python - 限制 google OR-Tools 上的系数值

Question

我遇到了与 The Stigler diet 非常相似的问题

我已经复制了结果我的数据在下面的代码中:

data = [
['f1', 10, 15, 17, 10],
['f2', 2, 11, 12, 14],
['f3', 5, 17, 16, 13],
['f4', 8, 12, 8, 16]
]

nutrients = [
    ["protein",15.5],
    ["carbohydrates",12.3]]

TM = 10
nutrients = [
    ["protein",15.5*TM],
    ["carbohydrates",12.3*TM]]

food = [[]] * len(data)

# Objective: minimize the sum of (price-normalized) foods.
objective = solver.Objective()
for i in range(0, len(data)):
    food[i] = solver.NumVar(0.0, solver.infinity(), data[i][0])
    objective.SetCoefficient(food[i], 4)
objective.SetMinimization()

# Create the constraints, one per nutrient.

constraints = [0] * len(nutrients)
for i in range(0, len(nutrients)):
    constraints[i] = solver.Constraint(nutrients[i][1], solver.infinity())
    for j in range(0, len(data)):
        constraints[i].SetCoefficient(food[j], data[j][i+3])


status = solver.Solve()

if status == solver.OPTIMAL:
    # Display the amounts (in dollars) to purchase of each food.
    price = 0
    num_nutrients = len(data[i]) - 3
    nutrients = [0] * (len(data[i]) - 3)
    for i in range(0, len(data)):
        price += food[i].solution_value()

        for nutrient in range(0, num_nutrients):
            nutrients[nutrient] += data[i][nutrient+3] * food[i].solution_value()

        if food[i].solution_value() > 0:
            print ("%s = %f" % (data[i][0], food[i].solution_value()))

    print ('Optimal  price: $%.2f' % (price))
else:  # No optimal solution was found.
    if status == solver.FEASIBLE:
        print ('A potentially suboptimal solution was found.')
    else:
        print ('The solver could not solve the problem.')

返回结果:

f1 = 0.770492 f3 = 8.868852 Optimal  price: $9.64

这很好，除了我有每种食物的上限:例如:

f1 = 4
f2 = 6
f3 = 5
f4 =2

如何将此部分添加到约束中？

Answer 1

您必须将它们设置为决策变量(在本例中似乎是吃多少食物)，并为每个食物添加一个描述其范围的上限。

所以在这种情况下:

upper_bounds = [4, 6, 5, 2]
# Objective: minimize the sum of (price-normalized) foods.
objective = solver.Objective()
for i in range(0, len(data)):
    food[i] = solver.NumVar(0.0, upper_bounds[i], data[i][0])
    objective.SetCoefficient(food[i], 4)
objective.SetMinimization()

请注意，solver.NumVar 采用 3 个参数，第一个是下限，第二个是上限，最后是其名称。希望这可以帮助。