我需要对 100k 到 500k 变量运行优化，但它给我最大方程长度达到错误。谁能帮我解决这个问题？时间不是限制，只要跑3-4个小时就可以了。
df1 = df_opt.head(100000).copy()
#initialize model
m= GEKKO()
m.options.SOLVER=1
#initialize variable
x = np.array([m.Var(lb=0,ub=100,integer=True) for i in range(len(df1))])
#constraints
m.Equation(m.sum(x)<=30000)
#objective
responsiveness = np.array([m.Const(i) for i in df1['responsivness'].values])
affinity_score = np.array([m.Const(i) for i in df1['affinity'].values])
cost = np.array([m.Const(i) for i in df1['cost'].values])
expr = np.array([m.log(i) - k * j \
for i,j,k in zip((1+responsiveness * affinity_score * x),x,cost)])
m.Obj(-(m.sum(expr)))
#optimization
m.solve(disp=False)
答案 0 :(得分：2)
创建问题时，Minimal Example that is complete 很重要。这是一个修改，它创建了一个包含 n 行的随机 DataFrame。
from gekko import GEKKO
import numpy as np
import pandas as pd
n = 10
df1 = pd.DataFrame({'responsivness':np.random.rand(n),\
'affinity':np.random.rand(n),\
'cost':np.random.rand(n)})
print(df1.head())
#initialize model
m= GEKKO(remote=False)
m.options.SOLVER=1
#initialize variable
x = np.array([m.Var(lb=0,ub=100,integer=True) for i in range(len(df1))])
#constraints
m.Equation(m.sum(x)<=30000)
#objective
responsiveness = np.array([m.Const(i) for i in df1['responsivness'].values])
affinity_score = np.array([m.Const(i) for i in df1['affinity'].values])
cost = np.array([m.Const(i) for i in df1['cost'].values])
expr = np.array([m.log(i) - k * j \
for i,j,k in zip((1+responsiveness * affinity_score * x),x,cost)])
m.Obj(-(m.sum(expr)))
#optimization
m.solve(disp=True)
这成功解决了 n=10 并选择了随机数。
--------- APM Model Size ------------
Each time step contains
Objects : 0
Constants : 30
Variables : 11
Intermediates: 0
Connections : 0
Equations : 2
Residuals : 2
Number of state variables: 11
Number of total equations: - 1
Number of slack variables: - 1
---------------------------------------
Degrees of freedom : 9
----------------------------------------------
Steady State Optimization with APOPT Solver
----------------------------------------------
Iter: 1 I: 0 Tm: 0.00 NLPi: 20 Dpth: 0 Lvs: 3 Obj: -1.35E+00 Gap: NaN
--Integer Solution: -1.34E+00 Lowest Leaf: -1.35E+00 Gap: 4.73E-03
Iter: 2 I: 0 Tm: 0.00 NLPi: 2 Dpth: 1 Lvs: 3 Obj: -1.34E+00 Gap: 4.73E-03
Successful solution
---------------------------------------------------
Solver : APOPT (v1.0)
Solution time : 1.519999999436550E-002 sec
Objective : -1.34078995171088
Successful solution
---------------------------------------------------
可以通过导航到 gk_model0.apm 或使用 m.path 来访问底层模型 m.open_folder()。
Model
Constants
i0 = 0.14255660947333681
i1 = 0.9112789578520111
i2 = 0.10526966142004568
i3 = 0.6255161023214897
i4 = 0.2434604974789274
i5 = 0.812768922376058
i6 = 0.555163868440599
i7 = 0.7286240480266872
i8 = 0.39643651685899695
i9 = 0.4664238475079081
i10 = 0.588654005219946
i11 = 0.7807594551372589
i12 = 0.623910408858981
i13 = 0.19421798736230456
i14 = 0.3061420839190525
i15 = 0.07764492888189267
i16 = 0.7276569154297892
i17 = 0.5630014016669598
i18 = 0.9633171115575193
i19 = 0.23310692223695684
i20 = 0.008089496373502647
i21 = 0.7533529530133879
i22 = 0.4218710975774087
i23 = 0.03329287687223692
i24 = 0.9136665338169284
i25 = 0.7528330460265494
i26 = 0.0810779357870034
i27 = 0.4183140612726107
i28 = 0.4381547602657835
i29 = 0.907339329732971
End Constants
Variables
int_v1 = 0, <= 100, >= 0
int_v2 = 0, <= 100, >= 0
int_v3 = 0, <= 100, >= 0
int_v4 = 0, <= 100, >= 0
int_v5 = 0, <= 100, >= 0
int_v6 = 0, <= 100, >= 0
int_v7 = 0, <= 100, >= 0
int_v8 = 0, <= 100, >= 0
int_v9 = 0, <= 100, >= 0
int_v10 = 0, <= 100, >= 0
End Variables
Equations
(((((((((int_v1+int_v2)+int_v3)+int_v4)+int_v5)+int_v6)+int_v7)+int_v8)+int_v9)+int_v10)<=30000
