Strategies for Compressing the Pareto Frontier: Application to Strategic Planning of Hydropower in the Amazon Basin

Zhongdi Qu, Marc Grimson, Yue Mao, Sebastian Heilpern, Imanol Miqueleiz, Felipe Siqueira Pacheco, Alexander Flecker, Carla P. Gomes

Abstract: The development of ethical AI decision-making systems requires considering multiple criteria, often resulting in a large spectrum of partially ordered solutions. At the core of this challenge lies the Pareto frontier, the set of all feasible solutions where no solution is dominated by another. In previous work, we developed both exact and approximate algorithms for generating the Pareto frontier for tree-structured networks. However, as the number of criteria grows, the Pareto frontier increases exponentially, posing a significant challenge for decision-makers. To address this challenge, we propose various strategies to efficiently compress the Pareto frontier, including an approximation method with optimality and polynomial runtime guarantees. We provide detailed empirical results on the strategies’ effectiveness in the context of strategic planning of the hydropower expansion in the Amazon basin. Our strategies offer a more manageable approach for navigating Pareto frontiers.