如何使用 python 和线性规划获得 objective 值以外的所有组合

Question

我用纸浆获得了最大利润6442143.99530000和每个产品的配额。但是，我想按排名顺序输出下一个次优解决方案而不是最优解决方案。可能吗？换句话说，我想获得分配给每个产品的所有组合。

这里需要几位专家的帮助。预先感谢您的帮助。

[temp.csv]

product,profit,min_alloc,max_alloc
Prod_A,19251.1503,5,50
Prod_B,11029.62628,5,50
Prod_C,49455.97051,5,50
Prod_D,2270.916437,5,50
Prod_E,20727.92984,5,50
Prod_F,41979.71183,5,50
Prod_G,10298.78459,5,50
Prod_H,9912.822331,5,50
Prod_I,4579.744941,5,50
Prod_J,25079.03564,5,50
Prod_K,3754.784861,5,50

[np_test.py]

import pandas as pd
import numpy as np
from pulp import *

pd.options.display.float_format = '{:.5f}'.format
total_capa = 200

df = pd.read_csv('temp.csv')

profit_sum = sum(df['profit'])

LP = LpProblem(name = "LP", sense = LpMaximize)

X1 = LpVariable(name='Prod_A', lowBound=5, upBound=50, cat='Integer')
X2 = LpVariable(name='Prod_B', lowBound=5, upBound=50, cat='Integer')
X3 = LpVariable(name='Prod_C', lowBound=5, upBound=50, cat='Integer')
X4 = LpVariable(name='Prod_D', lowBound=5, upBound=50, cat='Integer')
X5 = LpVariable(name='Prod_E', lowBound=5, upBound=50, cat='Integer')
X6 = LpVariable(name='Prod_F', lowBound=5, upBound=50, cat='Integer')
X7 = LpVariable(name='Prod_G', lowBound=5, upBound=50, cat='Integer')
X8 = LpVariable(name='Prod_H', lowBound=5, upBound=50, cat='Integer')
X9 = LpVariable(name='Prod_I', lowBound=5, upBound=50, cat='Integer')
X10 = LpVariable(name='Prod_J', lowBound=5, upBound=50, cat='Integer')
X11 = LpVariable(name='Prod_K', lowBound=5, upBound=50, cat='Integer')

np_product = np.array([X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11])


for profit in df['profit']:
    np_profit = np.array(df['profit'])
    

# OBJECTIVE function
LP.objective = sum(np_profit * np_product)
print('Objective: ', LP.objective, '\n')
   
# CONSTRAINTS
constraints = [
    X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10 + X11 == total_capa,
]

print('Constraints: ')
for i in constraints:
    print(i)

for i, c in enumerate(constraints):
    constraint_name = f"const_{i}"
    LP.constraints[constraint_name] = c

# SOLVE model
res = LP.solve()

# results
print('\nResults: ')
for v in LP.variables():
    print(f"{v} Product: {v.varValue:5.1f} EA")

print('\n', 'The objective funtion is ', value(LP.objective))

Result - Optimal solution found

Objective value:                6442143.99530000
Enumerated nodes:               0
Total iterations:               0
Time (CPU seconds):             0.01
Time (Wallclock seconds):       0.01

Option for printingOptions changed from normal to all
Total time (CPU seconds):       0.01   (Wallclock seconds):       0.01


Results:
Prod_A Product:   5.0 EA
Prod_B Product:   5.0 EA
Prod_C Product:  50.0 EA
Prod_D Product:   5.0 EA
Prod_E Product:  15.0 EA
Prod_F Product:  50.0 EA
Prod_G Product:   5.0 EA
Prod_H Product:   5.0 EA
Prod_I Product:   5.0 EA
Prod_J Product:  50.0 EA
Prod_K Product:   5.0 EA

 The objective funtion is  6442143.9953

Answer 1

据我所知，有两种方法可以实现：

使用像 Gurobi 这样的商业求解器及其解决方案池来收集 N 最佳解决方案。
求解您的模型，添加整数切割以排除找到的解并再次求解模型。重复直到你有足够的解决方案。 here.
解释了对这种整数切割建模的一种方法

稍微清理一下您的代码后，这里有一个工作示例可以找到接下来的 5 个最佳解决方案：

import pandas as pd
import numpy as np
import pulp


def print_solution(x):
    print('\nResults: ')
    for x in x.values():
        print(f"{x.name}: {x.varValue:5.1f} EA")
    print('\n', 'The objective funtion is ', pulp.value(prob.objective))


df = pd.read_csv('temp.csv')
profit = df["profit"].values
total_capa = 200

# the problem
prob = pulp.LpProblem(name="LP", sense=pulp.LpMaximize)

# Add variables
x = {}
for i, name in enumerate(df["product"].values):
    x[i] = pulp.LpVariable(name=name, lowBound=5, upBound=50, cat="Integer")

# OBJECTIVE function
prob.objective = sum(profit[i] * x[i] for i in range(len(x)))
print('Objective: ', prob.objective, '\n')

# CONSTRAINTS
prob.addConstraint(pulp.lpSum(x[i] for i in range(len(x))) == total_capa)

# SOLVE model
res = prob.solve()
print_solution(x)

# Add integer cut to exclude the optimal solution
bigM = 45
num_sols = 5
z = []
b = []
for k in range(num_sols):
    # helper variables
    z.append([pulp.LpVariable(name=f"z[{k},{i},]", cat="Integer") for i in range(len(x))])
    b.append([pulp.LpVariable(name=f"b[{k},{i},]", cat="Binary") for i in range(len(x))])

    prob.addConstraint(pulp.lpSum(z[k][i] for i in range(len(x))) >= 1)
    for i in range(len(x)):
        prob.addConstraint(z[k][i] <= x[i] - x[i].varValue + bigM * b[k][i])
        prob.addConstraint(z[k][i] <= -x[i] + x[i].varValue + bigM * (1-b[k][i]))

    # solve the model again
    prob.solve()
    print_solution(x)

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