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The purpose of this paper is to determine a set of routes for multiple salesmen starting at and turning back to the home depots. The objective of the algorithm is to be efficient and to minimize the total cost of all salesmen.

The new method first generates a SModel, then deletes all redundant edges in the model and reorganizes isolated paths. According to the given statistics, about 16.5 percent of the nodes have a degree greater than 2 in the SModel, which means that there must be redundant edges in the model. The authors refer to those edges connected to nodes with a degree greater than 2 as redundant candidate edges. By deleting redundant edges, the original graph is simplified to a great extent, then related operation is adopted to generate expected result.

A simple model is used to simplify the original graphs by deleting redundant edges. Based on the simplified results, two strategies are proposed to determine primal edges linking with home depot. Simulations are carried out to illustrate the performance of the proposed method.

Although new method can efficiently solve the variance of multiple traveling salesmen problem (MTSP) with multiple salesmen open path, it does not consider the workload balance. To a great extent, the total course time of this variance of MTSP is decided by the last achieved salesman's time cost.

This method can be used to simulate many everyday applications such as transportation logistics, job planning, vehicle scheduling, and so on. The main applications include print press scheduling, crew scheduling, school bus routing, mission planning, and the design of global navigation satellite surveying system networks. Moreover, it can be used to solve the problem of multiple traveling robots, and can be considered as a relaxation of the vehicle routing problem (VRP) with the capacity restrictions removed.

This paper proposes a new method to solve a heterogeneous MTSP with multiple depots and open paths. A simple model (SModel) is introduced to implement it. The model can transform a complicated graph into a simplified one. Based on the model, the subsequent workings of the new method involve merely linking paths together. Based on SModel, the greatest advantage of the new method is that it can find a global solution efficiently.