Convergent analysis on evolutionary algorithm with non-uniform mutation

Evolutionary algorithm (EA) with non-uniform mutation has the merits of even ldquolonger jumpsrdquo than Cauchy mutation at the early stage of the algorithm and much ldquofiner-tuningsrdquo than Gaussian mutation operator at the later stage. Empirical comparisons with the recently proposed EAs show its excellence solution quality and reliability. One unified algorithmic framework with non-uniform mutation operator and its convergence analysis based on this algorithmic framework are provided in this paper. Two lemmas and two theorems are presented to show the relevant convergence properties of unimodal and multimodal functions.