GEKKO 优化超出了方程范围（并且由于某种原因创建了变量）

Question

我正在尝试使用权重来确定价格，以优化在当地市场购买的商品的降价。我有每个用户购买的数量，以及一定的自耗参数：

cons = {'user1' :np.array([1,2,3,4]),
   'user2' : np.array([5,6,7,8]),
   'user3' : np.array([0.8,1,5,9]),
   'user4' : np.array([16,8,7,1])}
auto = {
    'user1': 0.7,
    'user2' : 0.6,
    'user3' : 0.32,
    'user4': 0.44
}

m=GEKKO(remote=False)
m.options.IMODE = 2
m.options.SOLVER = 1
m.options.CV_TYPE = 2
m.options.RTOL=1e-4
m.options.OTOL=1e-4

delta_user = {} # Price reduction for the margin of local-market shared energ
ml_bought={} # quantity bought in the local market
benefit_user = {} # quantity bought in the local market * price (delta)
self_cons = {} # weight factor - self consumption

fondos = m.Const(value =30)

delta_basic = 30/sum(cons['user1'] +cons['user2']+cons['user3']+cons['user4'])
delta_min = delta_basic*0.75
delta_max = delta_basic*1.25

for user in cons:
    # min, max and start values are calculated with the mean price to obtain that reduction
    delta_user[user] = m.Var(lb = delta_min, ub = delta_max, value= delta_basic)

    self_cons[user] = m.Param(auto[user])

    ml_bought[user] = m.Param(cons[user])

    benefit_user[user] = m.Intermediate(np.sum(ml_bought[user]*delta_user[user]))

# # Function: Sum of all reduced prices for the energy market cannot be greater than the maximum money available for the market. 
m.Equation(m.sum([benefit_user[user] for user in cons]) <= fondos)


m.Maximize(m.sum([benefit_user[user]*(self_cons[user]**2) for user in cons]))
m.solve()

问题解决了，但是这个方程得到的数量并没有小于应有的30，而是35.7：

m.Equation(m.sum([benefit_user[user] for user in cons]) <= fondos)

37.5 是我使用 Delta 的所有最大值时得到的值，但没有足够的钱

此外，我的目的是让每个用户拥有 1 个增量：

delta_use['user1'] = 0.3 #for example

相反，如果我运行以下代码，我会得到一个数组

delta_use['user1'] = [0.3, 0.3, 0.3, 0.3] # For example

显然出了什么问题，我只是不明白是什么

Answer 1

在

IMODE=2

中，使用

m.vsum()

函数获取跨数据维度的求和。

s = m.Var()
m.Equation(s == m.sum([benefit_user[user] for user in cons]))
m.Equation(m.vsum(s) <= fondos)

这强制执行正确的约束：

sum(s) = 30.0 <fondos 30

要获取单个值而不是决策变量数组，请使用

delta_user[user] = m.FV()

和

delta_user[user].STATUS=1

而不是

m.Var()

。这将计算整个数据维度的单个决策变量。它用

print(delta_user[user].value)

显示多个值，但它们在优化问题中被限制为相同的值。

这是修改后的完整脚本：

from gekko import GEKKO
import numpy as np

cons = {'user1' :np.array([1,2,3,4]),
   'user2' : np.array([5,6,7,8]),
   'user3' : np.array([0.8,1,5,9]),
   'user4' : np.array([16,8,7,1])}
auto = {
    'user1': 0.7,
    'user2' : 0.6,
    'user3' : 0.32,
    'user4': 0.44
}

m=GEKKO(remote=False)
m.options.IMODE = 2
m.options.SOLVER = 1
m.options.CV_TYPE = 2
m.options.RTOL=1e-4
m.options.OTOL=1e-4

delta_user = {} # Price reduction for the margin of local-market shared energ
ml_bought={} # quantity bought in the local market
benefit_user = {} # quantity bought in the local market * price (delta)
self_cons = {} # weight factor - self consumption

fondos = m.Const(value =30)

delta_basic = 30/sum(cons['user1'] +cons['user2']+cons['user3']+cons['user4'])
delta_min = delta_basic*0.75
delta_max = delta_basic*1.25

for user in cons:
    # min, max and start values are calculated with the mean price to obtain that reduction
    delta_user[user] = m.FV(lb = delta_min, ub = delta_max, value= delta_basic)
    delta_user[user].STATUS = 1

    self_cons[user] = m.Param(auto[user])
    ml_bought[user] = m.Param(cons[user])
    benefit_user[user] = m.Intermediate(np.sum(ml_bought[user]*delta_user[user]))

# # Function: Sum of all reduced prices
s = m.Var()
m.Equation(s == m.sum([benefit_user[user] for user in cons]))
m.Equation(m.vsum(s) <= fondos)


m.Maximize(m.sum([benefit_user[user]*(self_cons[user]**2) for user in cons]))
m.solve()

print(f'sum(s) = {sum(s.value)} < fondos {fondos.value}')
for user in cons:
    print('-'*30)
    print(f'user: {user}')
    print(f'delta_user: {delta_user[user].value[0]}')
    print(f'self_cons: {self_cons[user].value}')
    print(f'ml_bought: {ml_bought[user].value}')
    print(f'benefit_user: {benefit_user[user].value}')

这是求解器输出：

 Number of state variables:    53
 Number of total equations: -  49
 Number of slack variables: -  4
 ---------------------------------------
 Degrees of freedom       :    0
 
 ----------------------------------------------
 Model Parameter Estimation with APOPT Solver
 ----------------------------------------------
 
 Iter    Objective  Convergence
    0 -5.92655E+00  3.00000E+01
    1 -8.68352E+00  1.87498E-11
    2 -8.68352E+00  1.11022E-16
    3 -8.68352E+00  1.11022E-16
 Successful solution
 
 ---------------------------------------------------
 Solver         :  APOPT (v1.0)
 Solution time  :  0.019999999999999997 sec
 Objective      :  -8.683517899761338
 Successful solution
 ---------------------------------------------------

和打印结果：

sum(s) = 30.0 < fondos 30
------------------------------
user: user1
delta_user: 0.44749403341
self_cons: [0.7, 0.7, 0.7, 0.7]
ml_bought: [1.0, 2.0, 3.0, 4.0]
benefit_user: [0.44749403341, 0.89498806683, 1.3424821002, 1.7899761337]
------------------------------
user: user2
delta_user: 0.44749403341
self_cons: [0.6, 0.6, 0.6, 0.6]
ml_bought: [5.0, 6.0, 7.0, 8.0]
benefit_user: [2.2374701671, 2.6849642005, 3.1324582339, 3.5799522673]
------------------------------
user: user3
delta_user: 0.26849642005
self_cons: [0.32, 0.32, 0.32, 0.32]
ml_bought: [0.8, 1.0, 5.0, 9.0]
benefit_user: [0.21479713604, 0.26849642005, 1.3424821002, 2.4164677804]
------------------------------
user: user4
delta_user: 0.30149910501
self_cons: [0.44, 0.44, 0.44, 0.44]
ml_bought: [16.0, 8.0, 7.0, 1.0]
benefit_user: [4.8239856802, 2.4119928401, 2.1104937351, 0.30149910501]