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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. 

One of the main desired capabilities of the smart grid is ‘self‐healing’, which is the ability to quickly restore power after a disturbance. Due to critical outage events, customer demand or load is at times disconnected or shed temporarily. While deterministic optimisation models have been devised to help operators expedite load shed recovery by harnessing the flexibility of the grid's topology (i.e. transmission line switching), an important issue that remains unaddressed is how to cope with the uncertainty in generation and demand encountered during the recovery process. This study introduces two‐stage stochastic models to deal with these uncertain parameters, and one of them incorporates conditional value‐at‐risk to measure the risk level of unrecovered load shed. The models are implemented using a scenario‐based approach where the objective is to maximise load shed recovery in the bulk transmission network by switching transmission lines and performing other corrective actions (e.g. generator re‐dispatch) after the topology is modified. The benefits of the proposed stochastic models are compared with a deterministic mean‐value model, using the IEEE 118‐ and 14‐bus test cases. Experiments highlight how the proposed approach can serve as an offline contingency analysis tool, and how this method aids self‐healing by recovering more load shedding.