Gekko 返回错误的成功解决方案

编程问答 2022-05-25

问题描述

以下代码返回 Successful Solution Objective: 0.。但这不是最优解。最优解是-6。通过阅读其他问题，我认为在目标函数中使用非 Gekko 函数存在问题，但我使用的唯一非 Gekko 函数是 np.matmul。 np.matmul 是否适用于壁虎阵列？注意 sigma_post 是一个 nxn numpy 单位矩阵。

m = GEKKO(remote=False)
m.options.max_iter=1000
#m.options.ipopt_integer_tol=1
#m.solver_options = ['minlp_integer_tol 50']
#m.solver_options = ['minlp_max_iter_with_int_sol 1000',#                    'minlp_branch_method 1']
                    

N = 2
b = m.Array(m.Var,(N,n),lb=0,ub=1,integer=True)

for i in range(N):
    for j in range(n):
        if j in [qb_index_range[0],rb_index_range[0],wr_index_range[0]]:
            b[i][j].value = 1
        else:
            b[i][j].value = 0

print('b: ',b)

# CONSTRAINT: Each Lineup must be less than budget
z = np.array([None]*N)
for i in range(N):
    z[i] = m.Intermediate(sum(b[i,:]*list(info_df['cost'])))
    
m.Equations([z[i] <= budget for i in range(N)])


# CONSTRAINT: Each Lineup has one QB
z_1 = np.array([None]*N)
for i in range(N):
    z_1[i] = m.Intermediate(sum(b[i,qb_index_range[0]: qb_index_range[1]+1]))

m.Equations([z_1[i] == 1 for i in range(N)])


# CONSTRAINT: Each Lineup has one RB
z_2 = np.array([None]*N)
for i in range(N):
    z_2[i] = m.Intermediate(sum(b[i,rb_index_range[0]: rb_index_range[1]+1]))

m.Equations([z_2[i] == 1 for i in range(N)])


# CONSTRAINT: Each Lineup has one WR
z_3 = np.array([None]*N)
for i in range(N):
    z_3[i] = m.Intermediate(sum(b[i,wr_index_range[0]: wr_index_range[1]+1]))

m.Equations([z_3[i] == 1 for i in range(N)])

#OBJECTIVE: maximize with two lineups
sigma_1 = np.array([[None]*N for i in range(N)])
sig = np.matmul(np.matmul(b,sigma_post),b.T)

for i in range(N):
    for j in range(N):
        sigma_1[i][j] = m.Intermediate(sig[i][j])
        
        
m.Obj(-(sigma_1[0][0] + sigma_1[1][1]- 2*sigma_1[1][0]))

m.options.soLVER = 1 

m.solve(debug=0)

编辑： 为了透明，理想情况下我关心的目标函数在下面，但上面详述的更简单的目标函数会导致问题，所以我决定从那里开始故障排除。以下目标为 Warning: no more possible trial points and no integer solution Maximum iterations 的某些值抛出 mu，但 mu 不存在于约束中。非常感谢您的建议！

pi = 3.14159
eps = 1.0E-6

def normal_cdf(x,m):
    return 1/(1+m.exp(-1.65451*x))
    
def normal_pdf(x,m):
    return (1/((2*pi)**(.5)))*m.exp((x**2)/2)
    
def theta(s,m):
    return m.sqrt(s[0][0]+s[1][1] - 2*s[0][1])

# OBJECTIVE: Maximize 
mu_1 = np.array([None]*N)
for i in range(N):
    mu_1[i] = m.Intermediate(np.matmul(b[i,:],mu))


inter = m.if2(theta(sigma_1,m)-eps,.5*mu_1[0]+.5*mu_1[1],(mu_1[0]*normal_cdf((mu_1[0]-mu_1[1])/theta(sigma_1,m),m) + \
              mu_1[1]*normal_cdf((mu_1[1]-mu_1[0])/theta(sigma_1,m) + \
              theta(sigma_1,m)*normal_pdf((mu_1[0]-mu_1[1])/theta(sigma_1,m)))

m.Obj(-inter)

解决方法

使用 np.matmul 或任何其他允许对象而不是数字值的函数都没有问题。需要对象是因为 b 是 Gekko 类型值的数组，需要使用自动微分计算导数。您还可以使用新的 @ 运算符来简化表达式。您的原始问题陈述不完整，缺少许多定义。我添加了一些示例值，以便脚本可以在没有定义错误的情况下运行。这是guidelines to help reproduce the error。

N = 2
n = 3
qb_index_range = [0,2]
rb_index_range = [0,2]
wr_index_range = [0,2]
info_df = pd.DataFrame({'cost':np.ones(n)})
budget = 100
sigma_post = np.random.rand(n,n)

这是一个使用 np.matmul() 的例子，它也可以是点积 np.dot()。

sigma_1 = np.matmul(np.matmul(b,sigma_post),b.T)

这也可以用矩阵乘法运算符来写。

sigma_1 = b@sigma_post@b.T

这是完整的脚本。

from gekko import GEKKO
import numpy as np
import pandas as pd

m = GEKKO(remote=False)
m.options.max_iter=1000
                    
N = 2
n = 3
b = m.Array(m.Var,(N,n),lb=0,ub=1,integer=True)
qb_index_range = [0,2]
info_df = pd.DataFrame({'cost':np.ones(n)})
budget = 100
sigma_post = np.eye(n)

for i in range(N):
    for j in range(n):
        if j in [qb_index_range[0],rb_index_range[0],wr_index_range[0]]:
            b[i][j].value = 1
        else:
            b[i][j].value = 0

# CONSTRAINT: Each Lineup must be less than budget
z = [None]*N
for i in range(N):
    z[i] = m.Intermediate(sum(b[i,:]*list(info_df['cost'])))
m.Equations([z[i] <= budget for i in range(N)])


# CONSTRAINT: Each Lineup has one QB
z_1 = [None]*N
for i in range(N):
    z_1[i] = m.Intermediate(sum(b[i,qb_index_range[0]: qb_index_range[1]+1]))

m.Equations([z_1[i] == 1 for i in range(N)])


# CONSTRAINT: Each Lineup has one RB
z_2 = np.array([None]*N)
for i in range(N):
    z_2[i] = m.Intermediate(sum(b[i,rb_index_range[0]: rb_index_range[1]+1]))

m.Equations([z_2[i] == 1 for i in range(N)])

# CONSTRAINT: Each Lineup has one WR
z_3 = np.array([None]*N)
for i in range(N):
    z_3[i] = m.Intermediate(sum(b[i,wr_index_range[0]: wr_index_range[1]+1]))

m.Equations([z_3[i] == 1 for i in range(N)])

#OBJECTIVE: maximize with two lineups
#sigma_1 = np.matmul(np.matmul(b,b.T)
sigma_1 = b@sigma_post@b.T
                
m.Maximize(sigma_1[0][0] + sigma_1[1][1]- 2*sigma_1[1][0])

m.options.SOLVER = 1 

m.solve(debug=0,disp=False)

print(b)

这产生了一个成功的解决方案。无法验证正确的解决方案，因为原始问题陈述不完整。

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