Introducing convex layers to the Traveling Salesman Problem

TL;DR

This paper introduces a novel approach to the Traveling Salesman Problem by applying convex layers, inspired by human and social insect behaviors, and demonstrates its effectiveness on a 13-city instance.

Contribution

The paper proposes convex layers as a new method for solving TSP, leveraging insights from human cognition and social insect behavior.

Findings

Humans rely on convex hulls to perform well on TSP.

Convex layers can be used to improve TSP solutions.

Tour improvement algorithms on convex layers yield promising results.

Abstract

In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the TSP. On the other hand, experimental data also supports the hypothesis of convex hull i.e. human relies on convex hull to search for the optimal tour for the TSP. Secondly, from the paper published by Bonabeau, Dorigo and Theraulaz, social insect behavior would be able to help in some of the optimizing problems, especially the TSP. Thus, we propose convex layers to the TSP based on the argument that, by the analogy to the social insect behavior, untrained humans' cognition should be able to help in the TSP. Lastly, we will use Tour Improvement algorithms on convex layers to search for an optimal tour for a 13-cities problem to demonstrate the idea.