Catálogo de publicaciones - libros

In this chapter we propose a hybrid point generation scheme in the differential evolution (DE) algorithm. In particular, we propose a DE algorithm that uses a probabilistic combination of the point generation by the -distribution and the point generation by mutation. Numerical results suggest that the resulting algorithm is superior to the original version both in terms of the number of function evaluations and cpu times.

It is much more difficult to approximate the minimum of a function using noise-corrupted function evaluations than when the function can be evaluated precisely. This chapter is concerned with the question of exactly how much harder it is in a particular setting; namely, on average when the objective function is a Wiener process, the noise is independent Gaussian, and nonadaptive algorithms are considered.

In a variety of global random search methods, the minimum of a function is estimated using either one of linear estimators or the the maximum likelihood estimator. The asymptotic mean square errors (MSE) of several linear estimators asymptotically coincide with the asymptotic MSE of the maximum likelihood estimator. In this chapter we consider the non-asymptotic behaviour of different estimators. In particular, we demonstrate that the MSE of the best linear estimator is superior to the MSE of the the maximum likelihood estimator.

Whereas genetic algorithms and evolutionary methods involve a population of points, simulated annealing (SA) can be interpreted as a random walk of a single point inside a feasible set. The sequence of locations visited by SA is a consequence of the Markov Chain Monte Carlo sampler. Instead of running SA with multiple independent runs, in this chapter we study a multi-particle version of simulated annealing in which the population of points interact with each other. We present numerical results that demonstrate the benefits of these interactions on algorithm performance.

An early introductory text on Global Optimisation (GO), [], goes further than mathematical correctness in giving the reader an intuitive idea about concepts in GO. This chapter extends this spirit by introducing students and researchers to the concepts of Global Optimisation (GO) algorithms. The goal is to learn to read and interpret optimisation algorithms and to analyse their goodness. Before going deeper into mathematical analysis, it is good for students to get a flavour of the difficulty by letting them experiment with simple algorithms that can be followed by hand or spreadsheet calculations. Two simple one-dimensional examples are introduced and several simple NLP and GO algorithms arc elaborated. This is followed by some lessons that can be learned from investigating the algorithms systematically.

Development and applications of the open source software is a new and dynamic field. Important changes often happen in days and weeks. Thus some new non-traditional approaches of education should be investigated to meet the needs of open software adequately.

The general consideration of this problem is difficult. Therefore we start by relevant case studies. In this chapter we consider models of optimal sequential decisions with multiple objective functions as an example. The aim is to show that models can be implemented and updated by graduate students themselves. That reflects the usual procedures of the open source development. This way students not only learn the underlaying model but obtain the experience in the development of open source software.

In this case the step-by-step improvement of the model and software is at least as important as the final result that is never achieved in open source environment as usual. A short presentation of the basic ideas is in []. Note that doing this we accumulate some experience in the completely new field of education when all the information can be easily obtained by Internet. The users are doing just the creative part by filtering and transforming the information to meet their own objectives, to build their own models. The natural way is computer experimentation.

To make the task as easy as possible all the algorithms considered in this chapter are implemented as platform independent Java applets or servlets therefore readers can easily verify and apply the results for studies and for real life optimization models.

To address this idea the chapter is arranged in a way convenient for the direct reader participation. Therefore a part of the chapter is written as some ‘user guide’. The rest is a short description of optimization algorithms and models. All the remaining information is on web-sites, for example .

We consider the problem of visual analysis of the multidimensional medical data. A frequent problem in medicine is an assignment of a health state to one of the known classes (for example, healthy or sick persons). A particularity of medical data classification is the fact that the transit from the normal state to diseased one is often not so conspicuous. From the table of the parametric medical multidimensional data, it is difficult to notice which objects are similar, which ones are different, i.e., which class they belong to. Therefore it is necessary to classify the multidimensional data by various classification methods. However, classification errors arc inevitable and the results of classification in medicine must be as correct as possible. That is why it is advisable to use different types of data analysis methods, for example, in addition to visualize the multidimensional data (to project to a plane). A visual analysis allows us to estimate similarities and differences of objects, a partial assignment to one or another class in simple visual way. However, the shortcoming of this analysis is the fact that while projecting multidimensional data to a plane, a part of the information is inevitably lost. Thus, one of the agreeable methods is a combination of classification and visualization methods. This synthesis lets us to obtain a more objective conclusions on the analysed data. The results, obtained by the integrated method, proposed in this chapter, can help medics to preliminary diagnose successfully or have some doubt on the former diagnosis.

Many problems in engineering, physics, economic and other subjects may be formulated as optimization problems, where the minimum value of an objective function should be found. Mathematically the problem is formulated as follows where () is an objective function, are decision variables, and is a search space. Besides of the minimum *, one or all minimizers * : (*) = * should be found.

The design of a water distribution network [] involves identifying the optimal pipe network, the head pressures of the individual supply and demand nodes, and the flows between the nodes, including both the amount and the direction of flow. The objective is to find the minimum cost network which meets the demands specified. Despite the objective function often being simple, consisting of a linear combination of pipe diameters and lengths, the water distribution network design problem poses challenges for optimization tools due to the tight nonlinear constraints imposed by the modelling of the relationship between node heads, water flow in a pipe, and the pipe diameter.

Design problems of predictor-based self tuning digital control systems for different types of linear and non-linear dynamical plants are discussed. Control systems based on generalized minimum variance algorithms with amplitude and introduction rate restrictions for the control signal are considered in the article.