Diet Problem 

The diet recommendation problem is defined as the problem of determining an 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 can be 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. In both cases, the goal in the inverse setting is to obtain the preferences of the individuals. The inferred parameters can be used to obtain the optimal diet.

We have gathered data from different sources in order to be able to numerically verify inverse optimization models in the data-driven setting. We have gathered data from the National Health and Nutrition Examination Survey (NHANES) dietary data in order to provide raw observations for the models. These data can be divided into two different sets of data. The first set of data includes two days of detailed intake data including the type and amount of the food and the nutrients of each food. The second data sets include the aggregate nutrient intakes of each respondent for the two days of measurement. The United States Department of Agriculture (USDA) data for nutrients of different types of food were used to provide the parameters of the forward optimization problem which include nutrients of each food type per serving. It is worth mentioning that servings were used as the unit of measurement in the data to provide better comparison characteristics. The Dietary Approaches to Stop Hypertension (DASH) diet was considered as a potential target diet in order to construct nutrient constraints of the forward optimization problem. Samples from data are gathered for different scenarios. Samples target individuals at risk of blood pressure (or individuals whose doctors had told them they are at risk) but their blood pressure ratings show normal numbers. It is a reasonable deduction to assume that these people were probably trying better diets to control their blood pressure levels. Specific demographic criteria are also utilized to further filter the data to obtain individuals with similar attributes. The complete data set used in the project can be found in the following repository: