定义gekko中的最大函数时出错

Question

我在定义gekko-python中的max函数时遇到问题。

sum函数工作正常，但是当我创建另一个函数时，只需用max替换sum，然后抛出以下错误：

这是我使用的脚本的描述（包括模型，一些数据和结果）

#Model
import numpy as np
from gekko import GEKKO
import numpy as np
import pandas as pd
from pandas import ExcelWriter
from pandas import ExcelFile

m = GEKKO()  # Initialize gekko
m.options.SOLVER = 3  # IPOPT is an NLP solver
m.options.MAX_ITER = 10000 # maximum number of iterations
m.options.MAX_MEMORY = 6  # (2-10) memory allocation

R_sect_bin = {'W1': {'S1': 1}, 'W2': {'S1': 1, 'S2': 1, 'S4': 1}, 'W3': {'S1': 1, 'S2': 1, 'S3': 1, 'S4': 1, 'S5': 1, 'S6': 1}, 'W4': {'S4': 1}, 'W5': {'S4': 1, 'S5': 1, 'S6': 1}, 'W6': {'S6': 1}}
Input_Services_nonZero = {'S1': {'L1': 1, 'L3': 1}, 'S2': {'L2': 1}, 'S3': {'L4': 1}, 'S4': {'L1': 1}, 'S5': {'L3': 1}, 'S6': {'L1': 1, 'L2': 1}}

V = {}
for w in R_sect_bin:
    V[w] = {}
    for s in R_sect_bin[w]:
        V[w][s] = {}
        for l in Input_Services_nonZero[s]:
            V[w][s][l] = m.Var(value=10, lb=0, ub=100)

#functions:
sum_Vws1 = {}
def VWS1():
    global sum_Vws1
    for w in R_sect_bin:
        sum_Vws1[w] = {}
        for s in R_sect_bin[w]:
            sum_Vws1[w][s] = m.Intermediate(sum([V[w][s][l] for l in Input_Services_nonZero[s]]))
    return sum_Vws1
vws1 = VWS1()

sum_Vws2 = {}
def VWS2():
    global sum_Vws2
    for w in R_sect_bin:
        sum_Vws2[w] = {}
        for s in R_sect_bin[w]:
            sum_Vws2[w][s] = m.Intermediate(max([V[w][s][l] for l in Input_Services_nonZero[s]]))
    return sum_Vws2
vws2 = VWS2()

TypeError                                 Traceback (most recent call last)
<ipython-input-225-b48377242060> in <module>
     89             sum_Vws2[w][s] = m.Intermediate(max([V[w][s][l] for l in Input_Services_nonZero[s]]))
     90     return sum_Vws2
---> 91 vws2 = VWS2()
     92 
     93 #sum_Vws = {}

<ipython-input-225-b48377242060> in VWS2()
     87         sum_Vws2[w] = {}
     88         for s in R_sect_bin[w]:
---> 89             sum_Vws2[w][s] = m.Intermediate(max([V[w][s][l] for l in Input_Services_nonZero[s]]))
     90     return sum_Vws2
     91 vws2 = VWS2()

~\Anaconda3\lib\site-packages\gekko\gk_operators.py in __len__(self)
     23         return self.name
     24     def __len__(self):
---> 25         return len(self.value)
     26     def __getitem__(self,key):
     27         return self.value[key]

~\Anaconda3\lib\site-packages\gekko\gk_operators.py in __len__(self)
    132 
    133     def __len__(self):
--> 134         return len(self.value)
    135 
    136     def __getitem__(self,key):

TypeError: object of type 'int' has no len()

Answer 1

Hedengren教授的回答：

您需要使用内置的GEKKO max2或max3函数。否则，Python函数会创建一个不具有连续的一阶或二阶导数的表达式，并且基于渐变的求解器可能无法找到解。

您需要使用pip install gekko == 0.2rc6升级到最新的gekko版本（> 0.2rc5）才能使用max2或max3 Gekko函数。

以下是你可以在max2找到的max3或Gekko source的来源。

def max2(self,x1,x2):
    """ Generates the maximum value with continuous first and
    second derivatives. The traditional method for max value (max) is not
    continuously differentiable and can cause a gradient-based optimizer
    to fail to converge.

    Usage: y = m.max2(x1,x2)
    Input: GEKKO variable, parameter, or expression
    Output: GEKKO variable
    """

    # verify that x1 and x2 are valid GEKKO variables or parameters
    if isinstance(x1,(GKVariable,GKParameter)):
        xin1 = x1

    else:
        # create input variable if it is an expression
        xin1 = self.Var()
        self.Equation(xin1==x1)

    if isinstance(x2,(GKVariable,GKParameter)):
        xin2 = x2

    else:
        # create input variable if it is an expression
        xin2 = self.Var()
        self.Equation(xin2==x2)

    # build max object with unique object name
    max_name = 'max2_' + str(len(self._objects) + 1)
    self._objects.append(max_name + ' = max')

    # add connections between x and max object attribute x
    self._connections.append(xin1.name + ' = ' + max_name+'.x[1]')
    self._connections.append(xin2.name + ' = ' + max_name+'.x[2]')

    # add connections between y and max object attribute y
    y = self.Var()
    self._connections.append(y.name + ' = ' + max_name+'.y')

    return y

def max3(self,x1,x2):
    """ Generates the maximum value with a binary switch variable.
    The traditional method for max value (max) is not continuously
    differentiable and can cause a gradient-based optimizer to fail
    to converge.

    Usage: y = m.max3(x1,x2)
    Input: GEKKO variable, parameter, or expression
    Output: GEKKO variable
    """

    # add binary (intb) and output (y) variable
    intb = self.Var(0,lb=0,ub=1,integer=True)
    y = self.Var()

    # add equations for switching conditions
    #  intb=0 when x1>x2 and y=x1
    #  intb=1 when x2>x1 and y=x2
    self.Equation((1-intb)*(x2-x1) <= 0)
    self.Equation(intb*(x1-x2) <= 0)
    self.Equation(y==(1-intb)*x1+intb*x2)

    # change default solver to APOPT (MINLP)
    self.options.SOLVER = 1

    return y 

max2函数使用MPCC，而max3使用二进制变量。这些函数通过使用函数调用来帮助使用这些更复杂的建模形式。您只能将两个值与max2或max3进行比较，因此如果您有一个列表，那么您需要执行以下操作：

y[0] = m.max3(x[0],x[1])
y[1] = m.max3(x[2],y[0])
y[2] = m.max3(x[3],y[1])

等等

以下是有关why you need to use MPCCs or binary variables的其他信息。还有一个additional example here。