Many objective optimization and decision support for dairy cattle feed formulation

Livestock feed formulation has significant impacts on livestock production and the environment. Linear and nonlinear constraints, framed as nutritional requirements and specific objectives, present a continuous challenge in achieving optimal feed formulation. Many mathematical models, including linear programming, have been adopted to tackle this issue. However, this approach is often excessively restrictive, primarily focusing on cost minimization and overlooking variability in nutrient content and fulfillment of other objectives. Conventional feed formulation approaches, characterized by their limited operational scope and inadequacy for a robust decision-making process, present challenges to growers aiming to achieve objectives beyond cost minimization. This study proposes a many-objective optimization approach to solving the feed formulation problem and addressing this challenge. The framework optimizes nine objectives, including minimizing cost, weight and the number of feed components, and five nutritional constraints. By integrating feed nutritional constraints and objectives into a comprehensive framework, we aim to introduce flexibility and enhance decision-making. The proposed framework successfully balances the nine objectives, providing growers with a potentially adaptable and tailored solutions. Growers can achieve trade-offs across various objectives, enabling informed decision-making to optimize feed formulation, enhance livestock productivity, and promote environmental sustainability. Furthermore, visualization tools were utilized to improve the interpretability of the generated solutions. The results obtained demonstrate acceptable compromise across various objectives.