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Constructal design associated with genetic algorithm (GA) is employed to optimize the geometry of an isothermal Y-shaped cavity embedded into a solid conducting wall. The structure has four degrees of freedom (DOF). The main purpose is to minimize the maximum excess of temperature between the solid and the cavity by means of GA and exhaustive search (simulating every geometry combinations). Results showed that GA was well succeeded to find the best shapes which minimize the maximal excess of temperature with a number of simulations strongly lower than that required with exhaustive search, allowing the optimization of cavity under new constraint conditions.