Convergence conditions of genetic algorithms

Genetic Algorithms (henceforth G.A.) have been used during recent years as a valid option to classical optimization methods, such as heuristic ones, specially in problems with huge cardinal searching space, very common in NP-Complete problems. The goal of this work is the study of the necessary conditions (measured as the optimum values for the G.A. main parameters) to obtain the convergence in the shortest possible time. In order to reach this goal, we propose a dynamic model, based on biological models of evolution. This model will be defined by its differential equations, that well study to determinate the conditions that enable us to ensure the convergence of the algorithms and the conditions for accelerating this convergence.