Evolutionary algorithms

Abstract

Evolutionary Algorithms are probabilistic techniques that are inspired by the principle of natural evolution proposed by Charles Darwin. Evolutionary Algorithms are normally used to generate useful solutions to optimization and search problems using methods that are borrowed from the principles of natural evolution such as selection, crossover and mutation. An overview of these algorithms especially a particular class of these algorithms named Genetic Algorithm is provided. A description of the function of Evolutionary Algorithms together with an outline of the main classes into which it is divided is given. Consequently, a description of each component in the algorithm is presented. Moreover, Evolutionary Algorithms are modelled by Markov Processes thus the Markov model of the algorithm together with the conditions under which the algorithm with an elitist selection rule converges to the global minimum of an optimization problem irrespective of the search space is provided. Genetic Algorithm is one of the main classes of Evolutionary Algorithms. A description of the main components of this algorithm together with some examples on how these can be incorporated is given. A Genetic Algorithm is also modelled by Markov processes and the exact transition matrix of a Genetic Algorithm is presented. Furthermore, fifteen benchmark functions are used to test the efficiency and the performance of the Genetic Algorithm. The parameters considered for this analysis include the population size and the crossover rate. Also, Genetic Algorithm is compared to other traditional methods, namely Nelder and Mead Moving Simplex, Simulated Annealing and Pattern Search to find in which cases Genetic Algorithm performs better than the other techniques.