level: research
a review of 56 diet optimization papers found no approach that combines integer programming with goal programming to handle both fractional servings and conflicting nutrient targets. existing methods often produce impractical results like 1.7 eggs or 0.37 bananas, or fail entirely when nutrient goals clash. the proposed mixed integer goal programming (migp) formulation uses integer variables to ensure servings come in natural units, such as one egg or one tablespoon of oil, without post-hoc rounding.
the migp model replaces hard nutrient constraints with soft targets using goal programming deviations. it applies inverse-target normalization to balance optimization across multiple nutrients with different scales. per-food serving granularity is defined by the user, allowing flexibility in how each food is measured. this means the system can respect practical eating habits while still aiming to meet nutritional recommendations as closely as possible.
the work characterizes the integrality gap in the goal programming context, showing how much the objective worsens when forcing integer servings compared to continuous solutions. this gap helps quantify the trade-off between mathematical optimality and practical usability. the approach is designed for personalized meal planning, where individual preferences and dietary needs can be incorporated without leading to infeasible or unrealistic suggestions.
why it matters: this method makes automated meal planning more practical by generating diets with whole food servings, which can improve adherence and usability in nutrition apps and clinical settings.