An Innovative Damped Cuckoo Search Algorithm With a Comparative Study Against Other Adaptive Variants

Abstract

This paper aims to find the best variant of Cuckoo Search Algorithm that makes the step size of Lévy flight adaptive. For this reason, we introduce a new variant of CSA called Damped Cuckoo Search (DCS) in which the step size of Lévy flight is adaptive via the concept of damped oscillations that exist in most second order control systems. Moreover, we propose two other methods that tune the step size of Lévy flight based on chaotic maps. Then a deep comparative study is conducted among almost all variants of CSA that appeared in the last decade that modifies the step size of Lévy flight. All these variants are tested on CEC2017 benchmark functions. Statistical analyses are performed using the Friedman test followed by four post-hoc procedures to hold paired comparisons between the proposed DCS and the other CSA variants. Also, graphical statistical analyses are conducted on all variants via Box Plots. Finally, convergence graphs for all the variants are illustrated as well to show the speed of solution improvement over generations. Simulation results prove that the proposed DCS outperforms all other variants with a large degree of significance. Moreover, DCS increases the speed of convergence in comparison with the other variants. The box plot graphs prove that DCS has the most compact distribution for all results obtained in all runs on most functions.

Keywords

• Adaptive step size
• box plots
• CEC2017 benchmark functions
• damped cuckoo search
• damped oscillations
• Friedman test