In this paper we obtain bounds on the probability of convergence to the optimal solution for the compact genetic algorithm (cGA) and the population based incremental learning (PBIL). Moreover, we give a sufficient condition for convergence of these algorithms to the optimal solution and compute a range of possible values for algorithm parameters at which there is convergence to the optimal solution with a predefined confidence level.

EDA, PBIL, cGA, Markov process, submartingale, subregular functions, optimal convergence probability
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© 2011 by the Massachusetts Institute of Technology
2011
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