Informatica

The heliostat field of Solar Central Receiver Systems takes up to 50% of the initial investment and can cause up to 40% of energetic loss in operation. Hence, it must be carefully optimized. Design procedures usually rely on particular heliostat distribution models. In this work, optimization of the promising biomimetic distribution model is studied. Two stochastic population-based optimizers are applied to maximize the optical efficiency of fields: a genetic algorithm, micraGA, and a memetic one, UEGO. As far as the authors know, they have not been previously applied to this problem. However, they could be a good option according to their structure. Additionally, a Brute-Force Grid is used to estimate the global optimum and a Pure-Random Search is applied as a baseline reference. Our empirical results show that many different configurations of the distribution model lead to very similar solutions. Although micraGA exhibits poor performance, UEGO achieves the best results in a reduced time and seems appropriate for the problem at hand.

This paper reviews the interplay between global optimization and probability models, concentrating on a class of deterministic optimization algorithms that are motivated by probability models for the objective function. Some complexity results are described for the univariate and multivariate cases.

The optimal financial investment (Portfolio) problem was investigated by leading financial organizations and scientists. Nobel prizes were awarded for the Modern Portfolio Theory (MPT) and further developments. The aim of these works was to define the optimal diversification of the assets depending on the acceptable risk level.

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.