We extend an approach to global convergence for genetic algorithms via a homogeneous Markov chain argument that does not depend on mutation. Our result is a proof of convergence to a set of populations which contain the optimal.
Gunar E. Liepins,
"Global convergence of genetic algorithms", Proc. SPIE 1766, Neural and Stochastic Methods in Image and Signal Processing, (16 December 1992); doi: 10.1117/12.130817; https://doi.org/10.1117/12.130817