GEKKO 的二进制优化

Question

我试图通过随机定义一个 NxN 对称矩阵和一个 N 维偏置向量来解决带有qobj的 Gekko 的二次二元优化问题。 然而，我观察到计算时间非常低：2e-2s 用于解决 N=20 和 0.05s 以解决 200 维问题。 此外，我的迭代次数永远不会超过 3-4 次。 我在这里错过了什么吗？

import numpy as np
N = 20
#create square symmetric matrix for the quadratic term
b = np.random.normal(0,1,(N,N))
Q = (b + b.T)/2
#bias vector for linear term
c=np.random.normal(0,1,N)
from gekko import GEKKO
m = GEKKO(remote=False)
z = m.Array(m.Var,N,integer=True,lb=0,ub=1,value=1)
m.qobj(c,A=Q,x=z,otype='min')
m.solve(disp=True)

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Answer 1

切换到混合 Integer 解决方案的 APOPT 求解器。

m.options.SOLVER=1

这是完整的脚本。 MIQP 问题通常非常快。 如果问题是非线性 (NLP) 与混合 integer 元素 (MINLP)，它会显着减慢。

import numpy as np
N = 200
#create square symmetric matrix for the quadratic term
b = np.random.normal(0,1,(N,N))
Q = (b + b.T)/2
#bias vector for linear term
c=np.random.normal(0,1,N)
from gekko import GEKKO
m = GEKKO(remote=False)
z = m.Array(m.Var,N,integer=True,lb=0,ub=1,value=1)
m.qobj(c,A=Q,x=z,otype='min')
m.options.SOLVER=1
m.solve(disp=True)
print(z)

[[0.0] [1.0] [1.0] [0.0] [1.0] [1.0] [1.0] [1.0] [1.0] [0.0] [1.0] [1.0]
 [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [0.0] [1.0] [1.0] [1.0]
 [1.0] [1.0] [1.0] [1.0] [0.0] [1.0] [0.0] [1.0] [1.0] [0.0] [0.0] [0.0]
 [0.0] [1.0] [1.0] [0.0] [0.0] [1.0] [1.0] [1.0] [1.0] [1.0] [0.0] [1.0]
 [1.0] [1.0] [0.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [0.0]
 [0.0] [1.0] [0.0] [0.0] [0.0] [0.0] [1.0] [1.0] [0.0] [0.0] [0.0] [0.0]
 [1.0] [1.0] [0.0] [0.0] [1.0] [1.0] [0.0] [1.0] [1.0] [0.0] [1.0] [1.0]
 [0.0] [1.0] [0.0] [0.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0]
 [0.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0]
 [1.0] [1.0] [1.0] [0.0] [0.0] [0.0] [1.0] [1.0] [1.0] [1.0] [1.0] [1.0]
 [0.0] [0.0] [1.0] [1.0] [0.0] [1.0] [0.0] [1.0] [0.0] [1.0] [1.0] [1.0]
 [0.0] [0.0] [0.0] [0.0] [1.0] [0.0] [0.0] [1.0] [1.0] [0.0] [0.0] [1.0]
 [1.0] [1.0] [0.0] [1.0] [0.0] [0.0] [1.0] [1.0] [1.0] [1.0] [0.0] [1.0]
 [0.0] [0.0] [0.0] [0.0] [0.0] [0.0] [1.0] [1.0] [1.0] [1.0] [1.0] [0.0]
 [0.0] [0.0] [1.0] [1.0] [1.0] [1.0] [0.0] [1.0] [0.0] [0.0] [1.0] [1.0]
 [0.0] [0.0] [0.0] [1.0] [1.0] [1.0] [0.0] [1.0] [0.0] [1.0] [0.0] [0.0]
 [0.0] [1.0] [1.0] [1.0] [0.0] [1.0] [1.0] [0.0]]