Convergence rate of evolutionary algorithms for a class of convex objective functions

Probabilistic optimization algorithms that mimic the process of biological evo lution are usually subsumed under the term evolutionary algorithms This work extends the convergence theory of evolutionary algorithms by presenting a su cient convergence condition for those evolutionary algorithms that do not necessarily gen erate a sequence of feasible points such that the associated objective function values decrease monotonically to the global minimum Moreover it is investigated how fast the sequence of objective function values generated by an evolutionary algo rithm approaches the minimumof strongly convex functions in a probabilistic sense The theoretical analysis presented here distinguishes from related studies in three points First it does not require advanced calculus Second only the rst partial derivatives of the objective function are assumed to exist Third one obtains sharp bounds on the convergence rates for a class of functions being a superset of the class of quadratic functions with positive de nite Hessian matrix

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