Abstract
Cuckoo search algorithm is one of the most prominent meta-heuristic optimization algorithms which is applied to various applications. The discovery probability is the one and the only tuning parameter of the cuckoo search algorithm. The physical meaning of this parameter contradicts its implementation in the standard algorithm. Therefore, this study concerns the correction to the definition and implementation of the cuckoo search algorithm to resolve this conflict. Moreover, a novel algorithm called double exponential cuckoo search is proposed, in which the discovery probability became adaptive based on the concept of the double Mersenne numbers. The proposed algorithm is compared to nine other variants to find the best variant that makes the discovery probability adaptive. All the variants are compared and tested on 30 and 50 dimensions of CEC2017 benchmark functions. The results have been statistically proved using the sign test, Wilcoxon signed-rank test, and Friedman test. Moreover, multiple graphical methods are also used to visualize the median performance such as Violin plots and mean convergence graphs. Simulation results prove the superior performance of the proposed algorithm over all other variants.