We introduce the $k$-Interconnected Multi-Depot Multi-Traveling Salesmen Problem, a new problem that resembles some network design and location routing problems but carries the inherent difficulty of not having a fixed set of depots or terminals. We propose a heuristic based on a biased random-key genetic algorithm to solve it. This heuristic uses local search procedures to best choose the terminal vertices and improve the tours of a given solution. We compare our heuristic with a multi-start procedure using the same local improvements and we show that the proposed algorithm is competitive.