Quantification and reduction of spatially induced uncertainty in spatial optimization via deep reinforcement learning

Uncertainty has always been a significant yet unresolved issue in geography. Uncertainty in spatial optimization models, particularly in coverage maximization problems, stems from the limitations of binary coverage metrics for areal-based demand units. Traditional models classify units as either fully covered or not, ignoring partial coverage scenarios. This binary approach creates discrepancies between modeled and actual service demand, as even marginally covered units may count as fully serviced. The propagation of such errors is amplified by variations in the unit size and coverage thresholds, leading to suboptimal solutions in urban planning tasks such as urban greenway planning. To address these limitations, we proposed a deep reinforcement learning (DRL)-driven optimization framework that quantifies the optimality gap caused by spatially induced uncertainty and provides superior solutions. By employing a three-module structure that incorporates a graph neural network (GNN)-driven agent for data representation, a policy and a value network for decision-making, and a stochastic environment for simulating individual-level demand distributions, our model dynamically adapts to spatial uncertainty and generates robust solutions. We tested our framework in solving the maximal covering location problem for lines (MCLP-Line) for urban greenway route planning. The experimental results demonstrated that traditional mixed integer linear programming (MILP) methods yielded highly variable outcomes with different coverage metrics, whereas our proposed model consistently outperformed MILP across diverse scenarios. Our findings underscore the potential of modern AI-driven approaches in mitigating spatial uncertainty and achieving optimized solutions in geographic applications.