Precision animal feed formulation: An evolutionary multi-objective approach

Most livestock producers aim for optimal ways of feeding their animals. Conventional algorithms approach optimum feed formulation by minimizing feed costs while satisfying constraints related to nutritional requirements of the animal. The optimization process needs to be performed every time a nutritional requirement is changed due to the nonlinear relationship between the relaxation of the different nutritional requirements and the feed cost. Consequently, decision-making becomes a time-consuming trial and error process. In addition, the nonlinear relationship changes depending on the type of materials used, their nutritional compositions and costs as well as the animal's nutritional requirements. Therefore, in this work, we formulated a multi-objective feed formulation problem comprising of two objects - a) minimizing feed cost and b) minimizing deviation from the specified requirements. The problem is solved using a population-based evolutionary multi-objective optimization algorithm (NSGA-II) that results in an optimal set of comprised solutions in a single run. The availability of the entire set of comprised solutions facilitates the understanding of the relationship between different nutritional requirements and cost, thus leading to a more efficient decision-making process. We demonstrated the applicability of the proposed method by performing experimental simulations on several cases of dairy and beef cattle feed formulation.