Ing. Petr Pošík, Ph.D.

Symbolic regression (SR) is a powerful method for building predictive models from data without assuming any model structure. Traditionally, genetic programming (GP) was used as the SR engine. However, for these purely evolutionary methods it was quite hard to even accommodate the function to the range of the data and the training was consequently inefficient and slow. Recently, several SR algorithms emerged which employ multiple linear regression. This allows the algorithms to create models with relatively small error right from the beginning of the search. Such algorithms are claimed to be by orders of magnitude faster than SR algorithms based on classic GP. However, a systematic comparison of these algorithms on a common set of problems is still missing and there is no basis on which to decide which algorithm to use. In this paper we conceptually and experimentally compare several representatives of such algorithms: GPTIPS, FFX, and EFS. We also include GSGP-Red, which is an enhanced version of geometric semantic genetic programming, an important algorithm in the field of SR. They are applied as off-the-shelf, ready-to-use techniques, mostly using their default settings. The methods are compared on several synthetic SR benchmark problems as well as real-world ones ranging from civil engineering to aerodynamics and acoustics. Their performance is also related to the performance of three conventional machine learning algorithms: multiple regression, random forests and support vector regression. The results suggest that across all the problems, the algorithms have comparable performance. We provide basic recommendations to the user regarding the choice of the algorithm.

Symbolic Regression is a supervised learning technique for regression based on Genetic Programming. A popular algorithm is the Multi-Gene Genetic Programming which builds models as a linear combination of a number of components which are all built together. However, in recent years a different approach emerged, represented by the Sequential Symbolic Regression algorithm, which builds the model sequentially, one component at a time, and the components are combined using a method based on geometric semantic crossover. In this article we show that the SSR algorithm effectively produces linear combination of components and we introduce another sequential approach very similar to classical ensemble method of boosting. All algorithms are compared with MGGP as a baseline on a number of real-world datasets. The results show that the sequential approaches are overall worse than MGGP both in terms of accuracy and model size.

Symbolic regression is a machine learning task: given a training dataset with features and targets, find a symbolic function that best predicts the target given the features. This paper concentrates on dynamic regression tasks, i.e. tasks where the goal changes during the model fitting process. Our study is motivated by dynamic regression tasks originating in the domain of reinforcement learning: we study four dynamic symbolic regression problems related to well-known reinforcement learning benchmarks, with data generated from the standard Value Iteration algorithm. We first show that in these problems the target function changes gradually, with no abrupt changes. Even these gradual changes, however, are a challenge to traditional Genetic Programming-based Symbolic Regression algorithms because they rely only on expression manipulation and selection. To address this challenge, we present an enhancement to such algorithms suitable for dynamic scenarios with gradual changes, namely the recently introduced type of leaf nodes called Linear Combination of Features. This type of leaf node, aided by the error backpropagation technique known from artificial neural networks, enables the algorithm to better fit the data by utilizing the error gradient to its advantage rather than searching blindly using only the fitness values. This setup is compared with a baseline of the core algorithm without any of our improvements and also with a classic evolutionary dynamic optimization technique: hypermutation. The results show that the proposed modifications greatly improve the algorithm ability to track a gradually changing target.

We propose a new type of leaf node for use in Symbolic Regression (SR) that performs linear combinations of feature variables (LCF). LCF's weights are tuned using a gradient method based on back-propagation algorithm known from neural networks. Multi-Gene Genetic Programming (MGGP) was chosen as a baseline model. As a sanity check, we experimentally show that LCFs improve the performance of the baseline on a rotated toy SR problem. We then perform a thorougher experimental study on a number of artificial and real-world SR benchmarks. The usage of LCFs in MGGP statically improved the results in 5 cases out of 9, while it worsen them in only a single case.

The recently proposed Brent-STEP algorithm was generalized for separable functions by performing axis-parallel searches, interleaving the steps in individual dimensions in a round-robin fashion. This article explores the possibility to choose the dimension for the next step in a more "intelligent way", i.e. to optimize first along dimensions which are believed to bring the highest profit. We present here the results for the epsilon-greedy strategy, and for a method based on the internals of the Brent-STEP algorithm. Although the proposed methods work better than the round robin strategy in some situations, due to the marginal improvement they bring we suggest the round robin strategy to be used, thanks to its simplicity.

