diet.py

##@file diet.py 
# @brief model for the modern diet problem
"""
Copyright (c) by Joao Pedro PEDROSO and Mikio KUBO, 2012
"""
# todo: can we make it work as "from pyscipopt import *"?
from pyscipopt import Model, quicksum, multidict


def diet(F, N, a, b, c, d):
    """diet -- model for the modern diet problem
    Parameters:
        - F: set of foods
        - N: set of nutrients
        - a[i]: minimum intake of nutrient i
        - b[i]: maximum intake of nutrient i
        - c[j]: cost of food j
        - d[j][i]: amount of nutrient i in food j
    Returns a model, ready to be solved.
    """

    model = Model("modern diet")

    # Create variables
    x, y, z = {}, {}, {}
    for j in F:
        x[j] = model.addVar(vtype="I", name="x(%s)" % j)
        y[j] = model.addVar(vtype="B", name="y(%s)" % j)
    for i in N:
        z[i] = model.addVar(lb=a[i], ub=b[i], name="z(%s)" % j)
    v = model.addVar(vtype="C", name="v")

    # Constraints:
    for i in N:
        model.addCons(quicksum(d[j][i] * x[j] for j in F) == z[i], name="Nutr(%s)" % i)

    model.addCons(quicksum(c[j] * x[j] for j in F) == v, name="Cost")

    for j in F:
        model.addCons(y[j] <= x[j], name="Eat(%s)" % j)

    # Objective:
    model.setObjective(quicksum(y[j] for j in F), "maximize")
    model.data = x, y, z, v

    return model


def make_inst():
    """make_inst: prepare data for the diet model"""
    F, c, d = multidict({  # cost # composition
        "QPounder": [1.84, {"Cal": 510, "Carbo": 34, "Protein": 28,
                            "VitA": 15, "VitC": 6, "Calc": 30, "Iron": 20}],
        "McLean": [2.19, {"Cal": 370, "Carbo": 35, "Protein": 24, "VitA": 15,
                          "VitC": 10, "Calc": 20, "Iron": 20}],
        "Big Mac": [1.84, {"Cal": 500, "Carbo": 42, "Protein": 25,
                           "VitA": 6, "VitC": 2, "Calc": 25, "Iron": 20}],
        "FFilet": [1.44, {"Cal": 370, "Carbo": 38, "Protein": 14,
                          "VitA": 2, "VitC": 0, "Calc": 15, "Iron": 10}],
        "Chicken": [2.29, {"Cal": 400, "Carbo": 42, "Protein": 31,
                           "VitA": 8, "VitC": 15, "Calc": 15, "Iron": 8}],
        "Fries": [.77, {"Cal": 220, "Carbo": 26, "Protein": 3,
                        "VitA": 0, "VitC": 15, "Calc": 0, "Iron": 2}],
        "McMuffin": [1.29, {"Cal": 345, "Carbo": 27, "Protein": 15,
                            "VitA": 4, "VitC": 0, "Calc": 20, "Iron": 15}],
        "1% LFMilk": [.60, {"Cal": 110, "Carbo": 12, "Protein": 9,
                            "VitA": 10, "VitC": 4, "Calc": 30, "Iron": 0}],
        "OrgJuice": [.72, {"Cal": 80, "Carbo": 20, "Protein": 1,
                           "VitA": 2, "VitC": 120, "Calc": 2, "Iron": 2}],
    })

    N, a, b = multidict({  # min,max intake
        "Cal": [2000, None],
        "Carbo": [350, 375],
        "Protein": [55, None],
        "VitA": [100, None],
        "VitC": [100, None],
        "Calc": [100, None],
        "Iron": [100, None],
    })

    return F, N, a, b, c, d


if __name__ == "__main__":

    F, N, a, b, c, d = make_inst()

    for b["Cal"] in [None, 3500, 3000, 2500]:

        print("\nDiet for a maximum of {0} calories".format(b["Cal"] if b["Cal"] != None else "unlimited"))
        model = diet(F, N, a, b, c, d)
        model.hideOutput()  # silent mode
        model.optimize()

        print("Optimal value:", model.getObjVal())
        x, y, z, v = model.data
        for j in x:
            if model.getVal(x[j]) > 0:
                print("{0:30s}: {1:3.1f} dishes --> {2:4.2f} added to objective".format(j, model.getVal(x[j]),
                                                                                        model.getVal(y[j])))
        print("amount spent:", model.getObjVal())

        print("amount of nutrients:")
        for i in z:
            print("{0:30s}: {1:4.2f}".format(i, model.getVal(z[i])))