实现快速全局优化的跨越函数方法

本文提出了一种快速求解全局优化问题的跨越函数方法,与以填充函数法为代表的一类全局优化方法相比,本文定义的跨越函数直接凸显了在求解全局优化问题时构造辅助函数的目的,更重要的是跨越函数方法能够一步跨过函数值比当前局部极小值高的区域,而直接找到原函数f(x)的位于函数值比当前局部极小值低的区域中的局部极小点,加快了全局寻优的过程,并且通过有限次迭代,找到全局最优解.     

由任意初始点求解离散型约束全局优化问题

本文研究了带约束离散型非线性全局优化的求解问题.利用0-1变量提出了一个离散填充函数算法.该算法可由任意初始点出发,不断求得更好的局部极小点,以期得到离散全局最小点.文章同时讨论了所构造的填充函数的性质,给出了数值试验结果.     

求解Lipschitz型规划全局极小点的改进的填充函数法

1 引言 考虑问题 (P)min(x), x∈Ω其中F:ΩR~n→R是局部Lipschitz函数,Ω为紧集,且F(x)在Ω内有极小点。文[1,2,3]在一定条件下给出了求解一般非光滑规划全局极小点的填充函数法,并给出了求解的全过程。本文根据文[1,2,3]的思想,为求解(P),结合函数的特点,给出了一种改进     

整数规划问题的滤子填充函数算法

全局优化是最优化的一个分支,非线性整数规划问题的全局优化在各个方面都有广泛的应用.填充函数是解决全局优化问题的方法之一,它可以帮助目标函数跳出当前的局部极小点找到下一个更好的极小点.滤子方法的引入可以使得目标函数和填充函数共同下降,省却了以往算法要设置两个循环的麻烦,提高了算法的效率.本文提出了一个求解无约束非线性整数规划问题的无参数填充函数,并分析了其性质.同时引进了滤子方法,在此基础上设计了整数规划的无参数滤子填充函数算法.数值实验证明该算法是有效的.     

全局优化问题随机型方法综述

本文综述了七十年代以来全局优化问题随机型方法的若干研究成果,重点是最近几年的某些新结果.§1 引言全局优化问题足寻求实值日标函数 f:R~n→R 的全局极值点(例如极小点)x,即求一点 x∈R~n 使得     

求解全局最优化问题的一种修正打洞算法

文献(Levy A V,Montalvo A.The tunneling algorithm for the global minimization of functions.SIAM J Sci and Stat Comput,1985,6(1):15-29)给出了求解全局优化问题的打洞算法,以及这个算法在执行时存在几个缺点.针对这几个缺点,我们构造了两个修正的打洞函数,基于这两个函数,提出了一种求解全局最优化问题的修正打洞算法,该算法克服了打洞算法的一些缺点.数值试验也进一步说明了算法的有效性.     

一种快速且全局收敛的BP神经网络学习算法

目前误差反向传播(BP)算法在训练多层神经网络方面有很多成功的应用.然而,BP算法也有一些不足:收敛缓慢和易陷入局部极小点等.提出一种快速且全局收敛的BP神经网络学习算法,并且对该优化算法的全局收敛性进行分析和详细证明.实证结果表明提出的算法比标准的BP算法效率更高且更精确.     

基于不等式约束的一类新的增广lagrangian函数

本文提出了一类新的增广lagrangian函数,并证明了它的稳定点、整体极小点与原约束问题KKT点、整体极小点有1-1对应关系,增广lagrangian函数的局部极小点为原问题的局部极小点.     

遗传算法BP神经网络的预报研究和应用

针对目前 BP神经网络在实际气象预报应用中 ,网络结构难以确定以及网络极易陷入局部解问题 ,用遗传算法优化神经网络的连接权和网络结构 ,并在遗传进化过程中采取保留最佳个体的方法 ,建立基于遗传算法的 BP网络模型 ,并以广西的月降水量进行实例分析 ,计算结果表明 ,该方法预报精度高、而且稳定 .     

电力负荷预测的遗传神经网络模型研究

根据电力负荷预测的特点,提出遗传神经网络负荷预测模型,有效地克服了人工神经网络学习速度慢、存在局部极小点的固有缺陷,经实例验证,该方法能有效地提高预测精度和速度。     

Solving nonlinearly constrained global optimization problem via an auxiliary function method

This paper considers the nonlinearly constrained continuous global minimization problem. Based on the idea of the penalty function method, an auxiliary function, which has approximately the same global minimizers as the original problem, is constructed. An algorithm is developed to minimize the auxiliary function to find an approximate constrained global minimizer of the constrained global minimization problem. The algorithm can escape from the previously converged local minimizers, and can converge to an approximate global minimizer of the problem asymptotically with probability one. Numerical experiments show that it is better than some other well known recent methods for constrained global minimization problems.     

