A GA-Simplex Hybrid Algorithm for Global Minimization of Molecular Potential Energy Functions

In this paper we propose a hybrid genetic algorithm for minimizing molecular potential energy functions. Experimental evidence shows that the global minimum of the potential energy of a molecule corresponds to its most stable conformation, which dictates its properties. The search for the global minimum of a potential energy function is very difficult since the number of local minima grows exponentially with molecule size. The proposed approach was successfully applied to two cases: (i) a simplified version of more general molecular potential energy functions in problems with up to 100 degrees of freedom, and (ii) a realistic potential energy function modeling two different molecules.     

Iterative Convex Quadratic Approximation for Global Optimization in Protein Docking

An algorithm for finding an approximate global minimum of a funnel shaped function with many local minima is described. It is applied to compute the minimum energy docking position of a ligand with respect to a protein molecule. The method is based on the iterative use of a convex, general quadratic approximation that underestimates a set of local minima, where the error in the approximation is minimized in the L¹ norm. The quadratic approximation is used to generate a reduced domain, which is assumed to contain the global minimum of the funnel shaped function. Additional local minima are computed in this reduced domain, and an improved approximation is computed. This process is iterated until a convergence tolerance is satisfied. The algorithm has been applied to find the global minimum of the energy function generated by the Docking Mesh Evaluator program. Results for three different protein docking examples are presented. Each of these energy functions has thousands of local minima. Convergence of the algorithm to an approximate global minimum is shown for all three examples.     

求解全局优化问题的三角进化算法

This paper presents a hybrid heuristic-triangle evolution （TE） for global optimization. It is a real coded evolutionary algorithm. As in differential evolution （DE）, TE targets each individual in current population and attempts to replace it by a new better individual. However, the way of generating new individuals is different. TE generates new individuals in a Nelder- Mead way, while the simplices used in TE is 1 or 2 dimensional. The proposed algorithm is very easy to use and efficient for global optimization problems with continuous variables. Moreover, it requires only one （explicit） control parameter. Numerical results show that the new algorithm is comparable with DE for low dimensional problems but it outperforms DE for high dimensional problems.     

An Algorithm for Global Minimization of Linearly Constrained Quadratic Functions*

A branch and bound algorithm is proposed for finding an approximate global optimum of quadratic functions over a bounded polyhedral set. The algorithm uses Lagrangian duality to obtain lower bounds. Preliminary computational results are reported.     

A Trust-Region Algorithm for Global Optimization

We consider the global minimization of a bound-constrained function with a so-called funnel structure. We develop a two-phase procedure that uses sampling, local optimization, and Gaussian smoothing to construct a smooth model of the underlying funnel. The procedure is embedded in a trust-region framework that avoids the pitfalls of a fixed sampling radius. We present a numerical comparison to three popular methods and show that the new algorithm is robust and uses up to 20 times fewer local minimizations steps.     

Proof of Convergence for a Global Optimization Algorithm for Problems with Ordinary Differential Equations

A deterministic spatial branch and bound global optimization algorithm for problems with ordinary differential equations in the constraints has been developed by Papamichail and Adjiman [A rigorous global optimization algorithm for problems with ordinary differential equations. J. Glob. Optim. 24, 1–33]. In this work, it is shown that the algorithm is guaranteed to converge to the global solution. The proof is based on showing that the selection operation is bound improving and that the bounding operation is consistent. In particular, it is shown that the convex relaxation techniques used in the algorithm for the treatment of the dynamic information ensure bound improvement and consistency are achieved.     

一种改进的禁忌搜索算法及其在连续全局优化中的应用

禁忌搜索算法是一种元启发式的全局优化算法,是局部搜索算法的一种推广,已被成功地应用于许多组合优化问题中。本文针对有界闭区域上的连续函数全局优化问题,提出了一种改进的禁忌搜索算法,并进行了理论分析和数值实验。数值实验表明,对于连续函数全局优化问题的求解该算法是可行有效的,并且结构简单,迭代次数较少,是一种较好的全局启发式优化算法。     

A Simple Multistart Algorithm for Global Optimization

1.IntroductionConsidertheunconstrainedoptimizationproblem:findx*suchthatf(x*)~caf(x),(1)wheref(x)isanonlinearfllnctiondefinedonW"andXCR".Ourobjectiveistofindtheglobalminimizeroff(x)inthefeasibleset.Withoutassuminganyconditionsonf(x)globaloptimizationproblemsareunsolvableinthefollowingsensefnoalgorithmcanbeguaranteedtofindaglobalminimizerofageneralnonlinearfunctionwithinfinitelymanyiterations.Supposethatanalgorithmappliedtoanonlinearfunctionf(x)producesiteratesxlandterminatesafterKiterations.…     

A New Version of the Price's Algorithm for Global Optimization

We present an algorithm for finding a global minimum of a multimodal,multivariate function whose evaluation is very expensive, affected by noise andwhose derivatives are not available. The proposed algorithm is a new version ofthe well known Price's algorithm and its distinguishing feature is that ittries to employ as much as possible the information about the objectivefunction obtained at previous iterates. The algorithm has been tested on alarge set of standard test problems and it has shown a satisfactorycomputational behaviour. The proposed algorithm has been used to solveefficiently some difficult optimization problems deriving from the study ofeclipsing binary star light curves.     

