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As a new technique for auto programming and a novel kind of genotype/phenotype evolutionary algorithm, Gene Expression Programming (GEP in short) has been applied in many fields. But there are few works about its theoretical properties, except for several propositions with strict assumptions. By means of homogeneous finite Markov chains, this paper focuses on convergence properties of GEP algorithms under on mild conditions. At first, a conclusion is drawn that GEP algorithms with basic framework could not converge to the global optimum in probability. And then an improved variant is proposed and proved to be convergent.
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