Diet optimization: modeling iron and zinc absorption by nonlinear programming and piecewise linear approximation...

Area of Science:

• Nutritional Sciences
• Operations Research
• Computational Biology

Background:

• Accurate calculation of absorbable nonheme iron and zinc in diet models is crucial for nutritional assessment.
• Standard linear programming software struggles with nonlinear absorption equations, limiting diet model accuracy.

Purpose of the Study:

• To evaluate nonlinear programming (NLP) and piecewise linear approximation (PLA) for solving diet models with nonlinear iron and zinc absorption.
• To compare the effectiveness of NLP and PLA in generating accurate and efficient diet plans.

Main Methods:

• Developed mixed-integer and continuous diet models to optimize absorbable iron and zinc intake.
• Utilized literature-based nonlinear absorption equations and National Health and Nutrition Examination Survey data.
• Generated diet plans using both NLP and PLA techniques for comparative analysis.

Main Results:

• For mixed-integer models, PLA provided accurate solutions rapidly, surpassing NLP in consistency and quality.
• NLP faced time limits and occasional solution inaccuracies for iron (up to 2.1 mg deviation) and zinc (up to 0.2 mg deviation).
• NLP and PLA showed comparable performance for continuous diet models.

Conclusions:

• PLA is a practical and effective method for solving diet models with nonlinear iron and zinc absorption equations.
• Researchers can improve diet model accuracy by implementing NLP or PLA for absorption calculations.
• The study offers practical insights for enhancing nutritional modeling and menu planning.