Mixed Integer Goal Programming for Personalized Meal Optimization with User-Defined Serving Granularity

Determining what to eat to satisfy nutritional requirements is one of the oldest optimization problems in operations research, yet existing formulations have two persistent limitations: continuous variables produce impractical fractional servings (1.7 eggs, 0.37 bananas), and hard nutrient constraints cause infeasibility when targets conflict. A systematic review of 56 diet optimization papers found that none combine integer programming with goal programming to address both issues. We propose Mixed Integer Goal Programming (MIGP) for personalized meal optimization. The formulation uses integer variables for practical serving counts and goal programming deviations for soft nutrient targets...

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