A Gaussian Process Regression Model for the Traveling Salesman Problem

G. G.

doi:10.3844/jcssp.2012.1749.1758

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 a s an independent variable. If a predictive functio n 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 sea rch is proposed to solve a deterministic symmetric TSP with a single salesman. The first tour in the s ample is constructed by the nearest neighbor algorithm and it is used to construct other tours b y the random 2-exchange swap. These tours and their total distances are training data for a Gaussian pr ocess regression model. A GPR solution is further improved with the iterated 2-opt method. In the nu merical 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 pro blems. In some cases, it outperforms GA and SA. Conclusion: Our proposed algorithm is promising for solving th e TSP.

Highlights

The cutting plane method (Dantzig et al, 1954) or the branch and bound method (Little et al, 1963)
Traveling Salesman Problem (TSP) applications can be found in many fields including job sequencing on a single machine or assignment problems (Gilmore and Gomory, 1964), material handling in a warehouse (Ratliff and heuristics and approximation algorithms include the nearest neighbor algorithm or the so-called greedy algorithm (Bellmore and Nemhauser, 1968), LinKernighan heuristics (Lin and Kernighan, 1973; Helsgaun, 2000) and the k-opt heuristic (Helsgaun, 2009)
The key contributions of this study: We propose an algorithmic approach for solving a deterministic and symmetric TSP with a single salesman

Summary

INTRODUCTION

The cutting plane method (Dantzig et al, 1954) or the branch and bound method (Little et al, 1963). The Traveling Salesman Problem (TSP) is one of the most well-known NP-hard problems in the field of combinatorial optimization. TSP applications can be found in many fields including job sequencing on a single machine or assignment problems (Gilmore and Gomory, 1964), material handling in a warehouse (Ratliff and heuristics and approximation algorithms include the nearest neighbor algorithm or the so-called greedy algorithm (Bellmore and Nemhauser, 1968), LinKernighan heuristics (Lin and Kernighan, 1973; Helsgaun, 2000) and the k-opt heuristic (Helsgaun, 2009). Several algorithms are designed to solve the TSP problem. The key contributions of this study: We propose an algorithmic approach for solving a deterministic and symmetric TSP with a single salesman. The method integrates the Gaussian Process Regression (GPR) with the Nearest Neighbor algorithm (NN) and improves its possible permutations (order combinations), but the solution by using the iterated 2-opt method. Our GPR algorithm for solving TSP is explained and the comparing methods are described in brief.

MATERIALS AND METHODS

RESULTS

Findings

CONCLUSION