In this paper is presented an hybrid algorithm for finding the absolute extreme point of a multimodal scalar function of many variables. The algorithm is suitable when the objective function is expensive to compute, the computation can be affected by noise and/or partial derivatives cannot be calculated. The method used is a genetic modification of a previous algorithm based on the Price’s method. All information about behavior of objective function collected on previous iterates are used to chose new evaluation points. The genetic part of the algorithm is very effective to escape from local attractors of the algorithm and assures convergence in probability to the global optimum. The proposed algorithm has been tested on a large set of multimodal test problems outperforming both the modified Price’s algorithm and classical genetic approach
We model the evolution of biological and linguistic sequences by comparing their statistical properties. This comparison is performed by means of efficiently computable kernel functions, that take two sequences as an input and return a measure of statistical similarity between them. We show how the use of such kernels allows to reconstruct the phylogenetic trees of primates based on the mitochondrial DNA (mtDNA) of existing animals, and the phylogenetic tree of Indo-European and other languages based on sample documents from existing languages. Kernel methods provide a convenient framework for many pattern analysis tasks, and recent advances have been focused on efficient methods for sequence comparison and analysis. While a large toolbox of algorithms has been developed to analyze data by using kernels, in this paper we demonstrate their use in combination with standard phylogenetic reconstruction algorithms and visualization methods
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