Improvement of the Nearest Neighbor Heuristic Search Algorithm for Traveling Salesman Problem

Abstract

The Traveling Salesman Problem (TSP) is classified as a non-deterministic polynomial (NP) hard problem, which has found widespread application in several scientific and technological domains. Due to its NP-hard nature, it is very hard to solve effectively and efficiently. Despite this rationale, a multitude of optimization approaches have been proposed and developed by scientists and researchers during the last several decades. Among these several algorithms, heuristic approaches are deemed appropriate for addressing this intricate issue. One of the simplest and most easily implementable heuristic algorithms for TSP is the nearest neighbor algorithm (NNA). However, its solution quality suffers owing to randomness in the optimization process. To address this issue, this study proposes a deterministic NNA for solving symmetric TSP. It is an improved version of NNA, which starts with the shortest edge consisting of two cities and then repeatedly includes the closest city on the route until an effective route is established. The simulation is conducted on 20 benchmark symmetric TSP datasets obtained from TSPLIB. The simulation results provide evidence that the improved NNA outperforms the basic NNA throughout most of the datasets in terms of solution quality as well as computational time.