Mixed Integer Goal Programming for Personalized Meal Optimization

A recent preprint on arXiv introduces Mixed Integer Goal Programming (MIGP) aimed at optimizing personalized meal plans. This approach tackles two major challenges found in current diet optimization methods: the presence of continuous variables that lead to unrealistic fractional servings (such as 1.7 eggs or 0.37 bananas) and the issues arising from strict nutrient constraints that can lead to infeasibility when targets conflict. A comprehensive review of 56 diet optimization studies revealed that none have integrated integer programming with goal programming to solve these problems. The MIGP model employs integer variables for realistic serving sizes and utilizes goal programming deviations for flexible nutrient targets, incorporating inverse-target normalization to achieve balanced multi-nutrient optimization. It also allows for serving sizes in natural units, like one egg or one tablespoon of oil, without needing rounding. Additionally, the paper discusses the integrality gap within the goal programming framework.