An Exact ε-Constrained Optimization Framework for Balancing Efficiency and Risk Distribution in Spatial Restoration Planning

M. Moreno-Faguett, J. Castillo-Mandujano, J. Salgado-Rojas, V. Hermoso, M. J. Martínez-Harms, B. Larraín-Barrios, E. Álvarez-Miranda

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

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