The multiple traveling salesman problem (mTSP) is an extension of the well-known traveling salesman problem (TSP), requiring multiple agents to visit a set of nodes and return to their respective depot. This problem finds wide-ranging applications in robotics, transportation and networking, among other domains. Moreover, it can be readily extended to a vehicle routing problem (VRP) by introducing extra constraints. This article presents a hybrid method for addressing the multi-depot closed path mTSP by integrating a bias-randomized heuristic with iterative local search (ILS). Furthermore, this algorithm is enhanced with a self-tuning mechanism, eliminating the need for time-consuming fine-tuning processes. The results provided by this algorithm with a different number of depots are analyzed.