A Procedure based on the ANOVA Method for Estimating the Maximum Number of Generations for Optimization Genetic Algorithms

The present paper introduces a statistic method for estimating the maximum number of generations needed for obtaining the solution by genetic algorithms (GAs) applied in optimization problems. The most common procedure used until now is based on observations and on the intuition of the programmer for choosing the number of iterations for which the algorithm runs. This can cause a deficit either in the precision of the solution or in the runtime of the algorithm if the choice is not proper. We propose an alternative method that estimates after what number of generations there appear no more significant differences in the variance of the algorithm's results. This method is tested on optimization problems of various types: continuous/discontinuous, convex/non-convex, deterministic/stochastic. ANOVA (analysis of variance) method is used to compare the means of two or more independent random variables with normal distributions. The GA is run several times, for various numbers of generations. By gradually applying the statistical test of the ANOVA method, it is determined the moment from which no significant differences appear in the results. This method provides an optimum balance between the precision of the solution and the run time of the algorithm.