Solving for Food

As all perfectly-normal-people^TM do, I keep a spreadsheet of different foods and cost / what nutrients they contain. Cause if you are not optimizing, you're not living life to it's fullest!

But it always been me rougly eyeballing the measurments and trying to put together an optimal diet by hand. So when I find out about OR-Tools? Caching!

OR-Tools & Methodology

It's Googles contraint solver that they have open sourced. It contains a little bit of everything (graph, routing, etc.) but it's the constraint part I'm after. After all, what is an optimized diet but a list of constraints?

Some parts where easy, getting the basics down went quick! However the constrain for a max number of items was pure pain to implement, as I needed to work around the system to get something it could work with

The Data is quite manual. Livsmedelsverket have a good database but I needed to curate specific objects, as I had to do the prices myself. As well as the base needs are a bit tricky and up to interpretation

I used a paper from Livsmedelsverket näringsrekommendationer in combination with FDA recommendations and my own sound(-ish) judgement to determine what to keep in

Code

So, the good parts. Let's start with the relevant code, there is more for output formating / reading data / etc. but this is the main work chunk

# 1 = 100g, 10 = 10g, 100 = 1g - Other values for precision will NOT work properly (mainly output becoming wrong / ugly)
precision = [1, 10, 100][1]
# If you want to loosen the constraints to some percentage, 1 = 100%
constraintsPercentage = 0.95
# Limits how many items to include
maxItems = 10
# All values are increased to be able round to integers without loss of precision
scalingFactor = 1000

def main():
    # Scale upp with scalingFactor and apply constraintsPercentage / precision
    for values in rdi:
        values[1] = math.floor(values[1] * scalingFactor)
    for values in constraints:
        values[1] = math.floor(values[1] * scalingFactor * constraintsPercentage)
    for values in items:
        for index, v in enumerate(values[1:], start=1):
            values[index] = math.floor((v / precision) * scalingFactor)


    solver = pywraplp.Solver.CreateSolver("SCIP")

    # Variables
    # Created from constraints variable, min values for each nutrient
    x = {}
    # 0 or 1 if item is used, to enable maxItems to work
    y = {}
    for i in range(len(items)):
        # Limits max units per item for the solution
        max = 1000000
        x[i] = solver.IntVar(0, max, "")
        y[i] = solver.IntVar(0, 1, "")
        solver.Add(x[i] <= y[i] * max)

    # Constraints for nutrients
    for c in constraints:
        i = itemsHeader.index(c[0])
        min = c[1]
        solver.Add(solver.Sum(items[j][i] * x[j] for j in range(len(x))) >= min)
    # Limit to maxItems
    solver.Add(solver.Sum(y[i] for i in range(len(y))) <= maxItems)

    # Objective
    cost = []
    for i in range(len(x)):
        ic = itemsHeader.index("cost")
        cost.append(items[i][ic] * x[i])
    solver.Minimize(solver.Sum(cost))

    status = solver.Solve()

Not to horrible

Results

What is the best diet?

*DRUMROLL*

Cost is 18.8kr per day
8.3kr for 6.4dl of Milk (3%)
3.3kr for 410g of Wheat Flour
3.0kr for 90g of Broccoli
1.3kr for 70g of Yellow Peas
1.0kr for 30g of Sunflower Seeds
80 öre for 20g of Eggs
80 öre for 0.3dl of Rapeseed oil
40 öre for 40g of Carrots

I'm Swedish, can you tell?
For euro / US just divide by 10 and you get a rough approximation

Which gives you the following macro / micro nutrients
(RDI based on my own age / gender / weight / etc.)

Summary

Milk is awesome!
Also vegetables good, etc.

It was fun to play around with but don't know if created any bound breaking knowledge
Milk comes surprisingly (to me) high up with quite a bit to consume daily
410g of flour is almost 7dl so quite a bit of bread as well

Bread & Milk is most of the content, but seeing as they are both staples it's not to surprising
I thought potatoes would make it onto the list but they have exploded in price so that kicked them off it

Use a balanced diet, eat a bit of everything, not medical adviced, etc
But it does go to show that you can get everything you need for a bit under 600kr per month (€53)