Mathematical Optimization Framework for Personalized Hypertension Dietary Planning Using Multi-Objective Fuzzy Goal Programming Under Nutritional Uncertainty

Abdullah Hamad  Salman

Authors

Abdullah Hamad Salman College of the Basic Education, Mathematics Department, University of Babylon, Iraq

Keywords:

Hypertension, Fuzzy goal programming, Multi-objective optimization, Personalized nutrition, Dietary planning, Nutritional uncertainty, Healthcare decision support

Abstract

Blood pressure is one of the most common chronic diseases, and a leading cause of cardiovascular disease, stroke, renal failure, and early death. Although nutritional intervention is an integral part of BP control in non-pharmacologic ways, designing affordable, nutritionally adequate diets is a complex decision-making process. Typical linear programming models in the classical approach assume that food composition, nutritional requirements and nutritional targets are known quantities. Food preparation, market fluctuations, person-to-person health differences, and uncertainty in dietary recommendations, however, can influence these quantities in practice. In this paper, a multi-objective fuzzy goal programming model is proposed to solve the personalized hypertension diet planning problem in the context of nutritional uncertainty. The suggested model not only optimizes the dietary cost but also maximizes the dietary quality and cuts down on sodium intake without compromising the nutritional requirements for calcium, potassium, magnesium, protein, dietary fiber and vitamin E. Imprecise nutritional satisfaction is described by fuzzy membership functions and goal programming is used to convert the conflicting objectives into a single compromise model. Theoretical properties of the model are examined such as feasibility, convexity of the feasible region and continuity of the weighted deviation objective. The representative food data are used in a numerical experiment to demonstrate the behavior of the models and then analysis of sensitivity is undertaken to the price variation, higher nutritional requirement, limited availability and restriction on sodium. The outcomes suggest that the proposed fuzzy system is more flexible and explains the decisions better than the deterministic cost minimisation approach. The model is suitable for mathematical and research purposes only and should be used in conjunction with professional nutritional and medical advice.

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