Convergence analysis of cuckoo search algorithm based on martingale theory Online publication date: Mon, 20-Jun-2022
by Lijun Sun; Xiaodong Liu; Tianfei Chen; Ming Yan; Shaokui Ma
International Journal of Modelling, Identification and Control (IJMIC), Vol. 39, No. 2, 2021
Abstract: Cuckoo search (CS) algorithm is an emerging kind of biologically inspired algorithm that has been successfully applied in several areas. However, its mathematical theory has not yet been fully established up to now, and the theoretical analysis of convergence is relatively inadequate. In this article, the martingale theory is introduced for the first time to prove the convergence of CS, which replaces the ergodic analysis of the Markov chain. First of all, according to the basic principles of CS, we establish the mathematical model of the Markov chain and group state sequence, and its Markov properties are analysed, and then the optimal group state set is obtained. After that, the supermartingale of the cuckoo evolution sequence with an optimal fitness value is derived. In the end, based on the convergence theorem of supermartingale, it is demonstrated that the CS algorithm ensures global convergence.
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