A new initialization procedure for the distributed estimation of distribution algorithms

Estimation of distribution algorithms (EDAs) are one of the most promising paradigms in today’s evolutionary computation. In this field, there has been an incipient activity in the so-called parallel estimation of distribution algorithms (pEDAs). One of these approaches is the distributed estimation of distribution algorithms (dEDAs). This paper introduces a new initialization mechanism for each of the populations of the islands based on the Voronoi cells. To analyze the results, a series of different experiments using the benchmark suite for the special session on Real-parameter Optimization of the IEEE CEC 2005 conference has been carried out. The results obtained suggest that the Voronoi initialization method considerably improves the performance obtained from a traditional uniform initialization

A Genetic Tuning to Improve the Performance of Fuzzy Rule-Based Classification Systems with Interval-Valued Fuzzy Sets: Degree of Ignorance and Lateral Position

Fuzzy Rule-Based Systems are appropriate tools to deal with classification problems due to their good properties. However, they can suffer a lack of system accuracy as a result of the uncertainty inherent in the definition of the membership functions and the limitation of the homogeneous distribution of the linguistic labels. The aim of the paper is to improve the performance of Fuzzy Rule-Based Classification Systems by means of the Theory of Interval-Valued Fuzzy Sets and a post-processing genetic tuning step. In order to build the Interval-Valued Fuzzy Sets we define a new function called weak ignorance for modeling the uncertainty associated with the definition of the membership functions. Next, we adapt the fuzzy partitions to the problem in an optimal way through a cooperative evolutionary tuning in which we handle both the degree of ignorance and the lateral position (based on the 2-tuples fuzzy linguistic representation) of the linguistic labels. The experimental study is carried out over a large collection of data-sets and it is supported by a statistical analysis. Our results show empirically that the use of our methodology outperforms the initial Fuzzy Rule-Based Classification System. The application of our cooperative tuning enhances the results provided by the use of the isolated tuning approaches and also improves the behavior of the genetic tuning based on the 3-tuples fuzzy linguistic representation.Spanish Government TIN2008-06681-C06-01 TIN2010-1505

MODULI SPACE OF CALABI-YAU MANIFOLDS

We present an accessible account of the local geometry of the parameter space of Calabi-Yau manifolds. It is shown that the parameter space decomposes, at least locally, into a product with the space of parameters of the complex structure as one factor and a complex extension of the parameter space of the Kähler class as the other. It is also shown that each of these spaces is itself a Kähler manifold and is moreover a Kähler manifold of restricted type. There is a remarkable symmetry in the intrinsic structures of the two parameter spaces and the relevance of this to the conjectured existence of mirror manifolds is discussed. The two parameter spaces behave differently with respect to modular transformations and it is argued that the role of quantum corrections is to restore the symmetry between the two types of parameters so as to enforce modular invariance. © 1991

COMMENTS ON CONIFOLDS

Recently it has been shown that there are paths on the moduli space between two Calabi-Yau manifolds with different topology that have finite length. A priori, there exists the possibility that the singular manifold that is common to two different moduli spaces has two different Ricci-flat Kahler metrics, each being the limit of the Ricci-flat Kähler metric of the respective topologically distinct Calabi-Yau manifold. In this paper we show that this is not the case and the topology changing path is continuous even in the space of Ricci-flat Kähler metrics. The explicit form of the Ricci-flat Kähler metrics is calculated in the vicinity of the nodes for the conifold, the resolution and the deformation. A preliminary discussion of global issues is presented and it is shown that, owing to a topological obstruction, the manifold obtained as the result of independently resolving and deforming the nodes of a conifold in general cannot be Kähler

A PAIR OF CALABI-YAU MANIFOLDS AS AN EXACTLY SOLUBLE SUPERCONFORMAL THEORY

We compute the prepotentials and the geometry of the moduli spaces for a Calabi-Yau manifold and its mirror. In this way we obtain all the sigma model corrections to the Yukawa couplings and moduli space metric for the original manifold. The moduli space is found to be subject to the action of a modular group which, among other operations, exchanges large and small values of the radius, though the action on the radius is not as simple as R → 1 R. It is also shown that the quantum corrections to the coupling decompose into a sum over instanton contributions and moreover that this sum converges. In particular there are no "sub-instanton" corrections. This sum over instantons points to a deep connection between the modular group and the rational curves of the Calabi-Yau manifold. The burden of the present work is that a mirror pair of Calabi-Yau manifolds is an exactly soluble superconformal theory, at least as far as the massless sector is concerned. Mirror pairs are also more general than exactly soluble models that have hitherto been discussed since we solve the theory for all points of the moduli space. © 1991

AN EXACTLY SOLUBLE SUPERCONFORMAL THEORY FROM A MIRROR PAIR OF CALABI-YAU MANIFOLDS

We compute the prepotentials and the geometry of the moduli spaces for a Calabi-Yau manifold and its mirror. In this way we obtain all the sigma model corrections to the Yukawa couplings and moduli space metric for the original manifold. The moduli space is found to be subject to the action of a modular group which, among other operations, exchanges large and small values of the radius though the action on the radius is not as simple as R→ 1 R. It is shown also that the quantum corrections to the coupling decompose into a sum over instanton contributions and moreover that this sum converges. In particular there are no "sub-instanton" corrections. This sum over instantons points to a deep connection between the modular group and the rational curves of the Calabi-Yau manifold. The burden of the present work is that a mirror pair of Calabi-Yau manifolds is an exactly soluble superconformal theory, at least as far as the massless sector is concerned. Mirror pairs are also more general than exactly soluble models that have hitherto been discussed since we here solve the theory for all points of the moduli space. © 1991