Nut-Opt

Linear programming library for nutrition optimization.

Backend for my blog post on finding the optimal diet and identifying superfoods. Solves the following LP for a range of tradeoff parameters and plots the results:

Minimize $c^T\mathbf{x} + \gamma\mathcal{1}^T\mathbf{x}$

subject to $l \leq A\mathbf{x} \leq u$, $\mathbf{x} \geq 0$

where $c$ is the vector of calories per 100g, the ones vector $\mathcal{1}$ is the vector of weights in units of 100g, $\mathbf{x}$ is the vector of weights of each food in units of 100g, and $\gamma$ is the tradeoff variable. The constraints $l$ and $u$ are the lower and upper bounds on the nutrient features, respectively. The matrix $A$ is the matrix of constrained nutrients per 100g of each food.

Installation

git clone <url>
cd Nut-Opt
pip install .

Usage

python -m nutopt -f <food_list> -a <amino y/n> --n_sweep <n> --n_plot <n> --plotdir <dir>

-f is a space-separated list of foods to include in the optimization. If not specified, all foods are included.

-a is a flag to include amino acids in the optimization constraints. If not specified, amino acids are not included.

--n_sweep is the number of tradeoff parameters $\gamma$ to sweep over.

--n_plot is the number of superfoods to radar plot.

Data

The nutritional dataset in nutopt/data/ is from kaggle, originally sourced here.

Constraints

These are editable in nutopt/definitions.py. The default constraints are:

Macros

50 < total_fat (g) < 120

10 < saturated_fat (g) < 25

70 < protein (g) < 100

130 < carbohydrate (g) < 400

Vitamins

550 < choline (mg) < 2500

400 < folate (mcg) < 900

400 < folic_acid (mcg) < 900

16 < niacin (mg) < 30

5 < pantothenic_acid (mg) < 100

1.3 < riboflavin (mg) < 500

1.2 < thiamin (mg) < 200

3000 < vitamin_a (IU) < 8000

2.4 < vitamin_b12 (mcg) < 8

1.3 < vitamin_b6 (mg) < 4

90 < vitamin_c (mg) < 1000

600 < vitamin_d (IU) < 5000

15 < vitamin_e (mg) < 500

120 < vitamin_k (mcg) < 500

Minerals

1500 < sodium (mg) < 3000

1300 < calcium (mg) < 2000

0.9 < copper (mg) < 7

8 < iron (mg) < 35

400 < magnesium (mg) < 500

2.3 < manganese (mg) < 7

700 < phosphorous (mg) < 3500

4700 < potassium (mg) < 7000

55 < selenium (mcg) < 300

11 < zinc (mg) < 35

Amino Acids

0.287 < cystine (g) < inf

0.7 < histidine (g) < inf

1.4 < isoleucine (g) < inf

2.73 < leucine (g) < inf

2.1 < lysine (g) < inf

0.728 < methionine (g) < inf

0.875 < phenylalanine (g) < inf

1.05 < threonine (g) < inf

0.28 < tryptophan (g) < inf

0.875 < tyrosine (g) < inf

1.82 < valine (g) < inf

Carbohydrates

38 < fiber (g) < 55

0 < sugars (g) < 40

Fatty Acids

17 < polyunsaturated_fatty_acids (g) < 30

Other

50 < cholesterol (mg) < 250

0 < alcohol (g) < 5

100 < water (g) < 2000

Results

For all foods in the dataset and all default constraints active. The optimal tradeoff curve between calories and weight is shown below.

And here is the optimal diet for $\gamma = 1$ with weight in units of 100g:

Total calories: 871.1281429945614 kcal

Total weight: 1113.0965300000835 g

Weight (100g) Name

4.412183 Cauliflower, raw, green

1.453970 Watercress, raw

0.787405 Bamboo shoots, without salt, drained, boiled, cooked

0.657726 Chicken spread

0.588269 Cocoa, processed with alkali, unsweetened, dry powder

0.569966 Fish, raw, mixed species, roe

0.518734 Mushrooms, grilled, exposed to ultraviolet light, portabella

0.516959 Tofu, prepared with calcium sulfate, salted and fermented (fuyu)

0.506891 Cabbage, without salt, drained, boiled, cooked, chinese (pak-choi)

0.361921 Cereals ready-to-eat, FIBER ONE Bran Cereal, GENERAL MILLS

0.292224 Gelatin desserts, with aspartame, reduced calorie, dry mix

0.147996 Oil, soybean lecithin'

0.146714 Vitasoy USA Nasoya, Lite Silken Tofu

0.095675 Yeast extract spread

0.048087 Oil, wheat germ

0.023411 Mushrooms, raw, exposed to ultraviolet light, or crimini, italian, brown

0.002834 Desserts, unsweetened, tablets, rennin

Superfoods

Count of how many times foods appear in optimal diets.

Nutritional characteristics of the top four superfoods.