Assignment 5: Multi-criteria decision making

This week your task is to familiarize yourself with multi-criteria (or multi-objective) decision making (MCDM) and apply the method to the problem described below. Readings on MCDM can be found in the course folder.

Task

Your health is dependent on good nutrition. There are various aspects of healthy food which makes it difficult to design a balanced diet. To start with, one needs a certain amount of energy which should be contained in a diet including a certain amount of protein, a certain amount of calcium, etc.

Utility functions: The target levels for a selected set of nutrients (Table 1) give ten different utility functions: a utility function should achieve the value zero when a diet contains at least the recommended amount of the nutrient, and a negative value if the diet falls short of the recommended value, given by the negative ratio of the recommended amount and the actual amount in the diet –recommended_value/actual_value.

Restrictions: In cases where there is a risk of overdose, the diet must not contain more than a certain limit of the nutrient in question. These limits pose restrictions on valid diets. In addition, the diet must contain at least three and at most ten different food products.

Reporting the Results

You should optimize all the ten utility functions simultaneously, taking care that all the restrictions are satisfied. To enable culinaristic freedom you should maintain as diverse set of diets as possible. If you decide to use evolutionary algorithms, you can maintain a population of, say, 50 diets.

You can experiment with different modifications to the utility functions and the restrictions to achieve solutions to your taste.

Table 1. Recommended Amounts

Nutrient	Amount per Day	Overdose?
Energy	2200 kcal	> 2500 kcal
Protein	60 g	> 120 g
Calcium	800 mg	> 2500 mg
Iron	10 mg	> 20 mg
Magnesium	300 mg	no
Vit_B6	1.3 mg	> 4.2 mg
Vit_B12	3 μg	no
Vit_C	60 mg	no
Vit_D	5 μg	> 10 μg
Vit_E	10 mg	> 20 mg

The food products you can include in the diet are listed in the USDA National Nutrient Database (1.7MB in a tab-delimited ASCII format), gzipped (573kB) (downloaded from www.nutrition.gov).

Note: You can replace empty fields by 0 (zero).

Table 2. Abbreviated File Format

Field name	Type	Description
NDB_No.	A 5*	5-digit Nutrient Databank number
Shrt_Desc	A 60	60-character abbreviated description of food item†
Water	N 10.2	Water (g/100 g)
Energ_Kcal	N 10	Food energy (kcal/100 g)
Protein	N 10.2	Protein (g/100 g)
Lipid_Tot	N 10.2	Total lipid (fat)(g/100 g)
Ash	N 10.2	Ash (g/100 g)
Carbohydrt	N 10.2	Carbohydrate, by difference (g/100 g)
Fiber_TD	N 10.1	Total dietary fiber (g/100 g)
Sugar_Tot	N 10.2	Total sugars (g/100 g)
Calcium	N 10	Calcium (mg/100 g)
Iron	N 10.2	Iron (mg/100 g)
Magnesium	N 10	Magnesium (mg/100 g)
Phosphorus	N 10	Phosphorus (mg/100 g)
Potassium	N 10	Potassium (mg/100 g)
Sodium	N 10	Sodium (mg/100 g)
Zinc	N 10.2	Zinc (mg/100 g)
Copper	N 10.3	Copper (mg/100 g)
Manganese	N 10.3	Manganese (mg/100 g)
Selenium	N 10.1	Selenium (μg/100 g)
Vit_C	N 10.1	Vitamin C (mg/100 g)
Thiamin	N 10.3	Thiamin (mg/100 g)
Riboflavin	N 10.3	Riboflavin (mg/100 g)
Niacin	N 10.3	Niacin (mg/100 g)
Panto_acid	N 10.3	Pantothenic acid (mg/100 g)
Vit_B6	N 10.3	Vitamin B6 (mg/100 g)
Folate_Tot	N 10	Folate, total (μg/100 g)
Folic_acid	N 10	Folic acid (μg/100 g)
Food_Folate	N 10	Food folate (μg/100 g)
Folate_DFE	N 10	Folate (μg dietary folate equivalents/100 g)
Vit_B12	N 10.2	Vitamin B12 (μg/100 g)
Vit_A_IU	N 10	Vitamin A (IU/100 g)
Vit_A_RAE	N 10	Vitamin A (μg retinol activity equivalents/100g)
Retinol	N 10	Retinol (μg/100 g)
Vit_E	N 10.2	Vitamin E (alpha-tocopherol) (mg/100 g)
Vit_K	N 10.1	Vitamin K (phylloquinone) (μg/100 g)
Alpha_Carot	N 10	Alpha-carotene (μg/100 g)
Beta_Carot	N 10	Beta-carotene (μg/100 g)
Beta_Crypt	N 10	Beta-cryptoxanthin (μg/100 g)
Lycopene	N 10	Lycopene (μg/100 g)
Lut+Zea	N 10	Lutein+zeazanthin (μg/100 g)
FA_Sat	N 10.3	Saturated fatty acid (g/100 g)
FA_Mono	N 10.3	Monounsaturated fatty acids (g/100 g)
FA_Poly	N 10.3	Polyunsaturated fatty acids (g/100 g)
Cholestrl	N 10.3	Cholesterol (mg/100 g)
GmWt_1	N 9.2	First household weight for this item from the Weight file‡
GmWt_Desc1	A 120	Description of household weight number 1
GmWt_2	N 9.2	Second household weight for this item from the Weight file‡
GmWt_Desc2	A 120	Description of household weight number 2
Refuse_Pct	N 2	Percent refuse§

* Index field for the Abbreviated file.
† For a 200-character description and other descriptive information, link to the Food Description file.
‡ For the complete list and description of the measure, link to the Weight file.
§ For a description of refuse, link to the Food Description file.