Fine-grained parallel genetic algorithm: A global convergence criterion

This paper presents a fine-grained parallel genetic algorithm with mutation rate as a control parameter. The function of the mutation rate is similar to the temperature parameter in the simulated annealing [3,8,10]. The motiv ation behind this research is to develop a global convergence theory for th e fine-grained parallel genetic algorithms based on the simulated annealing model. There is a mathematical difficulty associated with the genetic algo rithms as they do not strictly come under the definition of an algorithm. A lgorithms normally have a starting point and a defined point of termination which genetic algorithms lack. The parallel genetic algorithm presented he re is a stochastic process based on Markov chain [2] model. It has been pro ven that fine-grained parallel genetic algorithm is an ergodic Markov chain and that it converges to the stationary distribution. The theoretical resu lt has been applied to in the context of optimisation of a deceptive functi on of 4-th order.