A Gaussian Process Regression Model for the Traveling Salesman Problem

Abstract

Problem statement: Traveling Salesman Problem (TSP) is a famous NP hard problem. Many approaches have been proposed up to date for solving TSP. We consider a TSP tour as a dependent variable and its corresponding distance as an independent variable. If a predictive function can be formulated from arbitrary sample tours, the optimal tour may be predicted from this function. Approach: In this study, a combined procedure of the Nearest Neighbor (NN) method, Gaussian Process Regression (GPR) and the iterated local search is proposed to solve a deterministic symmetric TSP with a single salesman. The first tour in the sample is constructed by the nearest neighbor algorithm and it is used to construct other tours by the random 2-exchange swap. These tours and their total distances are training data for a Gaussian process regression model. A GPR solution is further improved with the iterated 2-opt method. In the numerical experiments, our algorithm is tested on many TSP instances and it is compared with the Genetic Algorithm (GA) and the Simulated Annealing (SA) algorithm. Results: The proposed method can find good TSP tours within a reasonable computational time for a wide range of TSP test problems. In some cases, it outperforms GA and SA. Conclusion: Our proposed algorithm is promising for solving the TSP.