[en] The In-Core Fuel Management Optimization (OGCIN) problem, or design optimization of Load Patterns (PCs) are denominations for the optimization problem associated with the refueling operation in a reactor nuclear. The OCGIN is considered a problem of difficult resolution, considering aspects of combinatorial optimization and calculations of analysis and physics of reactors. In order to validate algorithms for the OGCIN solution, we use benchmark problems such as the Travelling Salesman Problem (TSP), because it is considered, like OGCIN, an NP-difficult problem. In the present work, we implemented the Population-Based Incremental Learning (PBIL) algorithm with binary coding and Gray coding and applied them to the optimization of the symmetric PCV Oliver30 and Rykel48 asymmetric PCV and implemented only the Gray coding in the OGCIN application of the cycle 7 of the Angra-1 Nuclear Plant, where we compared its performance with binary coding in. The results on average were 1311 and 1327 ppm of Boron for the binary and Gray codifications respectively, emphasizing that the binary codification obtained a maximum value of 1330 ppm, while the Gray code obtained a value of 1401 ppm, showing superiority, since the Boron concentration is an indicator of the PC cycle extension