(PTFS06-01-23) Mathematical Optimization as a Tool To Derive Food-Based Dietary Guidelines: Implication of the Mathematical Form of the Objective Function on Dietary Changes

Objectives: To find the most suitable statistical form of objective function for the derivation of the German food-based dietary guideline (FBDG) using an optimization model. The hypothesis is that the optimized diet is more acceptable for the target population the lower the number of food groups that changes from observed to optimized intake.

Methods: In Germany, an optimization model is applied to derive FBDG. To answer the objective, a simplified version of that model was used: It minimized the deviation from the average observed intakes (objective function) of 593 food groups (FoodEx2 codes) for German adults (n=10,419) while fulfilling constraints on acceptability (maximal food intakes at 95th percentile) and on 37 nutrients and energy (goal: 2029kcal/d, observed: 2229kcal/d). The objective function was expressed linear (simplex algorithm) in either absolute differences (linear-absolute, LA), in percentage of the observed intakes (linear-relative, LR), or with squared differences (dual method of Goldfarb and Idnani) as squared-absolute (SA) and squared-relative (SR). To inform our decision, indicators for the deviation from observed food intakes were analyzed: The number of food groups that increased, decreased and that attained 0g/d in the optimized diet (values rounded to two decimal places). Additionally, the number of groups that reached acceptability limits and variation in total quantity of food and beverages to be consumed were described.

Results: In each scenario, more food groups were increased than decreased. Though, the squared functions showed a higher percentage of food groups being altered: SA 96%, SR 56%. LA and LR changed 23% and 12% of the 593 food groups. In the absolute models, more food groups attained 0g/d than in the relative ones: 216 in SA vs. 50 in SR and 126 food groups in LA vs. 58 in LR. Using an absolute deviation, no acceptability limit was reached, whereas SR reached one and LR two limits. LA and SA remained approximately at the level of observed consumption, whilst both relative models led to a ~40% increase in total weight.

Conclusions: The LR function generated fewer, but more drastic changes. It had the lowest number of changed food groups while fulfilling the constraints, which might be the most suitable solution for the German FBDG leaving the biggest part of the diet unchanged.

Funding Sources: German Federal Ministry of Food and Agriculture