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Article

Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs

1
Forest Research Center and Laboratory Terra, School of Agriculture, University of Lisbon, Tapada da Ajuda, 1349-017 Lisboa, Portugal
2
Research Centre for Mathematics and Applications, University of Évora, Colégio Luis Verney, 7000-671 Évora, Portugal
3
Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, ul. Vavilova 40, 119333 Moscow, Russia
*
Author to whom correspondence should be addressed.
Academic Editor: Timothy A. Martin
Forests 2021, 12(9), 1244; https://doi.org/10.3390/f12091244
Received: 10 August 2021 / Revised: 29 August 2021 / Accepted: 8 September 2021 / Published: 15 September 2021
Decision making in modern forest management planning is challenged by the need to recognize multiple ecosystem services and to address the preferences and goals of stakeholders. This research presents an innovative a posteriori preference modeling and multi-objective integer optimization (MOIP) approach encompassing integer programming models and a new technique for generation and interactive visualization of the Pareto frontier. Due to the complexity and size of our management problems, a decomposition approach was used to build the Pareto frontier of the general problem using the Pareto frontiers of its sub-problems. The emphasis was on the approximation of convex Edgeworth–Pareto hulls (EPHs) for the sub-problems by systems of linear inequalities; the generation of Edgeworth–Pareto hulls by the convex approximation of the Pareto frontier evinced a very small discrepancy from the real integer programming solutions. The results thus highlight the possibility of generating the Pareto frontiers of large multi-objective integer problems using our approach. This research innovated the generation of Pareto frontier methods using integer programming in order to address multiple objectives, locational specificity requirements and product even-flow constraints in landscape-level management planning problems. This may contribute to enhancing the analysis of tradeoffs between ecosystem services in large-scale problems and help forest managers address effectively the demand for forest products while sustaining the provision of services in participatory management planning processes. View Full-Text
Keywords: integer programming; multi-objective optimization; Pareto frontier; decomposition approach; decision making; ecosystem integer programming; multi-objective optimization; Pareto frontier; decomposition approach; decision making; ecosystem
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MDPI and ACS Style

Marques, S.; Bushenkov, V.; Lotov, A.; G. Borges, J. Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs. Forests 2021, 12, 1244. https://doi.org/10.3390/f12091244

AMA Style

Marques S, Bushenkov V, Lotov A, G. Borges J. Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs. Forests. 2021; 12(9):1244. https://doi.org/10.3390/f12091244

Chicago/Turabian Style

Marques, Susete, Vladimir Bushenkov, Alexander Lotov, and José G. Borges. 2021. "Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs" Forests 12, no. 9: 1244. https://doi.org/10.3390/f12091244

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