Inverse Optimization and Inference models

Diet problem data resources

The diet recommendation problem is to determine the optimal intake of different food types satisfying some constraints on the nutrients while maximizing the preferences of an individual. In the inverse optimization setting of his problem, the preferences are inferred using a known pattern of the observed diet of the individual. Two different cases are considered. The first case considers a set of similar observations from different individuals with similar attributes and diet goals and the second case considers different days of intake data from the same individual.

The data used in this study is gathered from the National Health and Nutrition Examination Survey (NHANES) dietary data alongside the United States Department of Agriculture (USDA) data for nutrients of different types of food. In this study, we consider the Dietary Approaches to Stop Hypertension (DASH) diet and construct constraints based on it. The data gathered is filtered in a way to find individuals at risk of blood pressure (or individuals whose doctors had told them they are at risk) but their blood pressure ratings showed normal numbers. It is a reasonable deduction to assume that these people were probably trying better diets to control their blood pressure levels. Therefore, such respondents were considered for this example. Also, age limits of 40 to 50 were considered in the filtering process of the data for selected individuals. We have also analyzed the intakes of the individuals to make sure that they are following a good diet.

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A set of female individuals with the above criteria were considered. Further demographic and diet considerations (in order to select similar patients) led to selecting 11 different individuals’ one day of intake as the initial dataset for the model. In another setting, we only considered people that have consumed a reasonable amount of sodium and water. We consider these two nutrients as the main constraints in the DASH diet. 



In order to compare different potential data and their performance with the model, we used different data groups from the NHANES database. A group of middle-aged women with certain similar characteristics and a group of people with certain attributes in their diets. In the first group, we did not consider how the individual’s daily diet is reflecting on the constraints that the forward problem had and we relied on their own personal answer to questions regarding hypertension and also how prone they thought they were to type-2 diabetes. The result was a sparse set of variables and an inconclusive optimal solution in regards to the preferences. In the second group, we tried to obtain sub-optimal data. We prioritized the maximum sodium intake constraint and the water intake constraints as our main and most important constraints.