Optimizing resource allocation in computational sustainability: Models, algorithms and tools

Abstract

The 17 Sustainable Development Goals laid out by the United Nations include numerous targets as well as indicators of progress towards sustainable development. Decision-makers tasked with meeting these targets must frequently propose upfront plans or policies made up of many discrete actions, such as choosing a subset of locations where management actions must be taken to maximize the utility of the actions. These types of resource allocation problems involve combinatorial choices and tradeoffs between multiple outcomes of interest, all in the context of complex, dynamic systems and environments. The computational requirements for solving these problems bring together elements of discrete optimization, large-scale spatiotemporal modeling and prediction, and stochastic models.

This dissertation leverages network models as a flexible family of computational tools for building prediction and optimization models in three sustainability-related domain areas: 1) minimizing stochastic network cascades in the context of invasive species management; 2) maximizing deterministic demand-weighted pairwise reachability in the context of flood resilient road infrastructure planning; and 3) maximizing vertex-weighted and edge-weighted connectivity in wildlife reserve design. We use spatially explicit network models to capture the underlying system dynamics of interest in each setting, and contribute discrete optimization problem formulations for maximizing sustainability objectives with finite resources. While there is a long history of research on optimizing flows, cascades and connectivity in networks, these decision problems in the emerging field of computational sustainability involve novel objectives, new combinatorial structure, or new types of intervention actions. In particular, we formulate a new type of discrete intervention in stochastic network cascades modeled with multivariate Hawkes processes. In conjunction, we derive an exact optimization approach for the proposed intervention based on closed-form expressions of the objective functions, which is applicable in a broad swath of domains beyond invasive species, such as social networks and disease contagion. We also formulate a new variant of Steiner Forest network design, called the budget-constrained prize-collecting Steiner forest, and prove that this optimization problem possesses a specific combinatorial structure, restricted supermodularity, that allows us to design highly effective algorithms. In each of the domains, the optimization problem is defined over aspects that need to be predicted, hence we also demonstrate improved machine learning approaches for each.