Informatica

In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of R^m, in which some real-valued function f(x) assumes its optimal value. We consider here a global optimization algorithm. We present a stochastic approach, which is based on the simulated annealing algorithm. The optimization function f(x) here is discrete and with noise.

A multiextremal problem on the synthesis of external circuit of a tunable subnanosecond pulse TRAPATT-generator was investigated using algorithms of local optimization and cluster analysis.

One objective of this paper is to estimate the parameters p,d,q of an autoregressive fractionally integrated moving average ARFIMA (p,d,q) stochastic model by minimizing the squares of the residuals using a Bayesian global optimization techniques. We consider bilinear model, too because it is the simple extension of linear model, defined by adding a bilinear term to traditional ARMA model. Therefore, the second objective of the paper is to estimate parameters of a bilinear time series.

In some recent papers a discussion on global minimization algorithms for a broad class of functions was started. An idea is presented here why such a case is different from a case of Lipshitzian functions in respect with the convergence and why for a broad class of functions an algorithm converges to global minimum of an objective function if it generates an everywhere dense sequence of trial points.

A random walk dan be used to model various types of discrete random processes. It may be of interest at some point to find the peak of this function. A direct method of doing so involves evaluating the function at every point and recording the highest value. However, it may be desirable to find the peak without having, to evaluate the function at every point. A search technique was developed to find the peak of a random walk with a minimal number of function evaluations using probabilistic means to guess at where the peak will most likely occur given the parameters of a specific function. A computer program was written to implement the search strategy and a series-of random walk functions of varying lengths were generated to test its performance. Data was compiled and the results show that the search is capable of finding the peak with a significant reduction in the number of function evaluations needed for a point by point search, especially for functions of greater walk length.

In well-known statistical models of global optimization only values of objective functions are taken into consideration. However, efficient algorithms of local optimization are also based on the use of gradients of objective functions. Thus, we are interested in a possibility of the use of gradients in statistical models of multimodal functions, aiming to create productive algorithms of global optimization.

The problems and results in constructing the statistical models of multimodal functions are reviewed. The rationality of the search for global minimum is formulated axiomatically and the features of the corresponding algorithm are discussed. The results of some applications of the proposed algorithm are presented.

The maximization problem for an objective function f given on a feasible region X is considered, where X is a compact subset of Rⁿ and f belongs to a set of continuous multiextremal functions on X can be evaluated at any point x in X without error, and its maximum M=max x∈Xf(x) together with a maximizer x^*(a point x^* in X such that M=f(x^*)) are to be approximated. We consider a class of the global random search methods, underlying an apparatus of the mathematical statistics and generalizing the so-called branch and bound methods.

In the paper the global optimization is described from the point of an interactive software design. The interactive software that implements numeric methods and other techniques to solve global optimization problems is presented. Some problems of such a software design are formulated and discussed.

In this paper the problem of optimization of multivariate multimodal functions observed with random error is considered. Using the random function for a statistical model of the objective function the minimization procedure is suggested. This algorithm is convergent on a discrete set. To avoid computational difficulties, the modified algorithm is defined by substituting the parameters of minimization procedure by their estimates.