Design of Passive Analog Electronic Circuits Using Hybrid Modified UMDA algorithm

Hybrid evolutionary passive analog circuits synthesis method based on modified Univariate Marginal Distribution Algorithm (UMDA) and a local search algorithm is proposed in the paper. The modification of the UMDA algorithm which allows to specify the maximum number of the nodes and the maximum number of the components of the synthesized circuit is proposed. The proposed hybrid approach efficiently reduces the number of the objective function evaluations. The modified UMDA algorithm is used for synthesis of the topology and the local search algorithm is used for determination of the parameters of the components of the designed circuit. As an example the proposed method is applied to a problem of synthesis of the fractional capacitor circuit

GPGCD: An iterative method for calculating approximate GCD of univariate polynomials

We present an iterative algorithm for calculating approximate greatest common divisor (GCD) of univariate polynomials with the real or the complex coefficients. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. The problem of approximate GCD is transfered to a constrained minimization problem, then solved with the so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. We demonstrate that, in some test cases, our algorithm calculates approximate GCD with perturbations as small as those calculated by a method based on the structured total least norm (STLN) method and the UVGCD method, while our method runs significantly faster than theirs by approximately up to 30 or 10 times, respectively, compared with their implementation. We also show that our algorithm properly handles some ill-conditioned polynomials which have a GCD with small or large leading coefficient.Comment: Preliminary versions have been presented as doi:10.1145/1576702.1576750 and arXiv:1007.183

Construction of the Midge History Match Model

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Evolutionary Synthesis of Analog Electronic Circuits Using EDA Algorithms

Disertační práce je zaměřena na návrh analogových elektronických obvodů pomocí algoritmů s pravěpodobnostními modely (algoritmy EDA). Prezentované metody jsou na základě požadovaných charakteristik cílových obvodů schopny navrhnout jak parametry použitých komponent tak také jejich topologii zapojení. Tři různé metody využití EDA algoritmů jsou navrženy a otestovány na příkladech skutečných problémů z oblasti analogových elektronických obvodů. První metoda je určena pro návrh pasivních analogových obvodů a využívá algoritmus UMDA pro návrh jak topologie zapojení tak také hodnot parametrů použitých komponent. Metoda je použita pro návrh admitanční sítě s požadovanou vstupní impedancí pro účely chaotického oscilátoru. Druhá metoda je také určena pro návrh pasivních analogových obvodů a využívá hybridní přístup - UMDA pro návrh topologie a metodu lokální optimalizace pro návrh parametrů komponent. Třetí metoda umožňuje návrh analogových obvodů obsahujících také tranzistory. Metoda využívá hybridní přístup - EDA algoritmus pro syntézu topologie a metoda lokální optimalizace pro určení parametrů použitých komponent. Informace o topologii je v jednotlivých jedincích populace vyjádřena pomocí grafů a hypergrafů.Dissertation thesis is focused on design of analog electronic circuits using Estimation of Distribution Algorithms (EDA). Based on the desired characteristics of the target circuits the proposed methods are able to design the parameters of the used components and theirs topology of connection as well. Three different methods employing EDA algorithms are proposed and verified on examples of real problems from the area of analog circuits design. The first method is capable to design passive analog circuits. The method employs UMDA algorithm which is used for determination of the parameters of the used components and synthesis of the topology of their connection as well. The method is verified on the problem of design of admittance network with desired input impedance function which is used as a part of chaotic oscillator circuit. The second method is also capable to design passive analog circuits. The method employs hybrid approach - UMDA for synthesis of the topology and local optimization method for determination of the parameters of the components. The third method is capable to design analog circuits which include also ac- tive components such as transistors. Hybrid approach is used. The topology is synthesized using EDA algorithm and the parameters are determined using a local optimization method. In the individuals of the population information about the topology is represented using graphs and hypergraphs.

Computation of sum of squares polynomials from data points

We propose an iterative algorithm for the numerical computation of sums of squares of polynomials approximating given data at prescribed interpolation points. The method is based on the definition of a convex functional $G$ arising from the dualization of a quadratic regression over the Cholesky factors of the sum of squares decomposition. In order to justify the construction, the domain of $G$, the boundary of the domain and the behavior at infinity are analyzed in details. When the data interpolate a positive univariate polynomial, we show that in the context of the Lukacs sum of squares representation, $G$ is coercive and strictly convex which yields a unique critical point and a corresponding decomposition in sum of squares. For multivariate polynomials which admit a decomposition in sum of squares and up to a small perturbation of size $\varepsilon$, $G^\varepsilon$ is always coercive and so it minimum yields an approximate decomposition in sum of squares. Various unconstrained descent algorithms are proposed to minimize $G$. Numerical examples are provided, for univariate and bivariate polynomials

A lexicographic multi-objective genetic algorithm for multi-label correlation-based feature selection

This paper proposes a new Lexicographic multi-objective Genetic Algorithm for Multi-Label Correlation-based Feature Selection (LexGA-ML-CFS), which is an extension of the previous single-objective Genetic Algorithm for Multi-label Correlation-based Feature Selection (GA-ML-CFS). This extension uses a LexGA as a global search method for generating candidate feature subsets. In our experiments, we compare the results obtained by LexGA-ML-CFS with the results obtained by the original hill climbing-based ML-CFS, the single-objective GA-ML-CFS and a baseline Binary Relevance method, using ML-kNN as the multi-label classifier. The results from our experiments show that LexGA-ML-CFS improved predictive accuracy, by comparison with other methods, in some cases, but in general there was no statistically significant different between the results of LexGA-ML-CFS and other methods