Evolutionary algorithms are population-based, metaheuristic, black-box optimization techniques from the wider family of evolutionary computation. Optimization algorithms within this family are often based on similar principles and routines inspired by biological evolution. Due to their robustness, the scope of their application is broad and varies from physical engineering to software design problems. Despite sharing similar principles based in common biological inspiration, these algorithms themselves are typically viewed as black-box program routines by the end user, without a deeper insight into the underlying optimization process. We believe that shedding some light into the underlying routines of evolutionary computation algorithms can make them more accessible to wider engineering public. In this paper, we formulate the evolutionary optimization process as a dynamic system simulation, and provide means to prototype evolutionary optimization routines in a visually comprehensible framework. The framework enables engineers to follow the same dynamic system modeling paradigm, they typically use for representation of their optimization problems, to also create the desired evolutionary optimizers themselves. Instantiation of the framework in a MatlabSimulink library practically results in graphical programming of evolutionary optimizers based on data-flow principles used for dynamic system modeling within the Simulink environment. We illustrate the efficiency of visual representation in clarifying the underlying concepts on executable flow-charts of respective evolutionary optimizers and demonstrate features and potential of the framework on selected engineering benchmark applications.

We propose a novel hybrid algorithm "Brent-STEP" for univariate global function minimization, based on the global line search method STEP and accelerated by Brent's method, a local optimizer that combines quadratic interpolation and golden section steps. We analyze the performance of the hybrid algorithm on various one-dimensional functions and experimentally demonstrate a significant improvement relative to its constituent algorithms in most cases. We then generalize the algorithm to multivariate functions, proposing a scheme to interleave evaluations across dimensions to achieve smoother and more efficient convergence. We experimentally demonstrate the highly competitive performance of the proposed multivariate algorithm on separable functions of the BBOB benchmark. The combination of good performance and smooth convergence on separable functions makes the algorithm an interesting candidate for inclusion in algorithmic portfolios or hybrid algorithms that aim to provide good performance on a wide range of problems.

This paper introduces a new scoring method for company default prediction. The method is based on a modified magic square (a spider diagram with four perpendicular axes) which is used to evaluate economic performance of a country. The evaluation is quantified by the area of a polygon, whose vertices are points lying on the axes. The axes represent economic indicators having significant importance for an economic performance evaluation. The proposed method deals with magic square limitations; e.g. an axis zero point not placed in the axes origins,, and extends its usage for an arbitrary (higher than 3) number of variables. This approach is applied on corporations to evaluate their economic performance and identify the companies suspected to default.

Genetic Programming has been very successful in solving a large area of problems but its use as a machine learning algorithm has been limited so far. One of the reasons is the problem of overfitting which cannot be solved or suppresed as easily as in more traditional approaches. Another problem, closely related to overfitting, is the selection of the final model from the population. In this article we present our research that addresses both problems: overfitting and model selection. We compare several ways of dealing with ovefitting, based on Random Sampling Technique (RST) and on using a validation set, all with an emphasis on model selection. We subject each approach to a thorough testing on artificial and real–world datasets and compare them with the standard approach, which uses the full training data, as a baseline.

Grammatical Evolution is an algorithm of Genetic Programming but it is capable of evolving programs in an arbitrary language given by a user-provided context-free grammar. We present a way how to apply Multi-Gene idea, known from Multi-Gene Genetic Programming, to Grammatical Evolution, just by modifying the given grammar. We also describe modifications which improve the behavior of such algorithm, called Multi-Gene Grammatical Evolution. We compare the resulting system to GPTIPS, an existing implementation of MGGP.

Visual representation of information, allowing to quickly communicate and share ideas, forms an important part of scientific and engineering progress, with applications varying from physics to software design. Engineers naturally utilize graphs and flowcharts to clarify concepts and prototype their applications. Traditionally, wide variety of engineering applications from civil to control engineering can be formulated in the form of an optimization problem. For some of the most challenging optimization problems, evolutionary algorithms and other population based iterative optimizers were proven useful in finding high quality solutions. In this paper we present a new data-flow framework to integrate these two worlds of visual representation and engineering optimization - textit{VisualEA} - a Matlab Simulink library for visual programming of evolutionary optimizers under the paradigm of dynamic systems, and demonstrate its potential on selected engineering applications.

