Exploiting the Connections of Evolutionary Algorithms and Stochastic Approximation

This work is our rst attempt in establishing the connections between evolutionary computation algorithms and stochastic approximation procedures By treating evo lutionary algorithms as recursive stochastic procedures we study both constant gain and decreasing step size algorithms We formulate the problem in a rather general form supply the su cient conditions for convergence both with probability one and in the weak sense Among other things our approach reveals the natural connection of the discrete iterations and the continuous dynamics ordinary di erential equations and or stochastic di erential equations We hope that this attempt will open up a new domain for further research and lead to in depth understanding of the underlying algorithms