Informatica

In this paper, we consider the so-called structured low rank approximation (SLRA) problem as a problem of optimization on the set of either matrices or vectors. Briefly, SLRA is defined as follows. Given an initial matrix with a certain structure (for example, Hankel), the aim is to find a matrix of specified lower rank that approximates this initial matrix, whilst maintaining the initial structure. We demonstrate that the optimization problem arising is typically very difficult; in particular, the objective function is multiextremal even in simple cases. We also look at different methods of solving the SLRA problem. We show that some traditional methods do not even converge to a locally optimal matrix.

We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a random objective function distributed according to the Wiener measure.

The paper deals with the use of formant features in dynamic time warping based speech recognition. These features can be simply visualized and give a new insight into understanding the reasons of speech recognition errors. The formant feature extraction method, based on the singular prediction polynomials, has been applied in recognition of isolated words. However, the speech recognition performance depends on the order of singular prediction polynomials, whether symmetric or antisymmetric singular prediction polynomials are used for recognition and as well on the fact even or odd order of these polynomials is chosen. Also, it is important to know how informative separate formants are, how the speech recognition results depend on other parameters of the recognition system such as: analysis frame length, number of the formants used in recognition, frequency scale used for representation of formant features, and the preemphasis filter parameters. Properly choosing the processing parameters, it is possible to optimize the speech recognition performance.

Recent changes in the intersection of the fields of intelligent systems optimization and statistical learning are surveyed. These changes bring new theoretical and computational challenges to the existing research areas racing from web page mining to computer vision, pattern recognition, financial mathematics, bioinformatics and many other ones.

The objective of this paper is the description, justification, and web-based implementation of polynomial time algorithms for equilibrium search of Quadratic Bimatrix Games (QBG). An algorithm is proposed combining exact and heuristic parts. The exact part has the Irelevant Fraud (IF) component for cases when an equilibrium exists with no pure strategies. The Direct Search (DS) component finds a solution if an equilibrium exists in pure strategies. The heuristic Quadratic Strategy Elimination (QSE) part applies IF and DS to reduced matrices obtained by sequential elimination of strategies that lead to non-positive IF solutions. Finally, penalties needed to prevent unauthorized deals are calculated based on Nash axioms of two-person bargaining theory. In the numeric experiments QSE provided correct solution in all examples. The novel results include necessary and sufficient conditions when the QBG problem is solved by IF algorithm, the development of software and the experimental testing of large scale QBG problems up to n=800. The web-site http://pilis.if.ktu.lt/~jmockus includes this and accompanying optimization models.

The Star Plot approach to high-dimensional data visualization is applied to multi-attribute dichotomies. It is observed that the areas of the plot for the two parts of a dichotomy may be used as an aggregate measure of their relative dominance. An optimization model is developed to determine a topology (or weighted configuration of the attributes) that maximizes the resolution of this measure with respect to a given set of reference dichotomies.

The paper deals with the intelligent functional model for optimizing the product design and its manufacturing process in hybrid manufacturing systems consisting of people, machines and computers. The knowledge‐based framework of an intelligent functional model has been developed. It furnishes the possibility for a product designer and manufacturer to find an optimal production plan in the early stage of the product design. The mathematical model formalization is provided. A consecutive optimization scheme has been applied for selecting an optimal alternative of a product design and its production plan. The proposed model is being implemented both in industry and university education process.

The paper analyzes the performance of parallel global optimization algorithm, which is used to optimize grillage-type foundations. The parallel algorithm is obtained by using the automatic parallelization tool. We describe briefly the layer structure of the Master–Slave Template library and present a detailed mathematical formulation of the application problem. Experiments are done on the homogeneous computer cluster of 7 IBM machines RS6000. The results of experiments are presented.

The problem of recursive estimation of a state of dynamic systems in the presence of time-varying outliers in observations to be processed has been considered. A learning phase used in the state estimation is investigated, assuming that the observations of a noisy output signal and that of a training one are given. A technique based on robust filtering by means of a bank of parallel Kalman filters and on the procedure of optimization of the state estimation itself is used, choosing, at each time moment, a current estimate, that ensures a minimal absolute deviation from the current value of the teaching signal. An approach, based on the relation between the mean squared deviation of state estimates from the true state and innovation sequence variance as well as on the fact that both variables achieve their minimum for the same filter from the respective Kalman filter bank, is proposed here for a working phase, where a training signal will be absent. The recursive technique based on an adaptive state estimation with optimization procedure is worked out. The results of numerical simulation of the linear discrete-time invariant (LTI) system (56) by computer using a bank, consisting of Kalman filters are given (Figs. 1–5).

Multicriteria sequencing problems with criteria ordered according to their importance are considered. Additional precedence and group technology constraints are imposed. We introduce a notion of a priority-generating vector function and suggest general techniques that form a base for the construction of polynomial time algorithms for numerous sequencing problems including all known polynomially solvable problems. A comprehensive survey of results for sequencing problems with ordered criteria is given as well.