Result: Diet optimization: modeling iron and zinc absorption by nonlinear programming and piecewise linear approximation using National Health and Nutrition Examination Survey

Background: The accuracy of the calculation of absorbable nonheme iron and zinc content in diet-model-generated menu plans can be improved by using nonlinear absorption equations. The resulting diet models cannot be solved with standard linear programming software. Objective: The aim of this study was to evaluate the effectiveness of nonlinear programming (NLP) and piecewise linear approximation (PLA) for solving diet models with nonlinear equations for nonheme iron and zinc absorption. Methods: A mixed-integer and a continuous diet model were developed to optimize absorbable iron and zinc intake, using different absorption equations available from the literature. Model input data were obtained from the National Health and Nutrition Examination Survey. Various diet plans were then generated applying both NLP and PLA techniques. Evaluation criteria included solution quality and computational efficiency. Results: For the mixed-integer diet model, PLA found accurate solutions within minutes, outperforming NLP in consistency and solution quality. NLP frequently hit the 1-h time limit and did not always find the best observed solution. In the worst cases, NLP either found no solution or the deviation was as large as 2.1 mg for absorbable iron. For absorbable zinc, the maximum deviation was only 0.2 mg. For the continuous diet model, NLP and PLA performed equally well in most cases. Conclusions: This study provides practical examples for researchers who seek to improve the accuracy of their diet models through the implementation of nonheme iron and zinc absorption equations using either NLP or PLA.