A hybrid inverse optimization-stochastic programming framework for network protection

Abstract

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.

Keywords:

• Inverse optimization
• disaster relief
• crisis management
• stochastic network protection
• multi-stage stochastic programs

Acknowledgements

We would like to thank Dr. David Woodruff of University of California, Davis for answering questions regarding the pysp package.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 See Tai et al. (2013) for an example using proposed solutions.

2 We define the $\mathcal{F}$ set for the inverse optimization model differently; see Appendix A.2.

3 We keep the row in N that contains the destination, which is different from X. J. Ban (2005) and J. X. Ban et al. (2006).

4 See Appendix C.1 for the flow error metrics for the IO α values because, as can be seen from Figure 5, the IO α values are different from the original α values.

Additional information

Funding

Allen was partially funded by a Graduate Fellowship in STEM Diversity while completing this research (formerly known as a National Physical Science Consortium Fellowship), which is funded by the Department of Defense. Allen was also supported by a Flagship and Dean’s Fellowships from the University of Maryland, College Park and has worked for Johns Hopkins University Applied Physics Lab in the summers. Terekhov and Gabriel have no funding sources or conflicts of interest to report.