A rigorous proof of a fundamental theorem in the drift analysis of evolutionary algorithms

A fundamental theorem in the drift analysis of EAs was initially presented in Jun He and Xin Yao's paper(Artificial Intelligence 127(1) (2001) 57–85). However, the theorem remained defective in spite of its successful applications in some specific cases. This paper points out those defects, then suggests some modifications on the theorem and introduces a new and rigorous proof. This work is expected to contribute to the solid foundation of runtime analysis of Evolutionary Algorithms.