Interactive livestock feed ration optimization using evolutionary algorithms

The profitability of the livestock industry largely depends on cost-effective feed ration formulation as feed accounts for between 60 and 80% of production costs. Therefore, feed formulation is a recurring problem for breeders. In addition, the presence of linear and non-linear constraints, and multiple possible combinations that are subject to upsurge makes the formulation of feed a Non-deterministic Polynomial-time hard (NP-hard) problem. Generally, feed formulation is done by specifying the nutritional requirements as rigid constraints and an algorithm attempts to find a feasible cost-effective formulation. However, relaxing the constraints can sometimes provide a huge reduction in the cost of feed while not seriously affecting the economic performance of the livestock. This entails the development of a feed formulation software that has an inbuilt mechanism to enable relaxation to the constraints based on the users' necessities. Accordingly, the problem formulation and the optimization algorithm should facilitate this. We modified the conventional problem formulation with a tolerance parameter (as a percentage of the actual value) to accommodate the relaxation of constraints. We solved this problem with differential evolution, a variant of evolutionary algorithms, which are good for handling NP-hard problems. In addition, the relaxation of the constraints was done in an interactive way using the proposed method without penalties. In other words, the proposed method is flexible and possesses the ability to search for a feasible and least-cost solution if available or otherwise, the best solution and finds the suitable feed components to be used in ration formulation at an optimal cost depending on the nutrient requirements and growth stage of the animal.