演化均匀优化算法

针对演化算法，使用随机法产生初始点带来的缺陷和均匀设计方法的优点，提出了演化均匀优化算法，进行了算法收敛性分析，并把它应用于多峰函数的数值优化计算，给出了计算示例，结果表明该方法是一种可行而且有效的优化算法．     

求一类多元多峰函数全局极小的区间斜率方法

Based on the interval analysis, an interval slope method is proposed for finding all global minimizers of a several peaks function f on domain X^0包含于R^n, which is given by interval slope discard tests and interval extension of objective function.Numerical results of representative test functions show that this method is practical and effective.     

基于神经网络的多目标演化优化方法

本文考虑在决策者偏好不明确的条件下，使系统获得最优的思想，提出了多目标决策系统最优解的概念。把前馈神经网络与演化算法相结合，用于多目标决策系统最优解的选取。给出了有关定理的证明和示例。     

一类全局优化问题的区间斜率算法

考虑下面的全局优化问题: global minimize f(x),f:X~0 R~1→R~1 (1)其中X~0=[a~0,b~0],f是X~0上连续的多峰函数.在本文中f在X~0上的全局极小值记为f~*,f在X~0上所有全局极小点集合记为X~*.以下恒假定X~*仅由有限个点组成. 我们的目标是求f~*及X~*.求解这一问题已有诸多方法,这些方法一般可分为确定型和非确定型两类.前者以Lipschitz导数法,填充函数法等为代表,它们依据某一     

求多峰函数全部全局最优解的改进遗传算法

本文研究了多峰优化问题,利用梯度算子和筛选策略,得到了一种可求解多峰函数全部最优解的改进型遗传算法.数值模拟结果表明,该算法在处理复杂多峰函数优化问题时,局部搜索能力和克服过早收敛能力方面相对于传统遗传算法均有很大提高.     

生长竞争型函数优化的蚁群算法

提出一种求解函数优化的生长竞争型蚁群算法.该方法利用植物生长的向光性机制,引入竞争机制,获取局部的最优解,再结合蚁群算法,实现全局优化.算法在MATLAB环境下,对一些典型的测试函数进行了求解和验证,实验结果表明该方法是一种求解函数优化的有效方法.     

DC函数优化问题的非精确邻近点算法

本文对DC函数(即两凸函数之差)的最小化问题提出了一个非精确邻近点算法,并证明此算法的下降性和全局收敛性.     

多层线性规划问题的整体优化算法

本文研究了求解多层线性规划问题的整体优化算法,利用流动等值面技术,证明了算法的有限终止性,并给出实际例子验证了算法的有效性.     

多目标优化问题的模糊交叉算法与收敛性

本文研究了目标权重未事先确知的多目标优化问题，建立可以同时确定目标权重与方案相对优属度的模糊交叉迭代算法，严格证明了该算法的局部收敛性．     

多峰多维密度模拟退火的可逆算法

在对多峰多维密度作模拟退火时,使用Markov链Monte Carlo方法常会遇到从逸出一个峰底进入另一个峰底的困难,因为这常常需要指数长的时间,从而在实际上使算法不可能实现.为了克服这个困难,建议用一个可逆设计生成一个Markov 链,运用它为工具所得到的模拟密度,在相当一般的情形下,可以成功地避免使算法陷入局部峰底的困难.     

求解约束优化问题的一个对偶算法

１．引言 考虑下述形式的不等式约束优化问题：其中 ＝０,１,…,ｍ,是连续可微函数．求解（１．１）的数值方法有很多,传统方法有乘子法,序列一次规划方法,等等（见 Ｂｅｒｔｓｅｋａｓ（１９８２）, Ｈａｎ（１９７６, １９７７））．近年来对求解（１．１）的原始－对偶算法的研究已成为非线性规划领域的新的热点,如ＥＩ－Ｂａｋｒｙ,Ｔａｐｉａ,Ｔｓｕｃｈｉｙａ　＆　Ｚｈａｎｇ（１９９６）,Ｙａｍａｓｈｉｔａ（１９９２,１９９６,１９９７）等;尽管这些原始－对偶算法具有好的收敛性质和计算效果,但其算法结构相对…     

一个求解不等式约束优化问题的势函数算法

A potential function algorithm is constructed for solving inequality constrainted optimization problems. It is proved that the sequences generated by the algorithm converge locally to a Kuhn-Tucker point under some suitable conditions. Finally, numerical results arc reported to show the validity of the algorithm.     

解无约束优化问题的一个新的带线搜索的信赖域算法

在传统信赖域方法的基础上, 提出了求解无约束最优化问题的一个新的带线搜索的信赖域算法. 该算法采用大步长 Armijo 线搜索技术获得迭代步长, 克服了每次迭代求解信赖域子问题时计算量较大的缺点, 因而适用于求解大型的优化问题. 在适当的条件下, 我们证明了算法的全局收敛性. 数值实验结果表明本文所提出的算法是有效的.     

AN ADAPTIVE MEMBRANE ALGORITHM FOR SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS

Membrane algorithms （MAs）, which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The em-pirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural net-work and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.     

A NEW NONMONOTONE TRUST REGION ALGORITHM FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS

Based on the nonmonotone line search technique proposed by Gu and Mo （Appl. Math. Comput. 55, （2008） pp. 2158-2172）, a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio ρk for evaluating the trial step dk whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.     

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     

A TRUST REGION ALGORITHM FOR CONSTRAINED NONSMOOTH OPTIMIZATION PROBLEMS

1. Introductioncrust region methods are an hoportat class Of iterative wthods for solving nonlinearoptbozation problems, and have been developed rapidly in recent twenty years (see [1]--[9] 1 115] )[16] etc.). FOr nonsmooth optbozation problems, as early as in 1984, Y. Yuan [21 [3] prOPosed atrust region method for the composite function f(x) = h(g(x)), where h is convex and g E C';L. Qi and J. Sam [4] proposed an inexaCt trust region method for the general unconstrainednonsmooth optchatio…     

A FEASIBLE DIRECTION ALGORITHM WITHOUT LINE SEARCH FOR SOLVING MAX-BISECTION PROBLEMS

This paper concerns the solution of the NP-hard max-bisection problems. NCP func-tions are employed to convert max-bisection problems into continuous nonlinear program-ming problems. Solving the resulting continuous nonlinear programming problem generatesa solution that gives an upper bound on the optimal value of the max-bisection problem.From the solution, the greedy strategy is used to generate a satisfactory approximate so-lution of the max-bisection problem. A feasible direction method without line searches isproposed to solve the resulting continuous nonlinear programming, and the convergenceof the algorithm to KKT point of the resulting problem is proved. Numerical experimentsand comparisons on well-known test problems, and on randomly generated test problemsshow that the proposed method is robust, and very efficient.