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.

通过逆向优化方法，我们提出一种学习决策者在路径规划问题中行为的方法，并在亚马逊最终里程路线研究挑战中测试了我们的方法。我们的结果展示了提出的逆向优化方法通过学习决策者在路径规划问题中的决策具有灵活性和实际潜力。