Evolutionary algorithms (EAs) belong to a group of classic optimizers these days, and can be used in many application areas. Autonomous mobile robotics is not an exception. EAs are utilized profusely for the purposes of localization and map building of unknown environment—SLAM. This paper concentrates on one particular class of EA, the so called differential evolution (DE). It addresses the problem of selecting a suitable set of parameter values for the DE algorithm applied to the task of continuous robot localization in a known environment under the presence of additive noise in sensorial data. The primary goal of this study is to find at least one type of perturbation vector from a set of known perturbation vector types, suitable to navigate a robot using 2D laser scanner (2DLS) sensorial system. The basic navigational algorithm used in this study uses a vector representation for both the data and the environment map, which is used as a reference data source for the navigation. Since the algorithm does not use a probability occupancy grid, the precision of the results is not limited by the grid resolution. The comparative study presented in this paper includes a relatively large amount of experiments in various types of environments. The results of the study suggest that the DE algorithm is a suitable tool for continuous robot localization task in an indoor environment, with or without moving objects, and under the presence of various levels of additive noise in sensorial data. Two perturbation vector types were found as the most suitable for this task on average, namely rand/1/exp and randtobest/1/bin.

Grammatical Evolution is a genetic programming algorithm utilizing context-free grammars in Backus Naur Form and linear, variable length genomes. This algorithm uses a single-point crossover operator, also termed ripple crossover for its effects on the evolved programs' parse trees. Recent study analyzed and compared the ripple crossover with a more traditional subtree crossover. Its results suggest that using subtree crossover, the algorithm converges faster but gets stuck in a local optimum, while using the ripple crossover the convergence is slower but better solutions are eventually found. The goal of this paper is to test the hypothesis that an algorithm which uses the subtree crossover in the initial phases, and switches to the ripple crossover in later phases, can take the best of both worlds: faster convergence in the beginning and better solutions found in the end.

Global localization algorithms belong to the key research areas in the field of autonomous mobile robotics. The ability to correctly estimate the initial position after activation or to recover the global position if orientation is lost is required from all modern autonomous systems. This article presents an algorithm for unmanned global navigation in a known environment containing noise and moving objects. Evolutionary algorithms (EA) form an important part of the discussed method. We also present a novel method of semisemantic classification of the environment in which a robot moves. This semisemantic description of the environment allows for a significantly better setup of the working parameters of individual EAs. It also enables to better connect EAs with the basic navigation methodology based on algebraic criteria, in other words, on the minimization of L1-norm. An extensive set of experimental results confirms that the connection of the semantic environment description and the navigation methods creates an important advantage.

In black-box function optimization, we can choose from a wide variety of heuristic algorithms that are suited to different functions and computation budgets. Given a particular function to be optimized, the problem we consider in this paper is how to select the appropriate algorithm. In general, this problem is studied in the field of algorithm portfolios; we treat the algorithms as black boxes themselves and consider online selection (without learning mapping from problem features to best algorithms a priori and dynamically switching between algorithms during the optimization run). We study some approaches to algorithm selection and present two original selection strategies based on the UCB1 multi-armed bandit policy applied to unbounded rewards. We benchmark our strategies on the BBOB workshop reference functions and demonstrate that algorithm portfolios are beneficial in practice even with some fairly simple strategies, though choosing a good strategy is important.

Four methods for global numerical black box optimization with origins in the mathematical programming community are described and experimentally compared with the state of the art evolutionary method, BIPOP CMA ES. The methods chosen for the comparison exhibit various features that are potentially interesting for the evolutionary computation community: systematic sampling of the search space (DIRECT, MCS) possibly combined with a local search method (MCS), or a multi start approach (NEWUOA, GLOBAL) possibly equipped with a careful selection of points to run a local optimizer from (GLOBAL). The recently proposed "comparing continuous optimizers" (COCO) methodology was adopted as the basis for the comparison. Based on the results, we draw suggestions about which algorithm should be used depending on the available budget of function evaluations, and we propose several possibilities for hybridizing evolutionary algorithms (EAs) with features of the other compared algorithms.

