Optimal agricultural spreading scheduling through surrogate-based optimization and MINLP models

The most commonly used definition of climate smart agriculture (CSA) is provided by the Food and Agricultural Organisation of the United Nations, which defines CSA as “agriculture that sustainably increases productivity, enhances resilience, reduces/removes greenhouse gas where possible, and enhances achievement of national food security and development goals”. In this definition, the principal goal of CSA is identified as food security and development, while productivity, adaptation, and mitigation are identified as the three interlinked pillars necessary for achieving this goal. In the context provided by the CSA, soils are seen as a lever to improve the carbon footprint of agriculture, namely through their role as carbon sinks. Improving soils and in particular agricultural soils’ content in soil organic carbon (SOC) in one of the measures enabling to improve the environmental impact of agricultural practices. In this context, composts can be seen as an important feedstock for sustainable farming. To support the development of organic amendment strategies enabling to increase soils’ SOC content, this work proposes a novel methodology to optimize the monthly scheduling of composts and mineral fertilizers amendments. The schedule proposed maximizes soil health - via improved SOC content - while ensuring optimal gross operating surplus from agriculture. This problem is subjected to certain operational, regulatory and soil-dynamics constraints which leads to a complex optimization problem and has to be solved in a relatively short time period for decision-making purposes. This is a nonlinear optimization problem (NLP) which is based on a soil-simulation model from which the analytic functions are not explicitly available for the optimization model. Operational and regulatory constraints are explicitly defined and integer and continuous variables are needed in the modeling. In order to effectively solve it in a deterministic way, a novel surrogate-modeling approach for the objective functions and constraints is proposed. Another novelty comes from the implementation of a continuous-variable-reduction procedure in order to build effective surrogates. The optimisation model results obtained from a real case study show that local optimal solutions can be identified with short computation times. The evaluated scenario shows that the optimized strategy could increase by 8% the carbon in soil after 13 years while increasing by 7% the estimated agricultural profit when compared to expert based application schedules.