Evolutionary programs are capable of finding good solutions to difficult op
timization problems. previous analysis of their convergence properties has
normally assumed the strategy parameters are kept constant, although in pra
ctice these parameters are dynamically altered. In this paper, we propose a
modified version of the 1/5-success rule for self-adaptation in evolution
strategies (ES). Formal proofs of the long-term behavior produced by our se
lf-adaptation method are included. Both elitist and non-elitist ES variants
are analyzed. Preliminary tests indicate an ES with our modified self-adap
tation method compares favorably to both a non-adapted ES and a 1/5-success
rule adapted ES.