如何在GEKKO中实现分段功能?

Question

我正在尝试通过GEKKO建模和解决一个非线性优化问题。目标函数如下:

m.Minimize(k*(w1*abs(x0-L10)+w2*abs(x1-L20))+β*Dindf[0]*(w1*alpha_beta(x0)+w2*alpha_beta(x1)+w1***alpha_beta**(x2)+w2*alpha_beta(x3)) +
k*(w1*abs(x2-x0) + w2*abs(x3-x1)+w1*abs(x4-x2) + w2*abs(x5-x3)))

问题是我需要alpha_beta(x)函数(wrt到决策变量，如下所示)是一个段形式，我如何编码这个函数，以便我可以解决这个问题?

def alpha_beta(x):
a = 0.0019727939
b = 0.0078887
Lmin, Lnom, Lmax = 0.8035, 2.3811, 3.084
return np.piecewise(x, [np.logical_and(Lmin <= x, x < Lnom),
np.logical_and(Lnom <= x, x <= Lmax)],
[lambda x: a * ((x - Lnom)**2) + 0.006226,
lambda x: b * ((x - Lnom)**2) + 0.006226, 0])

非常感谢!

Answer 1

使用m.if3()Gekko函数根据x的值使用不同的函数。同时，将目标函数中的abs()函数替换为Gekko版本的m.abs2()或m.abs3()(优先)。下面是一个示例脚本:

from gekko import GEKKO
m = GEKKO()
x = m.Var(lb=0.8035,ub=3.084)
def alpha_beta(x):
a = 0.0019727939
b = 0.0078887
Lnom = 2.3811
e1 = a*(x-Lnom)**2 + 0.006226
e2 = b*(x-Lnom)**2 + 0.006226
return m.if3(x-Lnom,e1,e2)

m.Minimize(alpha_beta(x)+m.abs3(-x))
m.solve()

生成解决方案x=0.8035。

Number of state variables:              9
Number of total equations: -            6
Number of slack variables: -            4
---------------------------------------
Degrees of freedom       :             -1

* Warning: DOF <= 0
----------------------------------------------
Steady State Optimization with APOPT Solver
----------------------------------------------
Iter: 1 I: 0 Tm: 0.00 NLPi: 3 Dpth: 0 Lvs: 0 Obj: 8.15E-01 Gap: 0.00E+00
Successful solution

---------------------------------------------------
Solver         :  APOPT (v1.0)
Solution time  :   1.290000000153668E-002 sec
Objective      :   0.814635932386315     
Successful solution
---------------------------------------------------