Finding the perfect lightweight hiking food

[#1]

This rabbit hole is just for fun: I found a huge spreadsheet that lists data for thousands of potential hiking foods.

My question is: What is the most lightweight mixture of foods that you can bring camping that has the ideal balance of macronutrients? (60% carbs, 20% protein, 20% fats). 

Thoughts:

1. You want to minimize the weighted average g/calories.

2. I'll assume you can get micronutrients by taking pills.

3. I'll assume variety/taste doesn't matter because the goal is to carry as little weight as possible.

4. I'm guessing that you want to ask JMP to try a lot of possible combinations with some maximum for the number of ingredients (10?) and tell it to hit the macronutrients goal and calculate and minimize the weighted average g/calories.

But how?

[#2]

I'd start by sorting the list by distance from ideal ratio

sqrt( (carbs-60)^2 + (protein-20)^2 + (fats-20)^2 )

... no I wouldn't. How about this:

Step 1: I'd start by sorting the list by weight and add 1 unit of lowest weight product to my bag.

Step 2: Then I'd look at the ratio of all the products in the bag and add 1 unit of the lowest weight that steers the ratio in the right direction.

Repeat step 2 until the bag is full. With or without replacement, according to taste.

Interesting problem. You should consult a nutritionist before starting this diet!

[#3]

I think your approach would work. I wonder if you could do Step 1 and then Step 2 (once) and then automate the iteration of Step 2.

[#4]

Yes, use JSL to run that loop. I don't think there is a builtin platform for filling a bag, though I'm not familiar with the consumer research area in JMP. 

You have another variable as well, calories, which I'm not accounting for. I'm not sure how to fit that in either. Perhaps you should figure out the calorie requirement for the hike and steer each subsequent selection with that as well.

[#5]

Hi @RatioModelOx453   And this may or may not fit in somewhere; excluding alcohol from the conversation, Calories only come from three things: carbs (approx 4 Calories/gram), protein (approx 4 Calories/gram) and fat (approx 9 Calories/gram). For our European friends, Calorie = kilocalorie.  

So your 60%/20%/20% could be by weight, or by energy load. Convention is by weight…

[#6]

Hello @MRB3855, 

it sounds like a problem you can be solving utilizing the knapsack algorithm, you may need to give it a little twist to take into account the fractions you mentioned.

[#7]

This is a great idea. I haven't used that algorithm before.