New filled functions for nonsmooth global optimization

The filled function method is an effective approach to find a global minimizer for a general class of nonsmooth programming problems with a closed bounded domain. This paper gives a new definition for the filled function, which overcomes some drawbacks of the previous definition. It proposes a two-parameter filled function and a one-parameter filled function to improve the efficiency of numerical computation. Based on these analyses, two corresponding filled function algorithms are presented. They are global optimization methods which modify the objective function as a filled function, and which find a better local minimizer gradually by optimizing the filled function constructed on the minimizer previously found. Numerical results obtained indicate the efficiency and reliability of the proposed filled function methods.     

Discrete global descent method for discrete global optimization and nonlinear integer programming

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10¹⁰⁴ feasible points have demonstrated the applicability and efficiency of the proposed method.     

A cut-peak function method for global optimization

A new method is proposed for solving box constrained global optimization problems. The basic idea of the method is described as follows: Constructing a so-called cut-peak function and a choice function for each present minimizer, the original problem of finding a global solution is converted into an auxiliary minimization problem of finding local minimizers of the choice function, whose objective function values are smaller than the previous ones. For a local minimum solution of auxiliary problems this procedure is repeated until no new minimizer with a smaller objective function value could be found for the last minimizer. Construction of auxiliary problems and choice of parameters are relatively simple, so the algorithm is relatively easy to implement, and the results of the numerical tests are satisfactory compared to other methods.     

A continuously differentiable filled function method for global optimization

In this paper, a new filled function method for finding a global minimizer of global optimization is proposed. The proposed filled function is continuously differentiable and only contains one parameter. It has no parameter sensitive terms. As a result, a general classical local optimization method can be used to find a better minimizer of the proposed filled function with easy parameter adjustment. Numerical experiments show that the proposed filled function method is effective.     

A filled function method with one parameter for unconstrained global optimization

The filled function method is considered as an efficient approach to solve the global optimization problems. In this paper, a new filled function method is proposed. Its main idea is as follows: a new continuously differentiable filled function with only one parameter is constructed for unconstrained global optimization when a minimizer of the objective function is found, then a minimizer of the filled function will be found in a lower basin of the objective function, thereafter, a better minimizer of the objective function will be found. The above process is repeated until the global optimal solution is found. The numerical experiments show the efficiency of the proposed filled function method.     

A Sequential Convexification Method (SCM) for Continuous Global Optimization

A new method for continuous global minimization problems, acronymed SCM, is introduced. This method gives a simple transformation to convert the objective function to an auxiliary function with gradually fewer local minimizers. All Local minimizers except a prefixed one of the auxiliary function are in the region where the function value of the objective function is lower than its current minimal value. Based on this method, an algorithm is designed which uses a local optimization method to minimize the auxiliary function to find a local minimizer at which the value of the objective function is lower than its current minimal value. The algorithm converges asymptotically with probability one to a global minimizer of the objective function. Numerical experiments on a set of standard test problems with several problems' dimensions up to 50 show that the algorithm is very efficient compared with other global optimization methods.     

A filled function method for constrained global optimization

In this paper, a filled function method for solving constrained global optimization problems is proposed. A filled function is proposed for escaping the current local minimizer of a constrained global optimization problem by combining the idea of filled function in unconstrained global optimization and the idea of penalty function in constrained optimization. Then a filled function method for obtaining a global minimizer or an approximate global minimizer of the constrained global optimization problem is presented. Some numerical results demonstrate the efficiency of this global optimization method for solving constrained global optimization problems.     

A filled function method applied to nonsmooth constrained global optimization

The filled function method is an effective approach to find a global minimizer. In this paper, based on a new definition of the filled function for nonsmooth constrained programming problems, a one-parameter filled function is constructed to improve the efficiency of numerical computation. Then a corresponding algorithm is presented. It is a global optimization method which modify the objective function as a filled function, and which find a better local minimizer gradually by optimizing the filled function constructed on the minimizer previously found. Illustrative examples are provided to demonstrate the efficiency and reliability of the proposed filled function method.