Extending a class of continuous estimation of distribution algorithms to dynamic problems

In this paper, a class of continuous Estimation of Distribution Algorithms (EDAs) based on Gaussian models is analyzed to investigate their potential for solving dynamic optimization problems where the global optima may change dramatically during time. Experimental results on a number of dynamic problems show that the proposed strategy for dynamic optimization can significantly improve the performance of the original EDAs and the optimal solutions can be consistently located.     

Computer-assisted multifactor optimization of selectivity in gas chromatography

Summary A computer-assisted method is presented for the simultaneous multifactor optimization (stationary phase loading, column temperature and carrier gas flow rate) of the analytical conditions for the optimum separation of multicomponent samples in gas chromatography. The optimization of the separation over the experimental region is based on a special polynomial from twelve preliminary experiments using the resolution as the selection criterion. Computer scanning technique was used for optimum selection in three dimensions. Excellent agreement was obtained between the predicted data and the experimental results.     

Stochastic approximation algorithm for minimax problems

A stochastic approximation algorithm for minimax optimization problems is analyzed. At each iterate, it performs one random experiment, based on which it computes a direction vector. It is shown that, under suitable conditions, it a.s. converges to the set of points satisfying necessary optimality conditions. The algorithm and its analysis bring together ideas from stochastic approximation and nondifferentiable optimization.     

Concurrent stochastic methods for global optimization

The global optimization problem, finding the lowest minimizer of a nonlinear function of several variables that has multiple local minimizers, appears well suited to concurrent computation. This paper presents a new parallel algorithm for the global optimization problem. The algorithm is a stochastic method related to the multi-level single-linkage methods of Rinnooy Kan and Timmer for sequential computers. Concurrency is achieved by partitioning the work of each of the three main parts of the algorithm, sampling, local minimization start point selection, and multiple local minimizations, among the processors. This parallelism is of a coarse grain type and is especially well suited to a local memory multiprocessing environment. The paper presents test results of a distributed implementation of this algorithm on a local area network of computer workstations. It also summarizes the theoretical properties of the algorithm.Research supported by AFOSR grant AFOSR-85-0251, ARO contract DAAG 29-84-K-0140, NSF grant DCR-8403483, and NSF cooperative agreement DCR-8420944.     

Scalarization of vector optimization problems

In this paper, we investigate the scalar representation of vector optimization problems in close connection with monotonic functions. We show that it is possible to construct linear, convex, and quasiconvex representations for linear, convex, and quasiconvex vector problems, respectively. Moreover, for finding all the optimal solutions of a vector problem, it suffices to solve certain scalar representations only. The question of the continuous dependence of the solution set upon the initial vector problems and monotonic functions is also discussed.The author is grateful to the two referees for many valuable comments and suggestions which led to major imporvements of the paper.     

宽带集中元件环行器计算机辅助设计

本文从散射矩阵本征值的频率关系出发,对宽带集中元件环行器所需的设计参数作了优化计算。文中采用乘子法将约束优化问题化为无约束优化问题。计算结果与实验结果较一致并证实了为得到宽带性能实验中出现的隔离双峰的现象。     

Image space approach to penalty methods

In this paper, we introduce a unified framework for the study of penalty concepts by means of the separation functions in the image space (see Ref. 1). Moreover, we establish new results concerning a correspondence between the solutions of the constrained problem and the limit points of the unconstrained minima. Finally, we analyze some known classes of penalty functions and some known classical results about penalization, and we show that they can be derived from our results directly.     

Remark on the well-posedness of the problem of minimization of integral functionals

In this note, we study the well-posedness of the problem of constrained minimization of an integral functional and show that global well-posedness is equivalent to pointwise well-posedness almost everywhere. Our result extends an earlier one by Zolezzi.This research was supported by NSF Grant No. DMS 88-02688.     

Second-order numerical method for domain optimization problems

This paper is concerned with a second-order numerical method for shape optimization problems. The first variation and the second variation of the objective functional are derived. These variations are discretized by introducing a set of boundary-value problems in order to derive the second-order numerical method. The boundary-value problems are solved by the conventional finite-element method.The authors would like to express their thanks to Mr. T. Masanao, who was an undergraduate student, for his cooperation and comments. They also thank Professor Y. Sakawa of Osaka University for his encouragement.A part of this paper was presented at the IFIP Conference on Control of Boundaries and Stabilization, Clermont-Ferrand, France, 1988.     

求解不等式约束优化问题的一个改进算法

本文改进了一个求解不等式约束优化问题的对偶算法，建立了一个相应的算法，进一步证明了该算法的收敛性．最后，给出数值结果以验证该算法的有效性。