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Budget-Constrained Demand-Weighted Network Design for Resilient Infrastructure

Our work is motivated by an important network design problem in climate adaptation. As floods become more frequent and severe due to climate change, it is increasingly crucial that road infrastructure be strategically upgraded to support post-disaster recovery efforts and normal functionality. We focus on the problem of allocating a fixed budget towards restoring edges to maximize the satisfied travel demand between locations in a network, which we formalize as the budget-constrained prize-collecting Steiner forest problem. We prove that the satisfiable travel demand objective exhibits restricted supermodularity over forests, and utilize this property to design an iterative algorithm based on maximizing successive modular lower bounds for the objective that finds better solutions than a baseline greedy approach. We also propose an extremely fast heuristic for maximizing modular functions subject to knapsack and graph matroid constraints that can be used as a subroutine in the iterative algorithm, or as a standalone method that matches the greedy baseline in terms of quality but is orders of magnitude faster. We evaluate the algorithms on synthetic data, and apply them to a real-world instance of retrofitting the Senegal national road network against flooding.