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Protected areas (PAs) are designated spaces where human activities arerestricted to preserve critical habitats. Decision-makers are challenged withbalancing a trade-off of financial feasibility with ecological benefit whenestablishing PAs. Given the long-term ramifications of these decisions and theconstantly shifting environment, it is crucial that PAs are carefully selectedwith long-term viability in mind.  Using AI tools like simulation and optimization is common for designatingPAs, but current decision models are primarily linear. In this paper, wepropose a derivative-free optimization framework paired with a nonlinearcomponent, population viability analysis (PVA). Formulated as a mixed integernonlinear programming (MINLP) problem, our model allows for linear andnonlinear inputs. Connectivity, competition, crowding, and other similarconcerns are handled by the PVA software, rather than expressed as constraintsof the optimization model. In addition, we present numerical results that serveas a proof of concept, showing our models yield PAs with similar expected riskto that of preserving every parcel in a habitat, but at a significantly lowercost.  The overall goal is to promote interdisciplinary work by providing a newmathematical programming tool for conservationists that allows for nonlinearinputs and can be paired with existing ecological software. Our code and dataare available at https://github.com/cassiebuhler/conservation-dfo.

Decision-Making for Land Conservation: A Derivative-Free Optimization Framework with Nonlinear Inputs