Combinatorial optimization and decision-making with applications in Computational Sustainability
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Combinatorial optimization and decision-making problems are critical in many real-world computational sustainability problems. The main goals for these projects are often to provide decision-support tools for various groups and institutions to help solve complex computation problems encountered in sustainable planning and development. This thesis mainly focuses on two real-world applications of combinatorial optimization and decision-making in computational sustainability. The first is a multiobjective optimization problem inspired by the real-world problem of placing hydropower dams in the Amazon basin. We propose a fully polynomial-time approximation scheme based on Dynamic Programming (DP) for computing the Pareto frontier within an arbitrarily small error margin on tree-structured networks. We also developed a complementary mixed integer programming (MIP) approach for approximating the Pareto frontier and methods for approximating high-dimensional Pareto frontiers. The second is an online matching problem coordinating citizen scientists for invasive species survey efforts. We developed a learning-augmented matching algorithm that can utilize partial information and provides good performance and approximation guarantees. For both applications, we provide not only practical solutions to real-world problems but also novel computational algorithms and techniques.
Approximation Algorithm; Combinatorial Optimization; Computational Sustainability; Hydropower; Multiobjective Optimization
Gomes, Carla P.
Bindel, David S.; Davis, Damek Shea
Ph. D., Applied Mathematics
Doctor of Philosophy
Attribution 4.0 International
dissertation or thesis
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