Algorithmic Optimization (Diet Solver)

This skill focuses on solving deterministic optimization problems where "close enough" (LLM) is not acceptable.

1. When to use Linear Programming (LP)

Use LP when you have:

• Objective: Maximize/Minimize a variable (Cost, Protein, User Preference).
• Variables: Quantities of ingredients (g of Chicken, cups of Rice).
• Constraints: "Must have < 2000mg Sodium", "Protein > 150g".

Don't use LLMs for this. LLMs cannot do math reliably.

2. Tooling: PuLP

PuLP is choice for Python.

import pulp

# 1. Define Problem
prob = pulp.LpProblem("Diet_Problem", pulp.LpMinimize)

# 2. Define Variables (Foods)
# lowBound=0 means you can't have negative food
food_vars = pulp.LpVariable.dicts("Food", food_list, lowBound=0, cat='Continuous')

# 3. Define Objective Function (Minimize Cost)
prob += pulp.lpSum([costs[f] * food_vars[f] for f in food_list])

# 4. Define Constraints (Nutritional Limits)
prob += pulp.lpSum([protein[f] * food_vars[f] for f in food_list]) >= 150, "Min_Protein"
prob += pulp.lpSum([cals[f] * food_vars[f] for f in food_list]) <= 2500, "Max_Calories"

# 5. Solve
prob.solve()

3. "Fuzzy" Optimization

Real humans don't eat optimal math. We need to add "Human Constraints":

• Variety: Constraint to limit "Chicken" to max 2 times/day.
• Palatability: Objective function should penalize repeating foods too often.
• Integer Constraints (MIP): Use cat='Integer' if user only eats whole eggs (not 0.3 eggs).

4. Performance

• LP is fast (milliseconds for hundreds of variables).
• MIP (Integer Programming) is NP-Hard. Be careful with too many integer constraints. Use strict timeouts.