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This paper presents the long term planning analysis of a power transmission system as a nonlinear integer mixed optimization problem that includes in the objective function the expected power not served as index that explicitly measures the reliability. This problem is solved combining the techniques of genetic algorithms for the optimization part and the state space enumeration for the reliability. As a real example, an expansion study of the power transmission system that serves the city of Pereira in Colombia is presented. [ABSTRACT FROM AUTHOR]