Informatica

We investigate the problem of detecting a point set’s deviation from uniformity in the unit hypercube. High uniformity is for example desirable in Monte Carlo methods for numerical integration, but also for obtaining a good worst-case bound in global optimization. In high dimensions, many points are required to get reliable results, so the point sets are preferably generated by fast methods such as quasirandom sequences. Unfortunately, assessing their uniformity often requires quadratic time. So, we present several numerical summary characteristics of point sets that can be computed in linear time. They do not measure uniformity directly, but by comparing them to reference values for the uniform distribution, deviations from uniformity can be quickly detected. The necessary reference values are also derived here, if possible exactly, else approximately.

This is a survey of the main achievements in the methodology and theory of stochastic global optimization. It comprises two complimentary directions: global random search and the methodology based on the use of stochastic models about the objective function. The main attention is paid to theoretically substantiated methods and mathematical results proven in the last 25 years.

The aim of this paper is to explore some features of the functional test generation problem, and on the basis of the gained experience, to propose a practical method for functional test generation. In the paper presented analysis of random search methods and adjacent stimuli generation allowed formulating a practical method for generating functional tests. This method incorporates the analyzed termination conditions of generation, exploits the advantages of random and deterministic search, as well as the feature that the sets of the selected input stimuli can be merged easily in order to obtain a better set of test patterns.

In the present paper, the method of structure analysis for multivariate functions was applied to examine the global sensitivity of three complex models: the HIV/AIDS infection spread, radar search, and the multiple criteria decisions.

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.