A hybrid inverse optimization-stochastic programming framework for network protection

Disaster management is a complex problem demanding sophisticated modeling approaches. We propose utilizing a hybrid method involving inverse optimization to parameterize the cost functions for a road network’s traffic equilibrium problem and employing a modified version of a two-stage stochastic model to make protection decisions using the information gained from inverse optimization. Inverse optimization allows users to take observations of solutions of optimization and/or equilibrium problems and estimate the parameter values of the functions defining them. In the case of multi-stage stochastic programs for disaster relief, using inverse optimization to parameterize the cost functions can prevent users from making incorrect protection decisions. We demonstrate the framework using two types of cost functions for the traffic equilibrium problem and two different networks. We showcase the value of inverse optimization by demonstrating that, in most of the experiments, different decisions are made when the stochastic network protection problem is parameterized by inverse optimization versus when it is parameterized using a uniform cost assumption. We also demonstrate that similar decisions are made when the stochastic network protection problem is parameterized by inverse optimization versus when it is parameterized by the original/“true” cost parameters.