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python - 如何在 python 中为优化求解器定义合适的目标函数

问题描述

我需要为 Scipy SLSQP slover 定义一个优化目标函数。困难在于我的目标函数中自变量的数量不固定。我试图使用以下代码：

from scipy.optimize import minimize, Bounds, LinearConstraint
import scipy.special as sc
import numpy as np
import pandas as pd
import warnings
warnings.filterwarnings("ignore")

Lmin, Lnom, Lmax = 0.8035, 2.3811, 3.084
L10, L20 = 2.3, 2.3
# one step look ahead
# Eindf = [1116, 1160, 841, 1116]
# Dindf = [44, 861, 275]
# Ldf = [4.2, 5.2, 4.8, 4.4]
Eindf = [1116, 1160, 841]
Dindf = [44, 861]
Ldf = [4.2, 5.2, 4.8]

R10, R20 = 0.1803, 0.1803
Rfc1, Rfc2 = R10 + 0.003, R20 + 0.0

if Rfc1 > Rfc2:
    w1 = (Rfc1 * np.exp((Rfc1-Rfc2)) + Rfc1) / (Rfc2 + np.exp((Rfc1-Rfc2))*Rfc1 + Rfc1)
    w2 = Rfc2 / (Rfc2 + np.exp((Rfc1-Rfc2))*Rfc1+ Rfc1)
else:
    w1 = ( Rfc1) / (Rfc2 + np.exp((Rfc1-Rfc2))*Rfc1+ Rfc1)
    w2 = (Rfc2 * np.exp((Rfc2-Rfc1) + Rfc2)) / (Rfc2 * np.exp((Rfc2-Rfc1))+ Rfc2 + Rfc1)

β = 0.00873 

Ratio_VtoR = 5.39
Dv_ΔL = 5.93e-7
RatioD_ΔL = 20 
Dr_ΔL = RatioD_ΔL * Dv_ΔL * Ratio_VtoR
k = (R10 * Dr_ΔL) / (Lmax - Lmin)

def alpha_beta(x):
    # a, b are params fitted for parabola functions
    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])

def func1(Dind): 
    crit = lambda x: (k*(w1*abs(x[0]-L10)+w2*abs(x[1]-L20))+\
                    β*Dind[0]*(w1*alpha_beta(x[0])+w2*alpha_beta(x[1]))+ β*Dind[1]*(w1*alpha_beta(x[2])+w2*alpha_beta(x[3]))+\
                      k*(w1*abs(x[2]-x[0]) + w1*abs(x[4]-x[2]) + w2*abs(x[3]-x[1])+w2*abs(x[5]-x[3])))
    return crit

def func2(Dind): 
    crit = lambda x: (k*(w1*abs(x[0]-L10)+w2*abs(x[1]-L20))+ β*Dind[1]*(w1*alpha_beta(x[2])+w2*alpha_beta(x[3]))+\
                      β*Dind[0]*(w1*alpha_beta(x[0])+w2*alpha_beta(x[1]))+\
                      k*(w1*abs(x[2]-x[0]) + w1*abs(x[4]-x[2]) + w2*abs(x[3]-x[1])+w2*abs(x[5]-x[3])))
    return crit
                     
def func(Dind):
    Cr1 = lambda x: (k*(w1*abs(x[0]-L10)+w2*abs(x[1]-L20)) +\
                     sum((β*Dind[i]*(w1*alpha_beta(x[2*i])+w2*alpha_beta(x[2*i+1])) +\
                    k*(w1*abs(x[2*(i+1)]-x[2*i]) + w2*abs(x[2*(i+1)+1]-x[2*i+1]))) for i in range(len(Dind))))                
    return Cr1

bounds = Bounds([Lmin]*2*len(Ldf), [Lmax]*2*len(Ldf))

A_mat = np.zeros((len(Ldf), 2*len(Ldf)))
for i in range(len(Ldf)):
    A_mat[i, 2*i] = 1
    A_mat[i, 2*i+1] = 1
    
linear_cons = LinearConstraint(A_mat, np.array(Ldf), (1.08 * np.array(Ldf)))

x0 = np.repeat(Ldf, 2) / 2 

res = minimize(func(Dindf), x0, method='trust-constr', constraints=linear_cons, options={'disp': 0, 'xtol':1e-5,
                'maxiter': 80, 'gtol':1e-7, 'verbose': 0}, bounds=bounds)
print(f'func:{res.x}')


res = minimize(func1(Dindf), x0, method='trust-constr', constraints=linear_cons, options={'disp': 0, 'xtol':1e-5,
                'maxiter': 80, 'gtol':1e-7, 'verbose': 0}, bounds=bounds)
print(f'func1:{res.x}')

res = minimize(func2(Dindf), x0, method='trust-constr', constraints=linear_cons, options={'disp': 0, 'xtol':1e-5,
                'maxiter': 80, 'gtol':1e-7, 'verbose': 0}, bounds=bounds)
print(f'func2:{res.x}')

我得到了输出：

func:[2.30419673 2.23050723 2.52527556 2.67472855 2.52537813 2.5305927 ]
func1:[2.30460228 2.22989643 2.52506878 2.67493795 2.52505983 2.54172443]
func2:[2.30369304 2.22975576 2.52527861 2.67474766 2.52559372 2.52896126]

为了更清楚，我放了几个优化案例。func() 是一种通用形式，用于处理任意数量的自变量。func1() 和 fucn2() 实际上是相同的，我只是改变了一些术语的顺序。而func1()、func2()的结构与func()相同。我不明白的是为什么优化结果不同？

标签： pythonfunctionoptimizationlambdascipy-optimize-minimize

解决方案

您已经错误地定义了其中一个功能，尽管我很难说哪个是“技术上正确的”。无论哪种方式，您的特殊情况函数都与通用函数在以下情况下显示的内容不匹配len(Dind) = 4：

form = ['k*(w1*abs(x[0]-L10)+w2*abs(x[1]-L20))']

for i in range(0,4):
  form.append(f'β*Dind[{i}]*(w1*alpha_beta(x[{2*i}])+w2*alpha_beta(x[{2*i+1}])) + k*(w1*abs(x[{2*(i+1)}]-x[{2*i}]) + w2*abs(x[{2*(i+1)+1}]-x[{2*i+1}]))')

print('+'.join(form))

这给了我：

crit = lambda x: k*(w1*abs(x[0]-L10)+w2*abs(x[1]-L20))+β*Dind[0]*(w1*alpha_beta(x[0])+w2*alpha_beta(x[1])) + k*(w1*abs(x[2]-x[0]) + w2*abs(x[3]-x[1]))+β*Dind[1]*(w1*alpha_beta(x[2])+w2*alpha_beta(x[3])) + k*(w1*abs(x[4]-x[2]) + w2*abs(x[5]-x[3]))+β*Dind[2]*(w1*alpha_beta(x[4])+w2*alpha_beta(x[5])) + k*(w1*abs(x[6]-x[4]) + w2*abs(x[7]-x[5]))+β*Dind[3]*(w1*alpha_beta(x[6])+w2*alpha_beta(x[7])) + k*(w1*abs(x[8]-x[6]) + w2*abs(x[9]-x[7]))

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