  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 results showcase the flexibility and real-world
potential of the proposed IO methodology to learn from decision-makers'
decisions in routing problems.

Optimization and Control;Machine Learning