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

TL;DR

This paper introduces a novel derivative-free optimization framework with nonlinear inputs for land conservation decision-making, enabling more ecologically and financially balanced protected area design.

Contribution

It develops a mixed integer nonlinear programming model incorporating nonlinear ecological factors via PVA, advancing decision tools for conservation planning.

Findings

Models achieve similar ecological risk as full habitat preservation

Significantly lower costs compared to preserving all parcels

Framework supports nonlinear ecological inputs in optimization

Abstract

Protected areas (PAs) are designated spaces where human activities are restricted to preserve critical habitats. Decision-makers are challenged with balancing a trade-off of financial feasibility with ecological benefit when establishing PAs. Given the long-term ramifications of these decisions and the constantly shifting environment, it is crucial that PAs are carefully selected with long-term viability in mind. Using AI tools like simulation and optimization is common for designating PAs, but current decision models are primarily linear. In this paper, we propose a derivative-free optimization framework paired with a nonlinear component, population viability analysis (PVA). Formulated as a mixed integer nonlinear programming (MINLP) problem, our model allows for linear and nonlinear inputs. Connectivity, competition, crowding, and other similar concerns are handled by the PVA software, rather than expressed as constraints of the optimization model. In addition, we present numerical results that serve as a proof of concept, showing our models yield PAs with similar expected risk to that of preserving every parcel in a habitat, but at a significantly lower cost. The overall goal is to promote interdisciplinary work by providing a new mathematical programming tool for conservationists that allows for nonlinear inputs and can be paired with existing ecological software. Our code and data are available at https://github.com/cassiebuhler/conservation-dfo.