Abstract
The allocation of feedstuff to intensively managed dairy cows to achieve different objectives is challenging due to the inherent complexity of the system and the combinatorial problem that has to be solved. Pareto-based multi-objective optimization approaches using evolutionary algorithms can help to address these challenges and show the trade-offs and synergies among various objectives. Here we present a framework for multi-objective optimization with the Differential Evolution (DE) algorithm applied to dairy feeding systems with grazing and concentrate supply to generate an approximation of the Pareto front. The available feed resources are located in different feeding areas, and the number of animals and groups of animals with similar feeding requirements are distributed across these areas for feeding purposes. To evaluate the DE algorithm, we performed two in-silico experiments to: (1) compare the solutions quality of single-objective DE with exact Linear Programming (LP) solutions, and (2) assess the influence of different stocking rates (number of cows/ha) on milk production, feed allocation and economic performance indicators. The DE solutions that minimize the feeding costs for different stocking rates (1.1–2.6 cows/ha) closely approached the solutions derived with LP, confirming the quality of the heuristic algorithm. The multi-objective model scenarios demonstrated that increasing stocking density would enhance milk production and gross margin per unit of area at largely unchanged productivity per animal by shifting the feed ration from roughage to a large proportion of supplementary concentrate feed. At low stocking rates solutions with high productivity and gross margin and a large proportion of roughage in the ration and limited supplementary feeding were identified. We conclude that the multi-objective optimization with a Pareto-based DE algorithm is highly effective to explore the interrelations among conflicting objectives and to find suitable solutions.
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