Bilevel optimization has been recognized as a 2-player Stackelberg game where players are represented as leaders and followers and each pursue their own set of objectives. Hierarchical optimization problems, which are a generalization of bilevel, are especially difficult because the optimization is nested, meaning that the objectives of one level depend on solutions to the other levels. We introduce a hierarchical optimization framework for spatially targeting multiobjective green infrastructure (GI) incentive policies under uncertainties related to policy budget, compliance, and GI effectiveness. We demonstrate the utility of the framework using a hypothetical urban watershed, where the levels are characterized by multiple levels of policy makers (e.g., local, regional, national) and policy followers (e.g., landowners, communities), and objectives include minimization of policy cost, implementation cost, and risk; reduction of combined sewer overflow (CSO) events; and improvement in environmental benefits such as reduced nutrient run-off and water availability.
Results/Conclusions
While computationally expensive, this hierarchical optimization framework explicitly simulates the interaction between multiple levels of policy makers (e.g., local, regional, national) and policy followers (e.g., landowners, communities) and is especially useful for constructing and evaluating environmental and ecological policy. Using the framework with a hypothetical urban watershed, we present trade-offs between policy cost and environmental benefits (e.g., water usage, nutrient run-off) using GI incentive policies; we also describe meta-modeling methods that can be used to make the problem computationally tractable. In addition, we introduce uncertainties related to policy budget, compliance, and GI effectiveness and show that robust policies (with respect to each uncertainty type) are possible at the expense of reductions in overall objective performance. Overall, the utility of hierarchical optimization as a framework for targeting incentives to promote effective GI is a promising and suitable method to ensure robust policies amidst conflicting objectives and uncertainty.