A Convex Hull Cheapest Insertion Heuristic for the Non-Euclidean TSP

TL;DR

This paper extends the convex hull cheapest insertion heuristic to non-Euclidean TSPs by using multidimensional scaling to project points into Euclidean space, enabling the heuristic's application.

Contribution

It introduces a novel approach combining multidimensional scaling with the heuristic to handle non-Euclidean metrics in TSP.

Findings

Effective in non-Euclidean spaces created by separators and L1 norm

Enables convex hull initialization for non-Euclidean TSPs

Demonstrates applicability beyond Euclidean TSPs

Abstract

The convex hull cheapest insertion heuristic produces good solutions to the Euclidean Traveling Salesperson Problem, but it has never been extended to the non-Euclidean problem. This paper uses multidimensional scaling to first project the points from a non-Euclidean space into a Euclidean space, enabling the generation of a convex hull that initializes the algorithm. To evaluate the proposed algorithm, non-Euclidean spaces are created by adding separators to the TSPLIB data-set, or by using the L1 norm as a metric.