The differential evolution (DE) algorithm is equipped with the recently proposed adaptive encoding (AE) which makes the algorithm rotationally invariant. The resulting algorithm, DEAE, should exhibit better performance on non separable functions. The aim of this article is to assess what benefits the AE has, and what effect it has for other function groups. DEAE is compared against pure DE, an adaptive version of DE (JADE), and an evolutionary strategy with covariance matrix adaptation (CMA ES). The results suggest that AE indeed improves the performance of DE, particularly on the group of unimodal non separable functions, but the adaptation of parameters used in JADE is more profitable on average. The use of AE inside JADE is envisioned.

Six population based methods for real valued black box optimization are thoroughly compared in this article. One of them, Nelder Mead simplex search, is rather old, but still a popular technique of direct search. The remaining five (POEMS, G3PCX, Cauchy EDA, BIPOP CMA ES, and CMA ES) are more recent and came from the evolutionary computation community. The recently proposed comparing continuous optimizers (COCO) methodology was adopted as the basis for the comparison. The results show that BIPOP CMA ES reaches the highest success rates and is often also quite fast. The results of the remaining algorithms are mixed, but Cauchy EDA and POEMS are usually slow.

JADE, an adaptive version of the differential evolution (DE) algorithm, is benchmarked on the testbed of 24 noiseless functions chosen for the Black Box Optimization Benchmarking workshop. The results of full featured JADE are then compared with the results of 3 other DE variants ("downgraded" JADE variants) to reveal the contributions of the algorithm components. Another adaptive DE variant benchmarked during BBOB 2010 is used as a reference algorithm. The results confirm that the original JADE outperforms the other (JA)DE versions, while the comparison with the other adaptive DE shows that the different sources of adaptivity make the algorithms suitable for different functions.

Several local search algorithms for real valued domains (axis parallel line search, Nelder Mead simplex search, Rosenbrock's algorithm, quasi Newton method, NEWUOA, and VXQR) are described and thoroughly compared in this article, embedding them in a multi start method. Their comparison aims (1) to help the researchers from the evolutionary community to choose the right opponent for their algorithm (to choose an opponent that would constitute a hard to beat baseline algorithm), (2) to describe individual features of these algorithms and show how they influence the algorithm on different problems, and (3) to provide inspiration for the hybridization of evolutionary algorithms with these local optimizers. The recently proposed Comparing Continuous Optimizers (COCO) methodology was adopted as the basis for the comparison. The results show that in low dimensional spaces, the old method of Nelder and Mead is still the most successful among those compared, while in spaces of higher dimensions, it is better to choose an algorithm based on quadratic modeling, such as NEWUOA or a quasi Newton method.

A simple parameter-less local optimizer able to solve deterministic problems with building blocks of bounded order is proposed in this article. The algorithm is able to learn and use linkage information during the run. The algorithm is algorithmically simple, easy to implement and with the exception of termination condition, it is completely parameter-free - there is thus no need to tune the population size and other parameters to the problem at hand. An empirical comparison on 3 decomposable functions, each with uniformly scaled building blocks of size 5 and 8, was carried out. The algorithm exhibits quadratic scaling with the problem dimensionality, but the comparison with the extended compact genetic algorithm and Bayesian optimization algorithm shows that it needs lower or comparable number of fitness function evaluations on the majority of functions for the tested problem dimensionalities.

This paper presents results of the BBOB 2009 benchmarking of 31 search algorithms on 24 noiseless functions in a black box optimization scenario in continuous domain. The runtime of the algorithms, measured in number of function evaluations, is investigated and a connection between a single convergence graph and the runtime distribution is uncovered. Performance is investigated for different dimensions up to 40 D, for different target precision values, and in different subgroups of functions. Searching in larger dimension and multi modal functions appears to be more difficult. The choice of the best algorithm also depends remarkably on the available budget of function evaluations.

Estimation of distribution algorithm using Cauchy sampling distribution is compared with the bi population CMA evolutionary strategy which was one of the best contenders in the black box optimization benchmarking workshop in 2009. The results clearly indicate that the CMA evolutionary strategy is in all respects a better optimization algorithm than the Cauchy estimation of distribution algorithm. This paper compares both algorithms in more detail and adds to the understanding of their key features and differences.

