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我正在尝试对烹饪食谱进行简单的优化。特点是系统将不得不同时优化多个配方，因为共同创建的约束尚未实现（例如：所有配方共有的核心）。

以下是显示 scipy 的错误：

         fun: 3.467601477010358
     jac: array([1.79999998, 2.04999998, 1.79999998, 2.04999998])
 message: 'Singular matrix C in LSQ subproblem'
    nfev: 6
     nit: 1
    njev: 1
  status: 6
 success: False
       x: array([0.99425684, 0.3895346 , 0.31931526, 0.14859794])

这里的代码：

import sys

import numpy as np
from scipy.optimize import minimize

ingredient = dict()
ingredient[0] = dict()
ingredient[0]['description'] = 'Corn'
ingredient[0]['price'] = 180

ingredient[1] = dict()
ingredient[1]['description'] = 'Rice'
ingredient[1]['price'] = 205

ingredient_count = len(ingredient)

product = dict()
product[0] = dict()
product[0]['description'] = "Bread 1"
product[0]['ingredient'] = dict()
product[0]['ingredient'][0] = dict()
product[0]["ingredient"][0]['min'] = 0
product[0]["ingredient"][0]['max'] = 36
product[0]["ingredient"][1] = dict()
product[0]["ingredient"][1]['min'] = 0
product[0]["ingredient"][1]['max'] = 100

product[1] = dict()
product[1]["description"] = "Bread 2"
product[1]['ingredient'] = dict()
product[1]['ingredient'][0] = dict()
product[1]["ingredient"][0]['min'] = 0
product[1]["ingredient"][0]['max'] = 36
product[1]["ingredient"][1] = dict()
product[1]["ingredient"][1]['min'] = 0
product[1]["ingredient"][1]['max'] = 100

product_count = len(product)


def function(x):
    totals = list()
    for product_index in product:
        total = 0
        for ingredient_index in product[product_index]['ingredient']:
            x_index = (ingredient_count * product_index) + ingredient_index
            total += (x[x_index] * ingredient[ingredient_index]['price'] / 100)
        totals.append(total)
    return totals


def function_sum(x):
    # p1 + p2 + ... + pn
    totals = function(x)
    return sum(totals)


def function_diff_sum(x):
    # p_min + (p1 - p_min) + (p2 - p_min) + ... + (pn - p_min)
    totals = function(x)
    min_total = min(totals)
    grand_total = min_total
    for total in totals:
        grand_total += total - min_total
    return grand_total

# Constraints


constraints = list()


def populate_constraints():
    for product_index in product:
        total_of_ingredients(product_index)
        for ingredient_index in product[product_index]['ingredient']:
            for constraint_type in product[product_index]['ingredient'][ingredient_index]:
                if constraint_type == 'min':
                    min_for_ingredient(product_index, ingredient_index)
                elif constraint_type == 'max':
                    max_for_ingredient(product_index, ingredient_index)


def min_for_ingredient(product_index, ingredient_index):
    x_index = (ingredient_count*product_index)+ingredient_index
    constraints.append({'type': 'ineq', 'fun': lambda x: x[x_index] - product[product_index]['ingredient'][ingredient_index]['min']})


def max_for_ingredient(product_index, ingredient_index):
    x_index = (ingredient_count*product_index) + ingredient_index
    constraints.append({'type': 'ineq', 'fun': lambda x: product[product_index]['ingredient'][ingredient_index]['max'] - x[x_index]})


def total_of_ingredients(product_index):
    # The total of ingredient for a product have to be 100.
    first_x_index = ingredient_count*product_index
    constraints.append({'type': 'eq', 'fun': lambda x: (sum(x[i] for i in range(first_x_index, ingredient_count)))-100})


def main():
    x0 = np.random.rand(1, product_count*ingredient_count)
    # x0 = np.array([36, 64, 36, 64])  # The solution that the optimizer should give
    populate_constraints()

    # There are 2 type of sum
    fun = function_sum
    # fun = function_diff_sum

    res = minimize(fun, x0, constraints=constraints)
    print(res)


if __name__ == '__main__':
    sys.exit(main())
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1 回答 1

1

如果我正确阅读了您的问题，那么您正在尝试解决最小化的线性规划问题

1.8*i_11 + 2.05*i_12 + 1.8*i_21 + 2.05*i_22

有约束

i_11 + i_12 = 100
i_21 + i_22 = 100
0 <= i_11 <= 36
0 <= i_12 <= 100
0 <= i_21 <= 36
0 <= i_22 <= 100

将变量排序为(i_11, i_12, i_21, i_22)并参考其文档以获取有关符号的详细信息，这很简单scipy.optimize.linprog：

c = [1.8, 2.05, 1.8, 2.05]
A_eq = [[1, 1, 0, 0], [0, 0, 1, 1]]
b_eq = [100, 100]
bounds = [(0, 36), (0, 100), (0, 36), (0, 100)]
output = linprog(c=c, A_eq=A_eq, b_eq=b_eq, bounds=bounds)

然后，output是以下内容OptimizeResult：

     con: array([3.13126236e-09, 3.13126236e-09])
     fun: 391.9999999946266
 message: 'Optimization terminated successfully.'
     nit: 5
   slack: array([], dtype=float64)
  status: 0
 success: True
       x: array([35.99999999, 64.00000001, 35.99999999, 64.00000001])
于 2019-12-08T10:11:09.673 回答