The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?

The TSP has several applications even in its purest formulation, such as planning, logistics, and the manufacture of microchips.

I have tried to solve the problem in my understanding, and I hope to have a new way to solve this problem.