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The application of nonlinear programming on ration formulation for dairy cattle.
J Li1, E Kebreab1, Fengqi You2
1Department of Animal Science, University of California, Davis 95616.
Journal of Dairy Science
|January 9, 2022
Summary
Iterative linear programming (iteLP) struggled with nonlinear constraints in dairy cattle ration formulation, while sequential quadratic programming (SQP) and mixed-integer nonlinear programming-based deterministic global optimization (MINLP_DGO) performed better, with SQP being faster.
Area of Science:
- Animal Science
- Operations Research
- Agricultural Economics
Background:
- Dairy cattle ration formulation requires optimizing least-cost diets while meeting complex nutritional requirements.
- Traditional linear programming methods may face challenges with nonlinear constraints common in feed formulation.
Purpose of the Study:
- To compare the efficacy of iterative linear programming (iteLP), sequential quadratic programming (SQP), and mixed-integer nonlinear programming-based deterministic global optimization (MINLP_DGO) for dairy cattle ration formulation.
- To evaluate the performance of these optimization techniques in terms of feasibility, cost-effectiveness, and computational time.
Main Methods:
- Least-cost diets were formulated for lactating cows, dry cows, and heifers using the Nutrient Requirements of Dairy Cattle (NRC, 2001) guidelines.
- Nutrient requirements (energy, protein, minerals) and constraints (dry matter intake, NDF, fat) were incorporated.
- Five hundred simulations were run, randomly selecting feed resources for each animal group, and applying iteLP, SQP, and MINLP_DGO.
Main Results:
- iteLP showed limited feasibility, particularly with nonlinear constraints, resulting in numerous infeasible solutions for all cow groups.
- SQP and MINLP_DGO demonstrated superior performance in handling nonlinear constraints, yielding feasible solutions across all simulations for dry cows and heifers.
- While SQP was computationally faster, MINLP_DGO provided feasible solutions in scenarios where SQP failed, indicating robustness in complex optimization problems.
Conclusions:
- iteLP is not suitable for dairy ration formulation when nonlinear constraints are present.
- SQP offers a computationally efficient approach for nonlinear ration optimization, while MINLP_DGO provides greater robustness for complex or challenging formulations.
- The choice between SQP and MINLP_DGO depends on the specific balance between computational speed and the need for guaranteed feasibility in dairy ration optimization.
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