Scaling Up Pareto Optimization for Tree Structures with Affine Transformations: Evaluating Hybrid Floating Solar-Hydropower Systems in the Amazon

Sustainability challenges inherently involve the consideration of multiple competing objectives. The Pareto frontier – the set of all optimal solutions that cannot be improved with respect to one objective without negatively affecting another – is a crucial decision-making tool for navigating sustainability challenges as it highlights the inherent trade-offs among conflicting objectives. Our research is motivated by the strategic planning of hydropower in the Amazon basin, one of the earth’s largest and most biodiverse river systems, where the need to increase energy production coincides with the pressing requirement of minimizing detrimental environmental impacts. We investigate an innovative strategy that pairs hydropower with Floating Photovoltaic Solar Panels (FPV). We provide a new extended multi-tree network formulation, which enables the consideration of multiple dam configurations. To address the computational challenge of scaling up the Pareto optimization framework to tackle multiple objectives across the entire Amazon basin, we further enhance the state-of-the-art algorithm for Pareto frontiers in tree-structured networks with two improvements. We introduce affine transformations induced by the sub-frontiers to compute Pareto dominance and provide strategies for merging sub-trees, significantly increasing the pruning of dominated solutions. Our experiments demonstrate considerable speedups, in some cases by more than an order of magnitude, while maintaining optimality guarantees, thus allowing us to more effectively approximate the Pareto frontiers. Moreover, our findings suggest significant shifts towards higher energy values in the Pareto frontier when pairing hybrid hydropower with FPV solutions, potentially amplifying energy production while mitigating adverse impacts.