Quantifying uncertainty in Pareto fronts arising from spatial data

Hildemann, Moritz; Verstegen, Judith A.

doi:10.1016/j.envsoft.2021.105069

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…We follow the method of Guariso and Sangiorgio (2020) who found that seeding the single objective optimal solution benefit the spread and convergence of the Pareto fronts. Hildemann and Verstegen (2021) found that the findings hold for a multi-objective land use allocation optimization under uncertainty using the NSGA II. Therefore, the single objective extreme solutions are computed and injected to the initial population: The single objective extreme solution of minimizing the soil loss rates is to have every sub-watershed conserved, and the single objective extreme solution for minimizing the labor requirement is to omit SWC-installations completely.…”

Section: Seedingmentioning

confidence: 69%

“…In their case, the DEM uncertainty propagated to different ski courses, indicating that DEM uncertainty could propagate to different borders of the subwatersheds. In our optimization algorithm, the uncertain distinction between sub-watersheds leads to solutions uncertain decision variable definitions: The number of decision variables can change (Hildemann and Verstegen, 2021), and the reference of a sub-watershed identifier to the area becomes ambiguous. Since the imposed difficulties and problem complexity would increase a lot, we did not consider that uncertainty in this study.…”

Section: Limitations and Future Workmentioning

confidence: 99%

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Multi-objective allocation optimization of soil conservation measures under data uncertainty

Hildemann

Pebesma

Verstegen

2022

Preprint

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Many regions worldwide face soil loss rates that endanger future food supply. The installation of soil and water conservation measures reduces soil loss rates but comes with high labor costs. A multi-objective optimization allows considering both soil loss rates and labor costs, but required spatial data contains uncertainties. Yet, spatial data uncertainty has not been considered in research for allocating soil and water conservation measures. We aim to overcome that research gap by optimizing conservation measure allocations despite spatial data uncertainties. We propose a multi-objective genetic algorithm that creates optimal solutions that indicate which watersheds should be conserved. Stochastic objective values are computed from uncertain soil and precipitation variables to evaluate and compare solutions. The study is conducted in three rural areas in Ethiopia. The highest soil loss rate uncertainties result in objective values ranging up to 14%. The associated yield loss ranges with soil loss rates under uncertainties are comparable to reported yield loss risks from droughts. The uncertainty of labor requirement objective values is localised to less then 5% of the area in all three study areas. However, ranges in labor requirement estimations become up to 15 labor days per hectare in areas where labor requirements are uncertain. Upon further analysis of common characteristics and patterns in optimal solutions, we also conclude that the results can be used to define a temporal order for planning and implementing conservation measures.

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Section: Seedingmentioning

confidence: 69%

Section: Limitations and Future Workmentioning

confidence: 99%

Multi-objective allocation optimization of soil conservation measures under data uncertainty

Hildemann

Pebesma

Verstegen

2022

Preprint

Self Cite

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show abstract

“…We follow the method of Guariso and Sangiorgio ( 2020 ), who found that seeding the single objective optimal solutions benefits the spread and convergence of the Pareto fronts. Hildemann and Verstegen ( 2021 ) found that the findings hold for a multi-objective land use allocation optimization under uncertainty using the NSGA II. Therefore, the single objective extreme solutions are computed and injected into the initial population: The single objective extreme solution for minimizing the soil loss rates is to have every sub-watershed selected.…”

Section: Methodsmentioning

confidence: 88%

Multi-objective Allocation Optimization of Soil Conservation Measures Under Data Uncertainty

Hildemann

Pebesma

Verstegen

2023

Environmental Management

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Many regions worldwide face soil loss rates that endanger future food supply. Constructing soil and water conservation measures reduces soil loss but comes with high labor costs. Multi-objective optimization allows considering both soil loss rates and labor costs, however, required spatial data contain uncertainties. Spatial data uncertainty has not been considered for allocating soil and water conservation measures. We propose a multi-objective genetic algorithm with stochastic objective functions considering uncertain soil and precipitation variables to overcome this gap. We conducted the study in three rural areas in Ethiopia. Uncertain precipitation and soil properties propagate to uncertain soil loss rates with values that range up to 14%. Uncertain soil properties complicate the classification into stable or unstable soil, which affects estimating labor requirements. The obtained labor requirement estimates range up to 15 labor days per hectare. Upon further analysis of common patterns in optimal solutions, we conclude that the results can help determine optimal final and intermediate construction stages and that the modeling and the consideration of spatial data uncertainty play a crucial role in identifying optimal solutions.

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“…They are mainly in the form of quantitative constraint, and are difficult to be taken into consideration due to the limitations of spatial optimization models (Strauch et al, 2019). For another thing, the non-linear relationship between some ES and land spatial layout prevents the direct measurement of these ES based on spatial layout (Hildemann & Verstegen, 2021), as a result, only those ES that are easily calculated can be embedded into spatial optimization (Wicki et al, 2021). These deficiencies limit the practical application of such ES-based spatial optimization methods.…”

Section: Existing Studies On This Issuementioning

confidence: 99%

A two‐step spatially explicit optimization approach of integrating ecosystem services (ES) into land use planning (LUP) to generate the optimally sustainable schemes

et al. 2023

Land Degrad Dev

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Xuzhou, as an industrial centre and typical resource‐based city in China, is facing serious pressure on development transformation. The embedding of ecosystem services (ES) into land use planning (LUP) is of great significance to realize the coupling of ecology and society. This paper proposed a two‐step spatially explicit optimization approach of integrating ES into LUP, with consideration of macro‐requirements, spatial heterogeneity, and the spatially explicit basis. The first step was to construct a linear optimization model to obtain the land quantity structure corresponding to the maximized ES value. The second step was to spatially allocate land use structure to maximize the suitability of spatial units providing ES. The results showed that the land use structure corresponding to the maximization ES value of Xuzhou was obtained to satisfy the welfare of habitant and to create the ecological competitiveness. The optimal spatial layout of Xuzhou with maximum spatial suitability of providing ES was acquired through spatial optimization of this approach. ES was matched to the units with the high spatial suitability, and the spatial potential of ES was released. The conflicts among supporting services, provisioning services, regulating services, and cultural services were well managed with the equipment of multi‐objective trade‐off technology. The proposed ES embedding approach has good performance in the optimal allocation of land resources for ES maximization and in managing trade‐offs during multi‐objectives programming. Therefore, it is expected to be widely used for ES‐oriented LUP formulation.

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Quantifying uncertainty in Pareto fronts arising from spatial data

Cited by 5 publications

References 13 publications

Multi-objective allocation optimization of soil conservation measures under data uncertainty

Multi-objective allocation optimization of soil conservation measures under data uncertainty

Multi-objective Allocation Optimization of Soil Conservation Measures Under Data Uncertainty

A two‐step spatially explicit optimization approach of integrating ecosystem services (ES) into land use planning (LUP) to generate the optimally sustainable schemes

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