Spatial targeting of agri-environmental policy using bilevel evolutionary optimization

In this study we describe the optimal designation of agri-environmental policy as a bilevel optimization problem and propose an integrated solution method using a hybrid genetic algorithm. The problem is characterized by a single leader, the agency, that establishes a policy with the goal of optimizing its own objectives, and multiple followers, the producers, who respond by complying with the policy in a way that maximizes their own objectives. We assume that the leader has perfect knowledge of policy outcomes for all parameterizations of agri-environmental policy. We use a hybrid genetic algorithm to simulate perfect knowledge of all policy outcomes in a bilevel optimization. Our hybrid genetic algorithm integrates a biophysical model (Soil and Water Assessment Tool; SWAT) with an economic model (profit maximization; DEA). The Soil and Water Assessment Tool (SWAT) is included to specify agency environmental objectives, and Data Envelopment Analysis (DEA) is used to model producer behavior in response to agri-environmental policy. We applied the resulting integrated modeling system to the analysis of an input tax on fertilizer in the Calapooia watershed in Oregon, USA. Application of the incentive policy at different geographical resolutions showed that bilevel optimization is effective for calculating optimal spatial targeting of agri-environmental policy. Surprisingly, the presented algorithm found multiple different policy configurations that achieved nearly identical results for the upper level (agency) objectives. This observation raises the possibility that additional objectives could incorporate equity, equality of outcome, and policy initiatives such as support for small farms at no additional cost.