A statistical approach to the traveling salesman problem

A statistical approach is shown to be adaptable to the N-city traveling salesman problem by considering route distances to be random variables which are continuous and normally distributed. A solution to the shortest route distance and path can be approximated by utilizing a Monte Carlo simulation to obtain a representative sample of possible journeys. The approach involves recursive statistical inference which is used to select next-city visits leading to the most probable minimum route path. A statistical selection of the minimum route path is computationally efficient and computer run time increases in proportion to the square of the number of cities as opposed to an (N - 1)! increase for a deterministic approach. The accuracy of the statistical approach is directly proportional to the number of Monte Carlo simulations.