Multi-objective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables

This paper proposes a new multi-objective estimation of distribution algorithm (EDA) based on joint modeling of objectives and variables. This EDA uses the multi-dimensional Bayesian network as its probabilistic model. In this way it can capture the dependencies between objectives, variables and objectives, as well as the dependencies learnt between variables in other Bayesian network-based EDAs. This model leads to a problem decomposition that helps the proposed algorithm to find better trade-off solutions to the multi-objective problem. In addition to Pareto set approximation, the algorithm is also able to estimate the structure of the multi-objective problem. To apply the algorithm to many-objective problems, the algorithm includes four different ranking methods proposed in the literature for this purpose. The algorithm is applied to the set of walking fish group (WFG) problems, and its optimization performance is compared with an evolutionary algorithm and another multi-objective EDA. The experimental results show that the proposed algorithm performs significantly better on many of the problems and for different objective space dimensions, and achieves comparable results on some compared with the other algorithms.

Regularized model learning in EDAs for continuous and multi-objective optimization

Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods.

Methods of visualization and analysis of cardiac depolarization in the three dimensional space

The master thesis presents methods for intellectual analysis and visualization 3D EKG in order to increase the efficiency of ECG analysis by extracting additional data. Visualization is presented as part of the signal analysis tasks considered imaging techniques and their mathematical description. Have been developed algorithms for calculating and visualizing the signal attributes are described using mathematical methods and tools for mining signal. The model of patterns searching for comparison purposes of accuracy of methods was constructed, problems of a clustering and classification of data are solved, the program of visualization of data is also developed. This approach gives the largest accuracy in a task of the intellectual analysis that is confirmed in this work. Considered visualization and analysis techniques are also applicable to the multi-dimensional signals of a different kind.

Composition of basalts from the north part of the Bougault anomaly, Mid-Atlantic Ridge 15°N

A quantitative model of development of magmatic and ore-magmatic systems under crests of mid-ocean ridges is constructed. Correct physical models of melting zone formation in approximation to active spreading, non-stationary dynamics of magma intrusion from a center of generation, filling of magma chambers of various shapes, feeding of fissure-type volcanoes, and retrograde boiling of melts during solidification of intrusive bodies beneath axial zones of spreading in crests of ridges are proposed. Physicochemical and mathematical theories of disintegration of multi-component solutions, growth of liquational drops of ore melts, and sublimation of components from magmatic gases are elaborated. Methods for constructing physically correct models of heat and mass transfer in heterophase media are devised. Modeling of development of magmatic and ore-magmatic systems on the basis of the Usov-Kuznetsov facies method and the Pospelov system approach are advanced. For quantitative models numerical circuits are developed and numerical experiments are carried out.