Spatial Targeting of Agri-Environmental Policy Using Bilevel Evolutionary Optimization

Abstract

Environmental policy related to agriculture is generally administered by a government agency charged with achieving legislative objectives. The enabling legislation of an agency typically establishes a set of tools that the agency uses to influence the behavior on non-governmental agricultural producers who are pursuing their own objectives. This circumstance is recognizable as a bilevel optimization, or Stackelberg game. In the instance of agri-environmental policy, there is a single leader, the agency, and agricultural producers who are followers. The agency moves first, establishing a policy with the goal of optimizing its own objectives, and the producers respond by complying with the policy in a way that maximizes their individual profits. Almost all analysis and simulation of agri-environmental policy to date employ a single level of optimization. Comparison of scenarios where several agency policies are stipulated and the producers optimize with those constraints is a common approach. Many studies use a sequential optimization, where an agency optimizes, and then the producers optimize. We observe that in practice the agency and the producers are all solving their optimization problems at the same time, a crucial feature that is not represented by scenarios or sequential optimization. Our hypothesis is that bilevel optimization provides a better representation agri-environmental policy implementation, and will provide a better method of calculating optimal trade-offs among multiple objectives. We describe a hybrid genetic algorithm for solution of multiple objective bilevel optimization problems, and show how to incorporate data envelopment analysis (DEA) to simulate producer behavior, and include the Soil and Water Assessment Tool (SWAT) to provide the information about environmental effects required by the agency to specify their objectives. We applied the resulting integrated modeling system to the analysis of an incentive policy in the Calapooia watershed in Oregon, USA, using synthetic economic data generated from the Census of Agriculture. Through bilevel optimization, we were able to spatially target agri-environmental policy to find multiple objective Pareto frontiers that dominate those available from other methods.