Estimation of distribution algorithm equipped with Cauchy sampling distribution is compared with the generalized generation gap algorithm with parent centric crossover. Both algorithms were already presented at the 2009 black box optimization benchmarking workshop where they often showed similar performance. This paper compares them in more detail and adds to the understanding of their key features and differences.

Estimation of distribution algorithm using Cauchy sampling distribution is compared with the iterative prototype optimization algorithm with evolved improvement steps. While Cauchy EDA is better on unimodal functions, iterative prototype optimization is more suitable for multimodal functions. This paper compares the results for both algorithms in more detail and adds to the understanding of their key features and differences.

Estimation of distribution algorithm equipped with Cauchy distribution (Cauchy EDA) is compared with Rosenbrock's local search algorithm. Both algorithms were already presented at the 2009 black box optimization benchmarking workshop where Cauchy EDA usually ranked better than Rosenbrock's algorithm. This paper compares them in more detail and adds to the understanding of their key differences.

Generalized generation gap algorithm with parent centric crossover is compared with Rosenbrock's optimization algorithm. Both algorithms were already presented at the BBOB 2009 workshop where they often showed similar performance. This paper compares them in more detail and adds to the understanding of their key features and differences.

Several population based methods (with origins in the world of evolutionary strategies and estimation of distribution algorithms) for black box optimization in continuous domains are surveyed in this article. The similarities and differences among them are emphasized and it is shown that they all can be described in a common framework of stochastic local search a class of methods previously defined mainly for combinatorial problems. Based on the lessons learned from the surveyed algorithms, a set of algorithm features (or, questions to be answered) is extracted. An algorithm designer can take advantage of these features and by deciding on each of them, she can construct a novel algorithm. A few examples in this direction are shown.

The restarted estimation of distribution algorithm (EDA) with Cauchy distribution as the probabilistic model is tested on the BBOB 2009 testbed. These tests prove that when using the Cauchy distribution and suitably chosen variance enlargment factor, the algorithm is usable for broad range of fitness landscapes, which is not the case for EDA with Gaussian distribution which converges prematurely. The results of the algorithm are of mixed quality and its scaling is at least quadratic.

The DIRECT global optimization algorithm is tested on the BBOB 2009 testbed. The algorithm is rather time and space consuming since it does not forget any point it samples during the optimization. Furthermore, all the sampled points are considered when deciding where to sample next. The results suggest that the algorithm is a viable alternative only for low dimensional search spaces (5D at most).

The generalized generation gap (G3) model of an evolutionary algorithm equipped with the parent centric crossover (PCX) is tested on the BBOB 2009 benchmark testbed. To improve its behavior on multimodal functions a multistart strategy is used. The algorithm shows promising results especially for the group of 'moderate' functions, but fails systematically on the group of 'multimodal' functions.

The restarted Rosenbrock's optimization algorithm is tested on the BBOB 2009 testbed. The algorithm turned out to be very efficient for functions with simple structure (independently of dimensionality), but is not reliable for multimodal or ill conditioned functions.

The restarted line search, or coordinate wise search, algorithm is tested on the BBOB 2009 testbed. Two different univariate search algorithms (fminbnd from MATLAB and STEP) were tried and compared. The results are as expected: line search method can optimize only separable functions, for other functions it fails. The STEP method is slightly slower, however, is more robust in the multimodal case. The line search algorithms also identified 2 functions of the test suite (in addition to separable problems) which might be easy for algorithms exploiting separability.

In continuous black-box optimization, various stochastic local search techniques are often employed, with various remedies for fighting the premature convergence. This paper surveys recent developments in the field (the most important from the author's perspective), analyzes the differences and similarities and proposes a taxonomy of these methods. Based on this taxonomy, a variety of novel, previously unexplored, and potentially promising techniques may be envisioned.

In this paper the problem of analysis of eye movements using sinusoidal head rotation test is presented. The goal of the method is to discard automatically the effect of the fast phase-saccades and consequently calculate the response of vestibular system in the form of phase shift and amplitude. The comparison of threshold detection and inductive models trained on saccades is carried out. After saccades detection we are left with discontinuous signal segments. This paper presents an approach to align them to form a smooth signal with the same frequencies that were originally present in the source signal. The approach is based on a direct estimation of the signal component parameters using the evolutionary strategy with covariance matrix adaptation. The performance of evolutionary approach is compared to least-square multimodal sinus fit.

