Tesis "Gradient Estimation Based Directions and its Use as a Local Search Operator in Evolutionary Algorithms"
Sustentante: José Virgilio Treviño Avalos
Director: Dr. Ricardo Landa Becerra, investigador Cinvestav Tamaulipas.
Sinodales: Dr. José Juan García Hernández y Dr. Javier Rubio Loyola, investigadores del Cinvestav Tamaulipas.
Resumen:
Through the centuries, many techniques have been proposed to find, or at worst to approximate the optimum of mathematical functions. Calculus inspired the creation of new methods, which use gradient and Hessian information. However the effectiveness of these methods is limited to functions that have continuous second derivatives.
Advances in silicon technology have exponentially incremented the computing power that researchers have available. This power has allowed the development of methods inspired by nature, these methods are called metaheuristics. An important class of metaheuristics are evolutionary algorithms, which are influenced by Darwinian evolution. Bio-inspired techniques require a great number of iterations to find good approximations, but they can operate even in non-derivable functions.
Developed in the fifties, the conjugate gradient method is a numerical optimization technique that uses first order information and has a convergence rate faster than the steepest descent but slower than methods that use second order information. The convergence speed of conjugate gradient methods is a consequence of the conjugacy of the search directions used, which means that searching in the same direction is avoided.
Conjugate gradient methods use gradients as basis vectors, this suggests that it should be possible to construct conjugate directions using gradients computed by an estimator. This thesis proposes the use of conjugate directions as a local search operator in evolutionary algorithms.