Constructal design is a method that conducts the designer toward flow (e.g., heat flux) architectures that have greater global performance. This numerical work uses this method to seek for the best geometry of a complex assembly of fins, i.e., an assembly where there is a cavity between the two branches of the T-Y-assembly of fins and two additional extended surfaces. The global thermal resistance of the assembly is minimized four times by geometric optimization subject to the following constraints: the total volume, the volume of fin material, the volume of the cavity, and the volume of the two additional extended surfaces. Larger amount of fin material improves the performance of the assembly of fins. The three times optimized global thermal resistance of the complex assembly of fins performs 32% better than the best T-Y-configuration under the same thermal and geometric conditions. The three times minimized global thermal resistance of the complex assembly of fins was correlated by power laws as a function of its corresponding optimal configurations.