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The multiple traveling salesman problem (MTSP) is an extension of the traveling salesman problem (TSP). It is found that the MTSP problem on a three-dimensional sphere has more research value. In a spherical space, each city is located on the surface of the Earth. To solve this problem, an integer-serialized coding and decoding scheme was adopted, and artificial electric field algorithm (AEFA) was mixed with greedy strategy and state transition strategy, and an artificial electric field algorithm based on greedy state transition strategy (GSTAEFA) was proposed. Greedy state transition strategy provides state transition interference for AEFA, increases the diversity of population, and effectively improves the accuracy of the algorithm. Finally, we test the performance of GSTAEFA by optimizing examples with different numbers of cities. Experimental results show that GSTAEFA has better performance in solving SMTSP problems than other swarm intelligence algorithms.

Artificial Electric Field Algorithm with Greedy State Transition Strategy for Spherical Multiple Traveling Salesmen Problem