问题描述
我对python了解不多，但我需要帮助来理解为什么我的优化方程会弹出
TypeError: 必须是实数，而不是 GK_Operators
我做错了什么？这个问题可以在apmonitor.com，hs87上找到。
from gekko import GEKKO
import math
m = GEKKO ()
#Parameters
a = 131.078
b = 1.48477 #Hock & Schittkowski say 1.48577
c = 0.90798
d0 = 1.47588
e0 = 1.47588
d = math.cos(d0)
e = math.sin(e0)
lim1 = 300
lim2 = 100
lim3 = 200
rate1 = 30
rate2 = 31
rate3 = 28
rate4 = 29
rate5 = 30
#var x1 >= 0,<= 400;
#var x2 >= 0,<= 1000;
#var x3 >= 340,<= 420;
#var x4 >= 340,<= 420;
#var x5 >= -1000,<= 1000; # Hock & Schittkowski say <= 10000
#var x6 >= 0,<= 0.5236;
add[1:3] > 0
slk[1:3]
x1 = m.Var(value = 390)
x2 = m.Var(value = 1000)
x3 = m.Var(value = 419.5)
x4 = m.Var(value = 340.5)
x5 = m.Var(value = 198.175)
x6 = m.Var(value = 0.5)
add1 = x1 - lim1 + slk1
add2 = x2 - lim2 + slk2
add3 = x2 - lim3 + slk3
m.Equations(300 - x3*x4*math.cos(b - x6)/a + c*x3^2*d/a)
m.Equations(-x3*x4*math.cos(b + x6)/a + c*x4^2*d/a)
m.Equations(-x3*x4*math.sin(b + x6)/a + c*x4^2*e/a)
m.Equations(200 - x3*x4*math.sin(b - x6)/a + c*x3^2*e/a == 0)
m.obj(rate1*x1 + (rate2-rate1)*add1)
m.obj(rate3*x2 + (rate4-rate3)*add2 + (rate5-rate4)*add3)
m.solve(disp=False)
print(x1.value)
print(x2.value)
print(x3.value)
print(x4.value)
print(x5.value)
print(x6.value)
解决方法
一些提示：
- 使用 Python 幂运算符
**而不是^ - 每个等式都必须有一个等式
==或不等式>、<、>=、<=。 - 使用
m.Array()在一行中定义多个变量，例如具有维度 3 的slk和add。 - 使用
disp=True查看求解器结果，尤其是在问题无法解决或存在错误的情况下。
这是您脚本的修改版本：
from gekko import GEKKO
import math
m = GEKKO ()
#Parameters
a = 131.078
b = 1.48477
c = 0.90798
d0 = 1.47588
e0 = 1.47588
d = math.cos(d0)
e = math.sin(e0)
lim1 = 300
lim2 = 100
lim3 = 200
rate1 = 30
rate2 = 31
rate3 = 28
rate4 = 29
rate5 = 30
add = m.Array(m.Var,3,lb=0)
slk = m.Array(m.Var,lb=0)
x1 = m.Var(value = 390,lb=0,ub=400)
x2 = m.Var(value = 1000,ub=1000)
x3 = m.Var(value = 419.5,lb=340,ub=420)
x4 = m.Var(value = 340.5,ub=420)
x5 = m.Var(value = 198.175,lb=-1000,ub=1000)
x6 = m.Var(value = 0.5,ub=0.5236)
m.Equation(add[0] == x1 - lim1 + slk[0])
m.Equation(add[1] == x2 - lim2 + slk[1])
m.Equation(add[2] == x2 - lim3 + slk[2])
m.Equation(300 - x3*x4*m.cos(b - x6)/a + c*x3**2*d/a == 0)
m.Equation(-x3*x4*m.cos(b + x6)/a + c*x4**2*d/a == 0)
m.Equation(-x3*x4*m.sin(b + x6)/a + c*x4**2*e/a == 0)
m.Equation(200 - x3*x4*m.sin(b - x6)/a + c*x3**2*e/a == 0)
m.Minimize(rate1*x1 + (rate2-rate1)*add[0])
m.Minimize(rate3*x2 + (rate4-rate3)*add[1] + (rate5-rate4)*add[2])
m.solve(disp=True)
print(x1.value)
print(x2.value)
print(x3.value)
print(x4.value)
print(x5.value)
print(x6.value)
求解器正确地得出问题不可行的结果。
EXIT: Converged to a point of local infeasibility. Problem may be infeasible.
An error occured.
The error code is 2
---------------------------------------------------
Solver : IPOPT (v3.12)
Solution time : 4.060000000026776E-002 sec
Objective : 5159.30673181783
Unsuccessful with error code 0
---------------------------------------------------
Creating file: infeasibilities.txt
Use command apm_get(server,app,'infeasibilities.txt') to retrieve file
@error: Solution Not Found
您可能在 APMonitor website 上找到的 Hock & Schitkowski 基准测试 87 是：
! Nonlinear electrical network
! The problem is corrected to conform to the problem as stated in
! D. M. Himmelblau,Applied Nonlinear Programming,! McGraw-Hill,1972,pp. 413-414
! except that jump-discontinuities in the objective function are
! omitted by stating it as the sum of two piecewise-linear terms
Model hs87
Parameters
a = 131.078
b = 1.48477 ! Hock & Schittkowski say 1.48577
c = 0.90798
d0 = 1.47588
e0 = 1.47588
d = cos(d0)
e = sin(e0)
lim[1] = 300
lim[2] = 100
lim[3] = 200
rate[1] = 30
rate[2] = 31
rate[3] = 28
rate[4] = 29
rate[5] = 30
End Parameters
Variables
add[1:3] > 0
slk[1:3]
x[1] = 390,>= 0,<= 400
x[2] = 1000,<= 1000
x[3] = 419.5,>= 340,<= 420
x[4] = 340.5,<= 420
x[5] = 198.175,>= -1000,<= 1000 ! Hock & Schittkowski say <= 10000
x[6] = 0.5,<= 0.5236
obj[1:2]
End Variables
Equations
! piecewise linear
add[1] = x[1] - lim[1] + slk[1]
add[2] = x[2] - lim[2] + slk[2]
add[3] = x[2] - lim[3] + slk[3]
x[1] = 300 - x[3]*x[4]*cos(b - x[6])/a + c*x[3]^2*d/a
x[2] = -x[3]*x[4]*cos(b + x[6])/a + c*x[4]^2*d/a
x[5] = -x[3]*x[4]*sin(b + x[6])/a + c*x[4]^2*e/a
200 - x[3]*x[4]*sin(b - x[6])/a + c*x[3]^2*e/a = 0
! best known objective = 8827.5977
obj[1] = rate[1]*x[1] + (rate[2]-rate[1])*add[1]
obj[2] = rate[3]*x[2] + (rate[4]-rate[3])*add[2] + (rate[5]-rate[4])*add[3]
End Equations
End Model
您可以通过 online interface 解决此问题。看起来你的方程不太正确，但它们很接近。您可以使用在线界面来比较答案。