A Computation Investigation of the Impact of Convex Hull subtour on the Nearest Neighbour Heuristic

Abstract

This study investigated the computational effect of a Convex Hull subtour on the Nearest Neighbour Heuristic. Convex hull subtour has been shown to theoretically degrade the worst-case performances of some insertion heuristics from twice optimal to thrice optimal, although other empirical studies have shown that the introduction of the convex hull as a subtour is expected to minimize the occurrences of outliers, thereby potentially improving the solution quality. This study was therefore conceived to investigate the empirical effect of a convex-hull-based initial tour on the Nearest Neighbour Heuristic vis-a-vis the traditional use of a single node as the initial tour. The resulting hybrid Convex Hull-Nearest Neighbour Heuristic (CH-NN) was used to solve the Travelling Salesman Problem. The technique was experimented using publicly available testbeds from TSPLIB. The performance of CH-NN vis-a-vis that of the traditional Nearest Neighbour solution showed empirically that Convex Hull can potentially improve the solution quality of tour construction techniques.