k-RNN: Extending NN-heuristics for the TSP

TL;DR

This paper introduces k-RNN, an extension of Nearest-Neighbor heuristics for the TSP, which improves solution quality by starting from multiple initial node permutations and selecting the best tour.

Contribution

The paper proposes the k-Repetitive-Nearest-Neighbor algorithm, extending existing heuristics to enhance TSP solution quality by considering multiple starting points.

Findings

2-RNN solutions are within 10-40% of the optimal tour

Solution quality remains relatively stable across different instances

The method improves upon traditional Nearest-Neighbor heuristics

Abstract

In this paper we present an extension of existing Nearest-Neighbor heuristics to an algorithm called k-Repetitive-Nearest-Neighbor. The idea is to start with a tour of k nodes and then perform a Nearest-Neighbor search from there on. After doing this for all permutations of k nodes the result gets selected as the shortest tour found. Experimental results show that for 2-RNN the solutions quality remains relatively stable between about 10% to 40% above the optimum.