Informatica

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 concentration of a substrate in a solution can be measured using amperometric signals of biosensors: in fact the maximum (steady state) current is measured which is calibrated in the units of concentration. Such a simple method is not applicable in the case of several substrates. In the present paper, the problem of evaluation of concentrations of several substrates is tackled by minimizing the discrepancy between the observed and modeled transition processes of the amperometric signal.

The optimization problems occurring in nonlinear regression normally cannot be proven unimodal. In the present paper applicability of global optimization algorithms to this problem is investigated with the focus on interval arithmetic based algorithms.

We investigate applicability of quantitative methods to discover the most fundamental structural properties of the most reliable political data in Lithuania. Namely, we analyze voting data of the Lithuanian Parliament. Two most widely used techniques of structural data analysis (clustering and multidimensional scaling) are compared. We draw some technical conclusions which can serve as recommendations in more purposeful application of these methods.

Recent publications on multidimensional scaling express contradicting opinion on multimodality of STRESS criterion. An example has been published with rigorously provable multimodality of STRESS. We present an example of data and the rigorous proof of multimodality of SSTRESS for this data. Some comments are included on widely accepted opinion that minimization of SSTRESS is easier than minimization of STRESS.

Multidimensional scaling (MDS) is well known technique for analysis of multidimensional data. The most important part of implementation of MDS is minimization of STRESS function. The convergence rate of known local minimization algorithms of STRESS function is no better than superlinear. The regularization of the minimization problem is proposed which enables the minimization of STRESS by means of the conjugate gradient algorithm with quadratic rate of convergence.

We consider finite population slotted ALOHA where each of n terminals has its own transmission probability pi. Given the overall traffic load λ, the probabilities pi are determined in such a way as to maximize throughput. This is achieved by solving a constrained optimization problem. The results of Abramson (1970) are obtained as a special case. Our recent results are improved (Mathar and Žilinskas, 1993).

We consider finite population slotted ALOHA where each of n terminals may have its own transmission probability pi. Given the traffic load λ, throughput is maximized via a constrained optimization problem. The results of Abramson (1985) are obtained as special case.

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.

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.