# Inverse Optimization for Routing Problems

arXiv: https://arxiv.org/abs/2307.07357 · HTML: https://mlsanity.com/paper/2307.07357/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 47 references that are in the map.
- First posted on arXiv 14 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [Random Reshuffling: Simple Analysis with Vast Improvements](https://mlsanity.com/paper/2006.05988/) (2020)
- [Inverse Optimization: Theory and Applications](https://mlsanity.com/paper/2109.03920/) (2021)
- [Inverse Optimization with Noisy Data](https://mlsanity.com/paper/1507.03266/) (2015)
- [Data-driven Inverse Optimization with Imperfect Information](https://mlsanity.com/paper/1512.05489/) (2015)
- [Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms](https://mlsanity.com/paper/2305.07730/) (2023)
- [Constrained Local Search for Last-Mile Routing](https://mlsanity.com/paper/2112.15192/) (2021)
- [Vehicle routing by learning from historical solutions](https://mlsanity.com/paper/1909.07893/) (2019)
- [Learning from Drivers to Tackle the Amazon Last Mile Routing Research Challenge](https://mlsanity.com/paper/2205.04001/) (2022)
- [Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods](https://mlsanity.com/paper/2008.00301/) (2020)
- [Network learning via multi-agent inverse transportation problems](https://mlsanity.com/paper/1609.04117/) (2016)
- [Amazon Last-Mile Delivery Trajectory Prediction Using Hierarchical TSP with Customized Cost Matrix](https://mlsanity.com/paper/2302.02102/) (2023)
- [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)

## Built on by (most cited first, 5 of 5)

- [Tight Generalization Bounds for Noiseless Inverse Optimization](https://mlsanity.com/paper/2605.08866/) (2026)
- [Scalable Kernel Inverse Optimization](https://mlsanity.com/paper/2410.23952/) (2024)
- [Efficient Online Inverse Optimization with O(d) Regret](https://mlsanity.com/paper/2609.13440/) (2026)
- [Adaptive decision-making for stochastic service network design](https://mlsanity.com/paper/2603.24369/) (2026)
- [Uncovering expert objectives in production planning via inverse optimization: An industrial case study](https://mlsanity.com/paper/2608.07398/) (2026)

## Abstract (arXiv)

We propose a method for learning decision-makers' behavior in routing problems using Inverse Optimization (IO). The IO framework falls into the supervised learning category and builds on the premise that the target behavior is an optimizer of an unknown cost function. This cost function is to be learned through historical data, and in the context of routing problems, can be interpreted as the routing preferences of the decision-makers. In this view, the main contributions of this study are to propose an IO methodology with a hypothesis function, loss function, and stochastic first-order algorithm tailored to routing problems. We further test our IO approach in the Amazon Last Mile Routing Research Challenge, where the goal is to learn models that replicate the routing preferences of human drivers, using thousands of real-world routing examples. Our final IO-learned routing model achieves a score that ranks 2nd compared with the 48 models that qualified for the final round of the challenge. Our examples and results showcase the flexibility and real-world potential of the proposed IO methodology to learn from decision-makers' decisions in routing problems.