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.
Highlights
Multiobjective evolutionary algorithms have attracted widespread attention and have been applied successfully in many areas, such as test task scheduling problem (TTSP) [1], reservoir operation [2], proportional integral and derivative (PID) controller [3], and distribution feeder reconfiguration (DFR) [4]
This paper focuses on exploring the effects of chaotic maps and giving comprehensive guidance for improving multiobjective evolutionary algorithms (MOEAs) by series of experiments
Chaos variables are loaded into the variable colony of the immune algorithm in the immune evolutionary algorithm, and the experimental results indicate that the new immune evolutionary algorithm improves the convergence performance and search efficiency [9]
Summary
Multiobjective evolutionary algorithms have attracted widespread attention and have been applied successfully in many areas, such as test task scheduling problem (TTSP) [1], reservoir operation [2], proportional integral and derivative (PID) controller [3], and distribution feeder reconfiguration (DFR) [4]. Results showed that none of these maps transcends other maps for all of the problems and desired criteria Those researches demonstrated that chaotic sequences replacing the random parameters in three phases, including initial population, crossover operator, and mutation operator, can improve the performance of evolutionary algorithms. NSGA-II is chosen as the main optimization algorithm, because it captures the core ideas and characteristics of MOEAs with the properties of a fast nondominated sorting procedure, an elitist strategy, a parameterless approach, and a simple yet efficient constrainthandling method [7] Despite these good aspects of NSGAII for solving MOPs, it may be entrapped into local optimal solutions. The criteria of convergence and distribution proposed by Deb et al [7] are adopted in this paper to evaluate the effects of the combinations of phases and chaotic maps on improving the performance of multiobjective evolutionary algorithms.
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