解非线性方程组。通过3个非线性方程组的实验表明,该混合算法收敛精度较高,收敛速度较快,是一种较好的求解非线性方程组的方法。     

利用粒子滤波原理求解非线性方程组

为了提高非线性方程组的求解精度,利用粒子滤波算法对非线性方程组问题进行求解计算。系统地介绍粒子滤波算法的基本原理及其优化算法的实现过程。将非线性方程组的求解问题转化为函数优化问题,并建立基于粒子滤波算法求解非线性方程组的优化模型。通过仿真实例验证所提方法的有效性。实验结果表明该方法能够准确、有效地解决非线性方程组的求解问题,这也为非线性方程组问题的研究提供一种有效的手段。     

基于社会认知算法的软件可靠性分配问题研究

针对软件可靠性分配问题中求解全局最优解的困难,在保证系统开发费用最低的前提条件下,将可靠性指标分配到每个模块中,并利用一种新的智能优化算法——社会认知算法来搜索模型的最优解。实验结果表明了社会认知算法在求解软件可靠性分配问题中的有效性。     

Conjugate direction particle swarm optimization solving systems of nonlinear equations

Solving systems of nonlinear equations is a difficult problem in numerical computation. For most numerical methods such as the Newton’s method for solving systems of nonlinear equations, their convergence and performance characteristics can be highly sensitive to the initial guess of the solution supplied to the methods. However, it is difficult to select a good initial guess for most systems of nonlinear equations. Aiming to solve these problems, Conjugate Direction Particle Swarm Optimization (CDPSO) was put forward, which introduced conjugate direction method into Particle Swarm Optimization (PSO)in order to improve PSO, and enable PSO to effectively optimize high-dimensional optimization problem. In one optimization problem, when after some iterations PSO got trapped in local minima with local optimal solution , conjugate direction method was applied with as a initial guess to optimize the problem to help PSO overcome local minima by changing high-dimension function optimization problem into low-dimensional function optimization problem. Because PSO is efficient in solving the low-dimension function optimization problem, PSO can efficiently optimize high-dimensional function optimization problem by this tactic. Since CDPSO has the advantages of Method of Conjugate Direction (CD) and Particle Swarm Optimization (PSO), it overcomes the inaccuracy of CD and PSO for solving systems of nonlinear equations. The numerical results showed that the approach was successful for solving systems of nonlinear equations.     

非线性方程组问题的粒子群-邻近点混合算法

非线性方程组问题是一类经典的数值计算问题,单纯的进化算法不但需要很高的进化代数,而且也不能保证100％收敛到全局最优解。为求解此问题,把粒子群算法和邻近点算法相混合,利用邻近点算法作为外层算法,粒子群算法作为内层算法进行求解。实验结果表明该算法对凸问题有较好的计算效果,是求解非线性方程组问题的一种有效算法。     

Neural-network-based approximate output regulation of discrete-time nonlinear systems.

The existing approaches to the discrete-time nonlinear output regulation problem rely on the offline solution of a set of mixed nonlinear functional equations known as discrete regulator equations. For complex nonlinear systems, it is difficult to solve the discrete regulator equations even approximately. Moreover, for systems with uncertainty, these approaches cannot offer a reliable solution. By combining the approximation capability of the feedforward neural networks (NNs) with an online parameter optimization mechanism, we develop an approach to solving the discrete nonlinear output regulation problem without solving the discrete regulator equations explicitly. The approach of this paper can be viewed as a discrete counterpart of our previous paper on approximately solving the continuous-time nonlinear output regulation problem.     

A New Approach for Solving Nonlinear Equations Systems

This paper proposes a new perspective for solving systems of complex nonlinear equations by simply viewing them as a multiobjective optimization problem. Every equation in the system represents an objective function whose goal is to minimize the difference between the right and left terms of the corresponding equation. An evolutionary computation technique is applied to solve the problem obtained by transforming the system into a multiobjective optimization problem. The results obtained are compared with a very new technique that is considered as efficient and is also compared with some of the standard techniques that are used for solving nonlinear equations systems. Several well-known and difficult applications (such as interval arithmetic benchmark, kinematic application, neuropsychology application, combustion application, and chemical equilibrium application) are considered for testing the performance of the new approach. Empirical results reveal that the proposed approach is able to deal with high-dimensional equations systems.     

基于粒子群算法的非线性方程组求解

将非线性方程组的求解问题转化为无约束极大极小优化问题，并应用一种新的进化计算（EC）方法——粒子群算法（PSO）求解此优化问题。数值实验的结果验证了该方法的可行性和有效性。     

Recovering temperature-dependent heat conductivity in 2D and 3D domains with homogenization functions as the bases

The paper solves the parameters identification problem in a nonlinear heat equation with homogenization functions as the bases, which are constructed from the boundary data of the temperature in the 2D and 3D space-time domains. To satisfy the over-specified Neumann boundary condition, a linear equations system is derived and then used to determine the expansion coefficients of the solution. Then, after back substituting the solution and collocating points to satisfy the governing equations, the space-time-dependent and temperature-dependent heat conductivity functions in 2D and 3D nonlinear heat equations are identified by solving other linear systems. The novel methods do not need iteration and solving nonlinear equations, since the unknown heat conductivities are retrieved from the solutions of linear systems. The solutions and the heat conductivity functions recovered are quite accurate in the entire space-time domain. We find that even for the inverse problems of nonlinear heat equations, the homogenization functions method is easily used to recover 2D and 3D space-time-dependent and temperature-dependent heat conductivity functions. It is interesting that the present paper makes a significant contribution to the engineering and science in the field of inverse problems of heat conductivity, merely solving linear equations and without employing iteration and solving nonlinear equations to solve nonlinear inverse problems.

     

非线性广义系统的右可逆性

研究了广义非线性系统的右可逆性,给出构造性的求逆算法以克服以往结果中需求解 非线性方程组的困难,从而使得求逆算法对任意足够光滑的非线性广义系统皆为可行.