Abstract This work proposed a new metaheuristic dubbed as Chaotic Lévy flight distribution (CLFD) algorithm, to address physical world engineering optimization problems that incorporate the chaotic maps in the elementary Lévy flight distribution (LFD). Hybridization aims to increase the LFD rate of convergence while also providing a problem‐free optimization approach. The proposed methodology is investigated for five case studies of constrained optimization issues followed by shape optimization of structural design. The outcomes from the CFLD algorithm are further contrasted with its fundamental version and other distinguished recently introduced algorithms. The computational analysis illustrates the dominance of CLFD over other considered optimizers. Moreover, the present investigation shows that CLFD is a robust technique that can efficiently find optimal mechanical design problems with a proper chaotic map selection.