One of the most popular optimization algorithms in engineering is built on a mathematical lie.
The 'Lévy flight' in Cuckoo Search doesn't actually produce a Lévy distribution in bounded domains, meaning its 'scale-free' search property is a myth. This invalidates the theoretical justification for thousands of applied engineering papers.
On the Probabilistic Consistency of Lévy-Flight Sampling in Cuckoo Search
SSRN · 6280939
This study examines the mathematical validity of Lévy flight sampling in the Cuckoo Search algorithm, a widely cited metaheuristic in optimization. Given its broad adoption across engineering applications, a rigorous assessment of its stochastic foundation is necessary. The analysis focuses on the probabilistic consistency of heavytailed step generation under bounded domains, clarifying the role of Lévy updates in populationbased optimization. A theoretical and analytical approach is applied tha