Real-world problems are often not fully characterized by a single optimal solution, as they frequently involve multiple competing objectives; it is therefore important to identify the so-called Pareto frontier, which captures solution trade-offs. We propose a fully polynomial-time approximation scheme based on Dynamic Programming (DP) for computing a polynomially succinct curve that approximates the Pareto frontier to within an arbitrarily small epsilon > 0 on tree-structured networks. Given a set of objectives, our approximation scheme runs in time polynomial in the size of the instance and 1/epsilon. We also propose a Mixed Integer Programming (MIP) scheme to approximate the Pareto frontier. The DP and MIP Pareto frontier approaches have complementary strengths and are surprisingly effective. We provide empirical results showing that our methods outperform other approaches in efficiency and accuracy. Our work is motivated by a problem in computational sustainability concerning the proliferation of hydropower dams throughout the Amazon basin. Our goal is to support decision-makers in evaluating impacted ecosystem services on the full scale of the Amazon basin. Our work is general and can be applied to approximate the Pareto frontier of a variety of multiobjective problems on tree-structured networks.

Cascades represent rapid changes in networks. A cascading phenomenon of ecological and economic impact is the spread of invasive species in geographic landscapes. The most promising management strategy is often biocontrol, which entails introducing a natural predator able to control the invading population, a setting that can be treated as two interacting cascades of predator and prey populations. We formulate and study a nonlinear problem of optimal biocontrol: optimally seeding the predator cascade over time to minimize the harmful prey population. Recurring budgets, which typically face conservation organizations, naturally leads to sparse constraints which make the problem amenable to approximation algorithms. Available methods based on continuous relaxations scale poorly, to remedy this we develop a novel and scalable randomized algorithm based on a width relaxation, applicable to a broad class of combinatorial optimization problems. We evaluate our contributions in the context of biocontrol for the insect pest Hemlock Wolly Adelgid (HWA) in eastern North America. Our algorithm outperforms competing methods in terms of scalability and solution quality and finds near-optimal strategies for the control of the HWA for fine-grained networks -- an important problem in computational sustainability.

Stochastic network design is a general framework for optimizing network connectivity. It has several applications in computational sustainability including spatial conservation planning, pre-disaster network preparation, and river network optimization. A common assumption in previous work has been made that network parameters (e.g., probability of species colonization) are precisely known, which is unrealistic in real- world settings. We therefore address the robust river network design problem where the goal is to optimize river connectivity for fish movement by removing barriers. We assume that fish passability probabilities are known only imprecisely, but are within some interval bounds. We then develop a planning approach that computes the policies with either high robust ratio or low regret. Empirically, our approach scales well to large river networks. We also provide insights into the solutions generated by our robust approach, which has significantly higher robust ratio than the baseline solution with mean parameter estimates.

Maintaining landscape connectivity is increasingly important in wildlife conservation, especially for species experiencing the effects of habitat loss and fragmentation. We propose a novel approach to dynamically optimize landscape connectivity. Our approach is based on a mixed integer program formulation, embedding a spatial capture-recapture model that estimates the density, space usage, and landscape connectivity for a given species. Our method takes into account the fact that local animal density and connectivity change dynamically and non-linearly with different habitat protection plans. In order to scale up our encoding, we propose a sampling scheme via random partitioning of the search space using parity functions. We show that our method scales to real-world size problems and dramatically outperforms the solution quality of an expectation maximization approach and a sample average approximation approach.

We propose a decision making framework to optimize the resilience of road networks to natural disasters such as floods. Our model generalizes an existing one for this problem by allowing roads with a broad class of stochastic delay models. We then present a fast algorithm based on the sample average approximation (SAA) method and network design techniques to solve this problem approximately. On a small existing benchmark, our algorithm produces near-optimal solutions and the SAA method converges quickly with a small number of samples. We then apply our algorithm to a large real-world problem to optimize the resilience of a road network to failures of stream crossing structures to minimize travel times of emergency medical service vehicles. On medium-sized networks, our algorithm obtains solutions of comparable quality to a greedy baseline method but is 30–60 times faster. Our algorithm is the only existing algorithm that can scale to the full network, which has many thousands of edges.

We develop a fast approximation algorithm called rounded dynamic programming (RDP) for stochastic network design problems on directed trees. The underlying model describes phenomena that spread away from the root of a tree, for example, the spread of influence in a hierarchical organization or fish in a river network. Actions can be taken to intervene in the network—for some cost—to increase the probability of propagation along an edge. Our algorithm selects a set of actions to maximize the overall spread in the network under a limited budget. We prove that the algorithm is a fully polynomial-time approximation scheme (FPTAS), that is, it finds (1−ε)-optimal solutions in time polynomial in the input size and 1/ε. We apply the algorithm to the problem of allocating funds efficiently to remove barriers in a river network so fish can reach greater portions of their native range. Our experiments show that the algorithm is able to produce near-optimal solutions much faster than an existing technique.

Many dynamic phenomena can be modeled as a diffusion process. For my dissertation, I study diffusion processes in the area of sustainability, such as how wildlife spreads over a fragmental landscape and how fish spread within a river network, and try to answer two important questions. 1) How to shape the diffusion by using a limited amount of resources, for example how to maximize the spread of birds by preserving a limited number of landscape units? 2) How to model the diffusion process and estimate the parameters of the model using incomplete and noisy observations? This document describes my current research progress and future research directions of answering these two important questions.

Diffusion processes in networks are increasingly used to model dynamic phenomena such as the spread of information, wildlife, or social influence. Our work addresses the problem of learning the underlying parameters that govern such a diffusion process by observing the time at which nodes become active. A key advantage of our approach is that, unlike previous work, it can tolerate missing observations for some nodes in the diffusion process. Having incomplete observations is characteristic of offline networks used to model the spread of wildlife. We develop an EM algorithm to address parameter learning in such settings. Since both the E and M steps are computationally challenging, we employ a number of optimization methods such as nonlinear and difference-of-convex programming to address these challenges. Evaluation of the approach on the Red-cockaded Woodpecker conservation problem shows that it is highly robust and accurately learns parameters in various settings, even with more than 80% missing data.

We address the problem of spatial conservation planning in which the goal is to maximize the expected spread of cascades of an endangered species by strategically purchasing land parcels within a given budget. This problem can be solved by standard integer programming methods using the sample average approximation (SAA) scheme. Our main contribution lies in exploiting the separable structure present in this problem and using Lagrangian relaxation techniques to gain scalability over the flat representation. We also generalize the approach to allow the application of the SAA scheme to a range of stochastic optimization problems. Our iterative approach is highly efficient in terms of space requirements and it provides an upper bound over the optimal solution at each iteration. We apply our approach to the Red-cockaded Woodpecker conservation problem. The results show that it can find the optimal solution significantly faster---sometimes by an order-of-magnitude---than using the flat representation for a range of budget sizes.