Learned upper bounds for the Time-Dependent Travelling Salesman Problem

TL;DR

This paper introduces a novel method for estimating tight upper bounds for the Time-Dependent Travelling Salesman Problem by leveraging machine learning and classical TSP solutions, validated on real city data.

Contribution

It proposes a new upper bounding technique combining LP and machine learning to improve solutions for the time-dependent TSP, especially in repeated-route scenarios.

Findings

Average gap of 0.001% between heuristic and best solutions

New best solutions found for 31 instances

Effective approach on real travel time data from Paris and London

Abstract

Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The main goal of this work is to define tight upper bounds for this problem by reusing the information gained when solving instances with similar features. This is customary in distribution management, where vehicle routes have to be generated over and over again with similar input data. To this aim, we devise an upper bounding technique based on the solution of a classical (and simpler) time-independent Asymmetric Travelling Salesman Problem, where the constant arc costs are suitably defined by the combined use of a Linear Program and a mix of unsupervised and supervised Machine Learning techniques. The effectiveness of this approach has been assessed through a computational campaign on the real travel time functions of two European cities: Paris and London. The overall average gap between our heuristic and the best-known solutions is about 0.001\%. For 31 instances, new best solutions have been obtained.