一类非光滑总体极值的区间算法

本文利用区间分析知识 ,构造了一类 n维非光滑函数总体极值的区间算法 ,理论分析和实例计算均表明本文算法安全可靠 ;能求出全部总体极小点 ;收敛速度也比以前方法[1] 明显加快     

一类约束全局优化的区间方法

在区间分析的基础上,对一类不等式约束的全局优化问题,给出几种新的不含全局极小的区域删除准则,提出了一个求不等式约束全局优化问题的区间算法.数值结果表明算法是可行和有效的.     

非线性比式和问题的全局优化算法

In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1) that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained.The proposed algorithm is convergent to the global minimum of(P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Nume...     

Convergence of a Simulated Annealing Algorithm for Continuous Global Optimization

In this paper a simulated annealing algorithm for continuous global optimization will be considered. The algorithm, in which a cooling schedule based on the distance between the function value in the current point and an estimate of the global optimum value is employed, has been first introduced in Bohachevsky, Johnson and Stein (1986) [2], but without any proof of convergence. Here it will be proved that, under suitable assumptions, the algorithm is convergent     

变测度的积分型全局优化算法

郑权等首先提出积分-水平集求总极值的方法,实现算法中采用Monte-Carlo 随机投点产生近似水平集来缩小搜索区域范围,但这一算法可能失去总极值点．此后,邬 冬华等给出了一种修正的积分－水平集的方法,一种区域不收缩的分箱方法以保证总极 值点不被丢失．本文在此基础上采取对不同的箱子采用不同的测度这一策略,使水平值 更充分的下降,更快的达到全局极小值,以提高修正算法的计算效率．最后给出的数值算 例说明了算法是有效的．     

A Stochastic/Perturbation Global Optimization Algorithm for Distance Geometry Problems

We present a new global optimization approach for solving exactly or inexactly constrained distance geometry problems. Distance geometry problems are concerned with determining spatial structures from measurements of internal distances. They arise in the structural interpretation of nuclear magnetic resonance data and in the prediction of protein structure. These problems can be naturally formulated as global optimization problems which generally are large and difficult. The global optimization method that we present is related to our previous stochastic/perturbation global optimization methods for finding minimum energy configurations, but has several key differences that are important to its success. Our computational results show that the method readily solves a set of artificial problems introduced by Moré and Wu that have up to 343 atoms. On a set of considerably more difficult protein fragment problems introduced by Hendrickson, the method solves all the problems with up to 377 atoms exactly, and finds nearly exact solution for all the remaining problems which have up to 777 atoms. These preliminary results indicate that this approach has very good promise for helping to solve distance geometry problems.     

全局优化问题的一个无参数填充函数算法

填充函数法是求解全局优化问题的一种有效的确定性算法,方法的关键在于填充函数的构造.对于一般无约束优化问题提出了一个新的无参数填充函数,通过定义证明了此填充函数能保持填充性质.利用其理论性质设计了相应的算法并对几个经典的算例进行了数值实验,实验结果表明算法有效可行.     

一类齐次多项式优化问题的一个全局优化算法

对图像与信号处理中遇到的一类齐次多项式优化问题,本文首先借助平移技术将目标函数转化为凸函数,然后结合初始点技术提出了求解该类问题的一个全局优化算法.与求解该类问题的幂方法相比,本文给出的方法不但能在一般情形下保证算法的全局收敛性,而且数值结果表明在多数情况下可以得到问题的一个全局最优值解.     

Convergence of the Simulated Annealing Algorithm for Continuous Global Optimization

A class of simulated annealing algorithms for continuous global optimization is considered in this paper. The global convergence property is analyzed with respect to the objective value sequence and the minimum objective value sequence induced by simulated annealing algorithms. The convergence analysis provides the appropriate conditions on both the generation probability density function and the temperature updating function. Different forms of temperature updating functions are obtained with respect to different kinds of generation probability density functions, leading to different types of simulated annealing algorithms which all guarantee the convergence to the global optimum.     

A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions

Genetic algorithms are stochastic search approaches based on randomized operators, such as selection, crossover and mutation, inspired by the natural reproduction and evolution of the living creatures. However, few published works deal with their application to the global optimization of functions depending on continuous variables.A new algorithm called Continuous Genetic Algorithm (CGA) is proposed for the global optimization of multiminima functions. In order to cover a wide domain of possible solutions, our algorithm first takes care over the choice of the initial population. Then it locates the most promising area of the solution space, and continues the search through an intensification inside this area. The selection, the crossover and the mutation are performed by using the decimal code. The efficiency of CGA is tested in detail through a set of benchmark multimodal functions, of which global and local minima are known. CGA is compared to Tabu Search and Simulated Annealing, as alternative algorithms.     

Almost Surely Convergent Global Optimization Algorithm Using Noise-Corrupted Observations

A new recursive algorithm for searching the global minimizer of a function is proposed when the function is observed with noise. The algorithm is based on switches between the stochastic approximation and the random search. The combination of SA with RS is not a new idea in such combination, the difficulty consists in creating a good switching rule and in designing an efficient method to reduce the noise effect. The proposed switching rule is easily realizable, the noise reducing method is effective, and the whole recursive optimization algorithm is simply calculated. It is proved that the algorithm a.s. converges to the global minimizer and is asymptotically normal. In comparison with existing methods, the proposed algorithm not only requires much weaker conditions, but also is more efficient as shown by simulation.