In real valued estimation of distribution algorithms, the Gaussian distribution is often used along with maximum likelihood (ML) estimation of its parameters. Such a process is highly prone to premature convergence. The simplest method for preventing premature convergence of gaussian distribution is to enlarge the maximum likelihood estimate of standard deviation $\sigma$ by a constant factor $k$ each generation. This paper surveys and broadens the theoretical models of the behaviour of this simple EDA on 1D problems and derives the limits for the constant $k$. The behaviour of this simple EDA with various values of $k$ is analysed and the agreement of the model with the reality is confirmed.

When a simple real valued estimation of distribution algorithm (EDA) with Gaussian model and maximum likelihood estimation of parameters is used, it converges prematurely even on the slope of the fitness function. The simplest way of preventing premature convergence by multiplying the variance estimate by a constant factor k each generation is studied. Recent works have shown that when increasing the dimensionality of the search space, such an algorithm becomes very quickly unable to traverse the slope and focus to the optimum at the same time. In this paper it is shown that when isotropic distributions with Gaussian or Cauchy distributed norms are used, the simple constant setting of $k$ is able to ensure a reasonable behaviour of the EDA on the slope and in the valley of the fitness function at the same time.

In real valued estimation of distribution algorithms, the Gaussian distribution is often used along with maximum likelihood (ML) estimation of its parameters. Such a process is highly prone to premature convergence. The simplest method for preventing premature convergence of Gaussian distribution is enlarging the maximum likelihood estimate of the standard deviation by a constant factor k each generation. Such a factor should be large enough to prevent convergence on slopes of the fitness function, but should not be too large to allow the algorithm converge in the neighborhood of the optimum. Previous work showed that for truncation selection such admissible k exists in 1D case. In this article it is shown experimentaly, that for the Gaussian EDA with truncation selection in high dimensional spaces no admissible k exists!

Evolutionary algorithms applied in real domain should profit from information about the local fitness function curvature. This paper presents an initial study of an evolutionary strategy with a novel approach for learning the covariance matrix of a Gaussian distribution. The learning method is based on estimation of the fitness landscape contour line between the selected and discarded individuals. The distribution learned this way is then used to generate new population members. The algorithm presented here is the first attempt to construct the Gaussian distribution this way and should be considered only a proof of concept; nevertheless, the empirical comparison on low-dimensional quadratic functions shows that our approach is viable and with respect to the number of evaluations needed to find a solution of certain quality, it is comparable to the state-of-the-art CMA-ES in case of sphere function and outperforms the CMA-ES in case of elliptical function.

The vast majority of population based optimization algorithms use selection in such a way that the non selected individuals do not have any effect on the evolution at all, even though they may carry a valueable information information about the search space areas where the search should be suppressed and/or about the local shape of the search distribution. This article describes a unified way of taking advantage of the information hidden in the non selected individuals in the framework of evolutionary algorithms: first, build a classifier discriminating between selected and non selected individuals, then turn the description of selected individuals into a search distribution, and sample new offspring from it. The concept is verified by a simple real valued evolutionary algorithm which outperforms the state of the art evolutionary strategy with covariance matrix adaptation (CMA ES) on selected test functions in all tested search space dimensionalities.

The proposed algorithm periodically rearranges the order of genes in the chromosome while the actual information about the inter-gene dependencies is calculated on-line through the run. Standard 2-point crossover, operating on the adapted chromosomal structure, is used to generate new solutions. Experimental results show that this algorithm is able to solve separable problems with strong intra building block dependencies among genes as well as the hierarchical problems.

