Vehicle routing by learning from historical solutions

TL;DR

This paper presents a decision support system for vehicle routing that learns from past human decisions using a probabilistic Markov model, enabling near-human routing quality without explicit optimization.

Contribution

It introduces a novel learning-based approach using a Markov model to replicate human routing decisions, reducing the need for custom VRP formulations.

Findings

Achieves routing results close to manual solutions

Performs well even with changing customer sets

Requires fewer manual adjustments to route plans

Abstract

The goal of this paper is to investigate a decision support system for vehicle routing, where the routing engine learns from the subjective decisions that human planners have made in the past, rather than optimizing a distance-based objective criterion. This is an alternative to the practice of formulating a custom VRP for every company with its own routing requirements. Instead, we assume the presence of past vehicle routing solutions over similar sets of customers, and learn to make similar choices. The approach is based on the concept of learning a first-order Markov model, which corresponds to a probabilistic transition matrix, rather than a deterministic distance matrix. This nevertheless allows us to use existing arc routing VRP software in creating the actual route plans. For the learning, we explore different schemes to construct the probabilistic transition matrix. Our results on a use-case with a small transportation company show that our method is able to generate results that are close to the manually created solutions, without needing to characterize all constraints and sub-objectives explicitly. Even in the case of changes in the client sets, our method is able to find solutions that are closer to the actual route plans than when using distances, and hence, solutions that would require fewer manual changes to transform into the actual route plan.