Distributionally Risk-Receptive and Robust Multistage Stochastic Integer Programs and Interdiction Models

TL;DR

This paper develops and analyzes new algorithms for solving distributionally risk-receptive and robust multistage stochastic mixed-integer programs, with applications to interdiction problems, demonstrating significant computational improvements and practical benefits in network vulnerability analysis.

Contribution

It introduces cutting plane and reformulation methods for DRR- and DRO-MSIPs, proves their finite convergence, and extends the framework to multistage stochastic disjunctive programs with applications.

Findings

Cutting plane approaches are significantly faster than reformulation methods.

Algorithms effectively solve distributionally ambiguous multistage interdiction problems.

Out-of-sample tests show the framework's utility in network vulnerability and data corruption mitigation.

Abstract

In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations of DRR- and DRO-MSIPs by presenting multistage stochastic disjunctive programs and algorithms for solving them. These frameworks are useful for optimization problems under uncertainty where the focus is on analyzing outcomes based on multiple decision-makers' differing perspectives, such as interdiction problems that are attacker-defender games having non-cooperative players. To assess the performance of the algorithms for DRR- and DRO-MSIPs, we consider instances of distributionally ambiguous multistage maximum flow and facility location interdiction problems that are important in their own right. Based on our computational results, we observe that the cutting plane-based approaches are 2800% and 2410% (on average) faster than the reformulation-based approaches for the foregoing instances with distributional risk-aversion and risk-receptiveness, respectively. Additionally, we conducted out-of-sample tests to showcase the significance of the DRR framework in revealing network vulnerabilities and also in mitigating the impact of data corruption.