In this paper the problem of analysis of eye movements using sinusoidal head rotation test is presented. The reflex generated by the rotational sinusoidal test is known as vestibulo-ocular reflex (VOR) producing nystagmus, which consists of slow and fast component. The goal of the method is to discard automatically the effect of the fast phase and consequently calculate the response of vestibular system in the form of phase shift and amplitude. This paper presents an approach to align the slow phases to form a smooth signal with the same frequencies that were originally present in the source signal. Two methods of direct search are compared: the Nelder-Mead simplex search and the evolutionary strategy with covariance matrix adaptation. The experimental evaluation on artificial and real-world signals revealed that the evolutionary strategy is more robust, scalable and reliable method, however, its success strongly depends on the saccades removal algorithm.

Applications of Genetic Algorithms

Many population-based real-valued optimization algorithms assume statistical independence of individual parts of solution. This assumption is only seldom fulfilled. In real domain, some coordinate transformations can be applied to reduce the dependency among variables which makes the optimization problem easier to solve. This article reviews two common linear transformations, principal and independent component analysis (PCA, ICA). Although ICA should work for our purposes better, it is shown that there are cases when PCA results in a better performance.

An evolutionary algorithm for the optimization of a function with real parameters is described in this paper. It uses a cooperative co-evolution to breed and reproduce successful mutation steps. The algorithm described herein is then tested on a suite of 10D and 30D reference optimization problems collected for the Special Session on Real-Parameter Optimization of the IEEE Congress on Evolutionary Computation 2005. The results are of mixed quality (as expected), but reveal several interesting aspects of this simple algorithm.

Vestibulo-ocular reflex (VOR) is an important source of diagnostic information for physicians. By analyzing it, they can recognize many disorders of the vestibular organ. The VOR signal is a response of the vestibular organ to the so called head rotation test. It is measured by tracking the eye movements, which are, however, distorted by saccades. After filtering the saccades out we are left with discontinuous signal segments. This paper presents an approach to align them to form a smooth signal with the same frequencies that were originally present in the source signal. The approach is based on a direct estimation of the signal component parameters. Two methods of direct search are compared.the Nelder-Mead simplex search and the evolutionary strategy with covariance matrix adaptation. The experimental evaluation on signals with 1 to 5 components revealed that the evolutionary strategy is more robust, scalable and reliable method

The article describes a new model of probability density function called distribution tree. The utility of such a model is demonstrated in evolutionary algorithms and its efficiency is compared to other optimization techniques on several reference problems. Despite its simplicity the model showed to be very efficient for several problems and its structure forms a solid basis for creating even better models.

The article describes possibilities of the statistical models application for optimization of evolutionary algorithm run so that it needs less evaluations.

The article decribes a new probabilistic model based on statistical principles and its creation process. The model is proposed as a generalized crossover operator in evolutionary algorithms. Several experiments comparing efficiency of such an algorithm to other evolutionary techniques were performed.

The article describes a new method for parental crossover based on KPCA. From the parent population non-linear features are extracted, the population is transformed to a new space; new individuals are randomly sampled in this space and are transformed back to original space. This approach seems to be verz efficient for small groups of highly dependant variables.

Článek stručně shrnuje dosavadní výsledky výzkumu na poli evolučních algoritmů odhadujících pravděpodobnostní rozdělení a prezentuje vlastní přínos autora v této oblasti.

Ekvalizace je nový evoluční operator, který v průběhu evoluce zachovává diverzitu populace. V tomto článku je popsáno použití tohoto operátoru jako hlavní a jediné součásti evolučního algoritmu, jehož výsledky jsou zde take uvedeny.

Ekvalizace je nový evoluční operátor, který v průběhu evoluce zachovává diverzitu populace. V tomto článku je popsáno použití tohoto operátoru jako hlavní a jediné součásti evolučního algoritmu, jehož výsledky jsou zde také uvedeny.

Článek o obecných souvislostech pri zavádení systémů managementu jakosti podle norem ISO 9000 do podniku. Zvláštní důraz je kladen na to, jak normám ISO 9000 vyhovuje systém STATISTICA a jak ulehčuje jejich zavádění.

Popis základních průmyslových modulů systému STATISTICA (Navrhování experimentů, Diagramy pro řízení jakosti, Analýza procesů). Popis je doplněn obrázky a několika příklady aplikace implementovaných metod.

Odvození a statistické ověření obecného tvaru fyzikálního modelu popisujícího vztah mezi konstantní úrovní výkonu a dobou, po kterou je člověk schopen tuto úroveň výkonu podávat.