An Exact ε-Constrained Optimization Framework for Balancing Efficiency and Risk Distribution in Spatial Restoration Planning
Spatial restoration planning requires balancing efficiency in biodiversity gains with the distribution of conservation benefits across species. We develop an exact mixed-integer linear optimization framework that prioritizes restoration while explicitly accounting for extinction risk. The model relies on a species–area–risk relationship approximated through piecewise-linear functions to ensure tractability while preserving the decision space. We define two objectives: maximizing total extinction risk reduction (efficiency) and minimizing the maximum species risk (equity). Using an ε-constraint approach, we generate a Pareto frontier describing the trade-off between aggregate gains and risk concentration. As all model variants share the same feasible space, trade-offs reflect genuine ecological tensions. The framework is general, extensible, and supports conservation decision-making.
Palabras clave: spatial prioritization conservation planning extinction risk multi-objective optimization ε-constraint ecological restoration MILP