# Data Driven VRP: A Neural Network Model to Learn Hidden Preferences for VRP

arXiv: https://arxiv.org/abs/2108.04578 · HTML: https://mlsanity.com/paper/2108.04578/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 10 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Network In Network](https://mlsanity.com/paper/1312.4400/) (2013)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [What game are we playing? End-to-end learning in normal and extensive form games](https://mlsanity.com/paper/1805.02777/) (2018)
- [Vehicle routing by learning from historical solutions](https://mlsanity.com/paper/1909.07893/) (2019)

## Built on by (most cited first, 2 of 2)

- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Probability estimation and structured output prediction for learning preferences in last mile delivery](https://mlsanity.com/paper/2201.10269/) (2022)

## Abstract (arXiv)

The traditional Capacitated Vehicle Routing Problem (CVRP) minimizes the total distance of the routes under the capacity constraints of the vehicles. But more often, the objective involves multiple criteria including not only the total distance of the tour but also other factors such as travel costs, travel time, and fuel consumption.Moreover, in reality, there are numerous implicit preferences ingrained in the minds of the route planners and the drivers. Drivers, for instance, have familiarity with certain neighborhoods and knowledge of the state of roads, and often consider the best places for rest and lunch breaks. This knowledge is difficult to formulate and balance when operational routing decisions have to be made. This motivates us to learn the implicit preferences from past solutions and to incorporate these learned preferences in the optimization process. These preferences are in the form of arc probabilities, i.e., the more preferred a route is, the higher is the joint probability. The novelty of this work is the use of a neural network model to estimate the arc probabilities, which allows for additional features and automatic parameter estimation. This first requires identifying suitable features, neural architectures and loss functions, taking into account that there is typically few data available. We investigate the difference with a prior weighted Markov counting approach, and study the applicability of neural networks in this setting.