Abstract
Multi-traveling salesman problem (MTSP) is an extension of traveling salesman problem, which is a famous NP hard problem, and can be used to solve many real world problems, such as railway transportation, routing and pipeline laying. In this paper, we analyze the general properties of MTSP, and find that the multiple depots and closed paths in the graph is a big issue for MTSP. Thus, a novel method is presented to solve it. We transform a complicated graph into a simplified one firstly, then an effective algorithm is proposed to solve the MTSP based on the simplified results. In addition, we also propose a method to optimize the general results by using 2-OPT. Simulation results show that our method can find the global solution for MTSP efficiently.
Highlights
The traveling salesman problem (TSP) is a typical combinatorial optimization problem
Liaw et al [18] proposed a hybrid genetic algorithm, which is based on tabu search, to solve the multiple traveling salesmen problem (MTSP)
This paper presents a novel method for solving a heterogeneous MTSP which allows salesmen to start from different depots and end their tours at the original depots
Summary
The SModel is proposed to implement the new method, MDCP (multiple depots and closed paths). After it has been generated, the subsequent workings of the MDCP are based on the model. Let G=(V, E, W) be a connected graph, where V={v1, v2,...,vn} is a set of cities, and E { vi , vj | vi , vj V , i j}. The graph is said to be symmetric if any ∈E satisfies wij = wji. Definition 2: d(i) and subD(i) denote the number of edges connecting to vi in a given graph. Definition 4: A tour denotes a route that starts at one node and ends at the same node. Definition 5: The edges connected to home depots in the final result are called primal edges
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