Two-stage Robust Optimization Approach for Enhanced Community Resilience Under Tornado Hazards

Catastrophic tornadoes cause severe damage and are a threat to human wellbeing, making it critical to determine mitigation strategies to reduce their impact. One such strategy, following recent research, is to retrofit existing structures. To this end, in this article we propose a model that considers a decision-maker (a government agency or a public-private consortium) who seeks to allocate resources to retrofit and recover wood-frame residential structures, to minimize the population dislocation due to an uncertain tornado. In the first stage the decision-maker selects the retrofitting strategies, and in the second stage the recovery decisions are made after observing the tornado. As tornado paths cannot be forecast reliably, we take a worst-case approach to uncertainty where paths are modeled as arbitrary line segments on the plane. Under the assumption that an area is affected if it is sufficiently close to the tornado path, the problem is framed as a two-stage robust optimization problem with a mixed-integer non-linear uncertainty set. We solve this problem by using a decomposition column-and-constraint generation algorithm that solves a two-level integer problem at each iteration. This problem, in turn, is solved by a decomposition branch-and-cut method that exploits the geometry of the uncertainty set. To illustrate the model's applicability, we present a case study based on Joplin, Missouri. Our results show that there can be up to 20 percent reductions in worst-case population dislocation by investing 15 million dollars in retrofitting and recovery; that our approach outperforms other retrofitting policies, and that the model is not over-conservative

Online First-Order Framework for Robust Convex Optimization

Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in ever more larger scale. However, the traditional approaches for solving RO formulations based on building and solving robust counterparts or the iterative approaches utilizing nominal feasibility oracles can be prohibitively expensive and thus significantly hinder the scalability of RO paradigm. We present a general and flexible iterative framework to solve robust convex optimization problems that is built on a fully online first-order paradigm. In contrast to the existing literature, a key distinguishing feature of our approach is that it requires access to only cheap first-order oracles for the original problem that are remarkably cheaper than pessimization or nominal feasibility oracles, while maintaining the same convergence rates. This, in particular, makes our approach much more scalable and hence preferable in large-scale applications. In the case of strongly convex functions, we also establish a new improved iteration complexity addressing an open question in the literature. Motivated by a robust portfolio optimization problem, we demonstrate the performance of our approach on robust quadratic programs with ellipsoidal uncertainty.Non UBCUnreviewedAuthor affiliation: Carnegie Mellon UniversityResearche