Inverse Optimization for Routing Problems

TL;DR

This paper introduces an inverse optimization approach to learn routing decision-makers' preferences from data, demonstrating its effectiveness in real-world delivery routing scenarios and achieving high competitive performance.

Contribution

The study develops a novel inverse optimization framework tailored for routing problems, including a specific hypothesis, loss function, and stochastic algorithm, validated on real-world data.

Findings

Achieved second place in the Amazon Last Mile Routing Challenge

Successfully learned routing preferences from thousands of real-world examples

Demonstrated the flexibility and practical potential of the IO methodology

Abstract

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.