The Effects of Using Chaotic Map on Improving the Performance of Multiobjective Evolutionary Algorithms

Abstract

Chaotic maps play an important role in improving evolutionary algorithms (EAs) for avoiding the local optima and speeding up the convergence. However, different chaotic maps in different phases have different effects on EAs. This paper focuses on exploring the effects of chaotic maps and giving comprehensive guidance for improving multiobjective evolutionary algorithms (MOEAs) by series of experiments. NSGA-II algorithm, a representative of MOEAs using the nondominated sorting and elitist strategy, is taken as the framework to study the effect of chaotic maps. Ten chaotic maps are applied in MOEAs in three phases, that is, initial population, crossover, and mutation operator. Multiobjective problems (MOPs) adopted are ZDT series problems to show the generality. Since the scale of some sequences generated by chaotic maps is changed to fit for MOPs, the correctness of scaling transformation of chaotic sequences is proved by measuring the largest Lyapunov exponent. The convergence metricγand diversity metric Δ are chosen to evaluate the performance of new algorithms with chaos. The results of experiments demonstrate that chaotic maps can improve the performance of MOEAs, especially in solving problems with convex and piecewise Pareto front. In addition, cat map has the best performance in solving problems with local optima.