Evaluating the Effects of Parameters Setting on the Performance of Genetic Algorithm Using Regression Modeling and Statistical Analysis

Abstract

Among various heuristics techniques, Genetic algorithm (GA) is one of the most widely used techniques which has successfully been applied on a variety of complex combinatorial problems. The performance of GA largely depends on the proper selection of its parameters values; including crossover mechanism, probability of crossover, population size and mutation rate and selection percent. In this paper, based on Design of Experiments (DOE) approach and regression modeling, the effects of tuning parameters on the performance of genetic algorithm have been evaluated. As an example, GA is applied to find a shortest distance for a well-known travelling salesman problem with 48 cities. The proposed approach can readily be implemented to any other optimization problem. To develop mathematical models, computational experiments have been carried out using a 4-factor 5-level Central Composite Design (CCD) matrix. Three types of regression functions models have been fitted to relate GA variables to its performance characteristic. Then, statistical analyses are performed to determine the best and most fitted model. Analysis of Variance (ANOVA) results indicate that the second order function is the best model that can properly represent the relationship between GA important variables and its performance measure (solution quality).