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.     

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 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.     

A Controlled Random Search Technique Incorporating the Simulated Annealing Concept for Solving Integer and Mixed Integer Global Optimization Problems

In this paper, a computational algorithm, named RST2ANU algorithm, has been developed for solving integer and mixed integer global optimization problems. This algorithm, which primarily is based on the original controlled random search approach of Price [22i], incorporates a simulated annealing type acceptance criterion in its working so that not only downhill moves but also occasional uphill moves can be accepted. In its working it employs a special truncation procedure which not only ensures that the integer restrictions imposed on the decision variables are satisfied, but also creates greater possibilities for the search leading to a global optimal solution. The reliability and efficiency of the proposed RST2ANU algorithm has been demonstrated on thirty integer and mixed integer optimization problems taken from the literature. The performance of the algorithm has been compared with the performance of the corresponding purely controlled random search based algorithm as well as the standard simulated annealing algorithm. The performance of the method on mathematical models of three realistic problems has also been demonstrated.     

Some Variants of the Controlled Random Search Algorithm for Global Optimization

We suggested some modifications to the controlled random search (CRS) algorithm for global optimization. We introduce new trial point generation schemes in CRS, in particular, point generation schemes using linear interpolation and mutation. Central to our modifications is the probabilistic adaptation of point generation schemes within the CRS algorithm.A numerical study is carried out using a set of 50 test problems many of which are inspired by practical applications. Numerical experiments indicate that the resulting algorithms are considerably better than the previous versions. Thus, they offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring direct search type methods.     

Partitioned Random Search for Global Optimization with Sampling Cost and Discounting Factor

The method of partitioned random search has been proposed in recent years to obtain an as good as possible solution for the global optimization problem (1). A practical algorithm has been developed and applied to real-life problems. However, the design of this algorithm was based mainly on intuition. The theoretical foundation of the method is an important issue in the development of efficient algorithms for such problems. In this paper, we generalize previous theoretical results and propose a sequential sampling policy for the partitioned random search for global optimization with sampling cost and discounting factor. A proof of the optimality of the proposed sequential sampling policy is given by using the theory of optimal stopping.     

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 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     

Optimal Scaling for Random Walk Metropolis on Spherically Constrained Target Densities

We consider the problem of optimal scaling of the proposal variance for multidimensional random walk Metropolis algorithms. It is well known, for a wide range of continuous target densities, that the optimal scaling of the proposal variance leads to an average acceptance rate of 0.234. Therefore a natural question is, do similar results hold for target densities which have discontinuities? In the current work, we answer in the affirmative for a class of spherically constrained target densities. Even though the acceptance probability is more complicated than for continuous target densities, the optimal scaling of the proposal variance again leads to an average acceptance rate of 0.234.     

Multiobjective Search Algorithm with Subdivision Technique

This paper presents a multiobjective search algorithm with subdivision technique (MOSAST) for the global solution of multiobjective constrained optimization problems with possibly noncontinuous objective or constraint functions. This method is based on a random search method and a new version of the Graef-Younes algorithm and it uses a subdivision technique. Numerical results are given for bicriterial test 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.     

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.     

柯西-布涅柯夫斯基不等式在优化中的应用

本文给出了柯西—布涅柯夫斯基不等式在非线性规划中应用的两个例子．     

A Staged Continuous Tabu Search Algorithm for the Global Optimization and its Applications to the Design of Fiber Bragg Gratings

A novel staged continuous Tabu search (SCTS) algorithm is proposed for solving global optimization problems of multi-minima functions with multi-variables. The proposed method comprises three stages that are based on the continuous Tabu search (CTS) algorithm with different neighbor-search strategies, with each devoting to one task. The method searches for the global optimum thoroughly and efficiently over the space of solutions compared to a single process of CTS. The effectiveness of the proposed SCTS algorithm is evaluated using a set of benchmark multimodal functions whose global and local minima are known. The numerical test results obtained indicate that the proposed method is more efficient than an improved genetic algorithm published previously. The method is also applied to the optimization of fiber grating design for optical communication systems. Compared with two other well-known algorithms, namely, genetic algorithm (GA) and simulated annealing (SA), the proposed method performs better in the optimization of the fiber grating design.     

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.     

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.     

A q-Analog of the Hook Walk Algorithm for Random Young Tableaux

A probabilistic algorithm, called the q-hook walk, is defined. For a given Young diagram, it produces a new one by adding a random box with probabilities, depending on a positive parameter q. The corresponding Markov chain in the space of infinite Young tableaux is closely related to the knot invariant of Jones, constructed via traces of Hecke algebras. For q = 1, the algorithm is essentially the hook walk of Greene, Nijenhuis, and Wilf. The q-hook formula and a q-deformation of Young graph are also considered.S. Kerov: Supported by a grant from CRM (Université de Montréal), during its Operator Algebras year     

基于模矢搜索和遗传算法的混合约束优化算法

近年,免梯度方法又开始引起大家的注意，由于不需要计算函数的梯度．特别适合用来求解那些无法得到梯度信息或需要花很大计算量才能得到梯度信息的问题．本文构造了一个基于模矢搜索和遗传算法的混合优化算法．在模矢搜索方法的搜索步，用一个类似于遗传算法的方法产生一个有限点集．算法是全局收敛的.     

一类非线性种群发展方程非局部柯西问题随机周期解的存在性

研究如下形式具有随机周期移民扰动的非线性种群发展方程的非局部柯西问题，{δp（r,t）/δt＋δp（r,t）/δr=-μ（r）p（r,t）＋f（t,p（r,t））,0＜r＜rm,t≥0,p（r,0）=p0（r）＋g（p（r,t0））,T＞t0＞0 p（0,t）=β（t）∫^r2 r1（k（r）h（r）p（r,t）dr这里，其他地区的种群迁入项厂以及非局部条件项g为紧算子，且厂是时间变量t的周期为T的周期函数．利用Shesfer不动点定理，可以证明上述柯西问题随机周期积分解的存在性．这篇论文的结果推广了前人的工作．