# Vehicle routing by learning from historical solutions

arXiv: https://arxiv.org/abs/1909.07893 · HTML: https://mlsanity.com/paper/1909.07893/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2019.

## Built on by (most cited first, 6 of 6)

- [Inverse Optimization for Routing Problems](https://mlsanity.com/paper/2307.07357/) (2023)
- [Data Driven VRP: A Neural Network Model to Learn Hidden Preferences for VRP](https://mlsanity.com/paper/2108.04578/) (2021)
- [Learn-n-Route: Learning implicit preferences for vehicle routing](https://mlsanity.com/paper/2101.03936/) (2021)
- [Probability estimation and structured output prediction for learning preferences in last mile delivery](https://mlsanity.com/paper/2201.10269/) (2022)
- [A Bi-Objective Approach to Last-Mile Delivery Routing Considering Driver Preferences](https://mlsanity.com/paper/2405.16051/) (2024)
- [Contextual Preference Distribution Learning](https://mlsanity.com/paper/2603.17139/) (2026)

## Abstract (arXiv)

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.