This paper presents a theoretical analysis of the convergence conditions fo
r evolutionary algorithms. The necessary and sufficient conditions, necessa
ry conditions, and sufficient conditions for the convergence of evolutionar
y algorithms to the global optima are derived, which describe their limitin
g behaviors. Their relationships are explored. Upper and lower bounds of th
e convergence rates of the evolutionary algorithms are given. (C) 2001 Else
vier Science B.V. All rights reserved.