寻找最佳加权平均值答案

【问题标题】：Finding optimal weighted average寻找最佳加权平均值
【发布时间】：2021-06-18 21:01:35
【问题描述】：

约束要求将每种成分 amount 乘以相同的因子，其中所有成分的营养组合必须在最小和最大营养范围内，而最佳解决方案是最接近最小/最大中值的总和。

我已将重量标准化为每克，因此要计算我所做的成分的营养成分amount[g] * ingredients[2][nutrient]。

碎牛肉营养总和：

calorie : 226.79616 * [ingredients][0][0] = 288.0311232
fat     : 226.79616 * [ingredients][0][1] = 22.679616
carb    : 226.79616 * [ingredients][0][2] = 0
protein : 226.79616 * [ingredients][0][3] = 19.470450336

所有成分营养综合结果：

calorie: 575.8359139999999
fat: 48.160351846999994
carb: 3.842780537
protein: 37.289324852

scalingMin = 557.7/575.8359139999999 = 0.96850506618

scalingMax = 669.24/575.8359139999999 = 1.16220607942

仅基于卡路里的最佳比例是1.06453936807，因此所有成分必须乘以相同的比例因子。

这是我到目前为止编写的代码，但我不确定如何处理这些限制。

from ortools.linear_solver import pywraplp

# get nutrients sum
def getNutritionalSumOfAllIngredients(list):
  numbs = [type for type in range(0, 4)]
  for key, ingredient in enumerate(list):
    for type, nutrient in enumerate(ingredient[2]):
      numbs[type] += (ingredient[1] * nutrient)
  return numbs

def main():
  nutrients = [
    ['calorie', 557.7, 669.24],
    ['fat', 39.04, 51.43],
    ['carb', 0, 13],
    ['protein', 31.19, 41.59]
  ]

  # name, amount (grams), [calorie, fat, net_carbs, protein] weight per gram
  ingredients = [
    ['ground beef', 226.79616, [1.27, 0.1, 0, 0.08585000000000001]],
    ['salt', 6.083333333333333, [0, 0, 0, 0]],
    ['black pepper', 1.0374999999999999, [1.255 , 0.0163, 0.19325, 0.05195]],
    ['cajun seasoning', 4, [0.46604999999999996, 0.010249999999999999, 0.06565, 0.0191]],
    ['mozzarella cheese', 28.34952, [1.5, 0.11175, 0.01095, 0.11085]],
    ['cheddar cheese', 56.69904, [2.02, 0.16655, 0.015449999999999998, 0.11435000000000001]],
    ['butter', 14.1875, [3.585, 0.40555, 0.0003, 0.00425]],
    ['cooked bacon', 28, [2.74, 0.21635000000000001, 0.006750000000000001, 0.17864999999999998]]
  ]
  
  solver = pywraplp.Solver('ScaleIngredients', pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)

  # # sum of all ingredients nutrition must be within each nutrients min/max i.e [557.7, 669.24, 'calorie']
  objectives = [solver.NumVar(item[1], item[2], item[0]) for item in nutrients]

  test = getNutritionalSumOfAllIngredients(ingredients)
  print(test)

【问题讨论】：

标签： python optimization or-tools

【解决方案1】：

CP-SAT 是一个纯积分求解器。它只模拟连续变量。

【讨论】：