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In this paper, we propose a logic-based Benders decomposition (LBBD), as well as an LBBD/gossip method to solve the heterogeneous multi-vehicle routing problem (HMVRP). HMVRP is a newly formalized extension of the NP-hard multi-traveling salesman problem (mTSP). First, a hybrid algorithm based on LBBD is formulated that decomposes the HMVRP into an assignment problem and a cluster of sequencing problems. The former is solved by a mixed integer linear programming (MILP) solver, and the latter by a dedicated TSP solver. Then, a gossip algorithm is constructed which utilizes the mentioned LBBD for local optimization to achieve better computational efficiency. The use of LBBD remarkably reduces the CPU time. Furthurmore, integrating the three layers of gossip algorithm, LBBD and the TSP solver, results in a very efficient solution method.