minimize (-((((((((((log((1+((((i0)*(i10)))*(int_v1))))-((i20)*(int_v1)))+(log((1+((((i1)*(i11)))*(int_v2))))-((i21)*(int_v2))))+(log((1+((((i2)*(i12)))*(int_v3))))-((i22)*(int_v3))))+(log((1+((((i3)*(i13)))*(int_v4))))-((i23)*(int_v4))))+(log((1+((((i4)*(i14)))*(int_v5))))-((i24)*(int_v5))))+(log((1+((((i5)*(i15)))*(int_v6))))-((i25)*(int_v6))))+(log((1+((((i6)*(i16)))*(int_v7))))-((i26)*(int_v7))))+(log((1+((((i7)*(i17)))*(int_v8))))-((i27)*(int_v8))))+(log((1+((((i8)*(i18)))*(int_v9))))-((i28)*(int_v9))))+(log((1+((((i9)*(i19)))*(int_v10))))-((i29)*(int_v10)))))
End Equations
End Model
您可以通过将模型修改为以下内容来避免使用大的符号表达式字符串：
from gekko import GEKKO
import numpy as np
import pandas as pd
n = 5000
df1 = pd.DataFrame({'responsiveness':np.random.rand(n),\
'affinity':np.random.rand(n),\
'cost':np.random.rand(n)})
print(df1.head())
#initialize model
m= GEKKO(remote=False)
m.options.SOLVER=1
#initialize variable
x = np.array([m.Var(lb=0,ub=100,integer=True) for i in range(len(df1))])
#constraints
m.Equation(m.sum(list(x))<=30000)
#objective
responsiveness = df1['responsiveness'].values
affinity_score = df1['affinity'].values
cost = df1['cost'].values
[m.Maximize(m.log(i) - k * j) \
for i,j,k in zip((1+responsiveness * affinity_score * x),x,cost)]
#optimization
m.solve(disp=True)
m.open_folder()
这给出了以下基础模型，该模型不会随着变量数量的增加而增加符号表达式的大小。
Model
Variables
int_v1 = 0, <= 100, >= 0
int_v2 = 0, <= 100, >= 0
int_v3 = 0, <= 100, >= 0
int_v4 = 0, <= 100, >= 0
int_v5 = 0, <= 100, >= 0
int_v6 = 0, <= 100, >= 0
int_v7 = 0, <= 100, >= 0
int_v8 = 0, <= 100, >= 0
int_v9 = 0, <= 100, >= 0
int_v10 = 0, <= 100, >= 0
v11 = 0
End Variables
Equations
v11<=30000
maximize (log((1+((0.16283879947305288)*(int_v1))))-((0.365323493448101)*(int_v1)))
maximize (log((1+((0.3509872155181691)*(int_v2))))-((0.12162206443479917)*(int_v2)))
maximize (log((1+((0.20134572143617518)*(int_v3))))-((0.47137701674279087)*(int_v3)))
maximize (log((1+((0.287818142242232)*(int_v4))))-((0.12042554857067544)*(int_v4)))
maximize (log((1+((0.48997709502894166)*(int_v5))))-((0.21084485862098745)*(int_v5)))
maximize (log((1+((0.6178277437136291)*(int_v6))))-((0.42602122419609056)*(int_v6)))
maximize (log((1+((0.13033555293152563)*(int_v7))))-((0.8796057438355324)*(int_v7)))
maximize (log((1+((0.5002025885707916)*(int_v8))))-((0.9703263879586648)*(int_v8)))
maximize (log((1+((0.7095523321888202)*(int_v9))))-((0.8498606490337451)*(int_v9)))
maximize (log((1+((0.6174815809937886)*(int_v10))))-((0.9390903075640681)*(int_v10)))
End Equations
Connections
int_v1 = sum_1.x[1]
int_v2 = sum_1.x[2]
int_v3 = sum_1.x[3]
int_v4 = sum_1.x[4]
int_v5 = sum_1.x[5]
int_v6 = sum_1.x[6]
int_v7 = sum_1.x[7]
int_v8 = sum_1.x[8]
int_v9 = sum_1.x[9]
int_v10 = sum_1.x[10]
v11 = sum_1.y
End Connections
Objects
sum_1 = sum(10)
End Objects
End Model
我修复了 Gekko 中的一个错误，因此您应该能够在下一个 Gekko 版本中使用 m.Equation(m.sum(x)<=30000) 而不是将 x 转换为列表。此修改现在适用于以前失败的较大模型。我用 n=5000 对其进行了测试。
Number of state variables: 5002
Number of total equations: - 2
Number of slack variables: - 1
---------------------------------------
Degrees of freedom : 4999
----------------------------------------------
Steady State Optimization with APOPT Solver
----------------------------------------------
Iter: 1 I: 0 Tm: 313.38 NLPi: 14 Dpth: 0 Lvs: 3 Obj: -6.05E+02 Gap: NaN
--Integer Solution: -6.01E+02 Lowest Leaf: -6.05E+02 Gap: 6.60E-03
Iter: 2 I: 0 Tm: 0.06 NLPi: 2 Dpth: 1 Lvs: 3 Obj: -6.01E+02 Gap: 6.60E-03
Successful solution
---------------------------------------------------
Solver : APOPT (v1.0)
Solution time : 313.461699999985 sec
Objective : -600.648283994940
Successful solution
---------------------------------------------------
求解时间增加到 313.46 秒。还有更多的处理时间来编译模型。您可能希望从较小的模型开始并检查它会增加多少计算时间。我还建议您使用 remote=False 在本地解决，而不是在远程服务器上解决。
整数优化问题可能会随着变量的增加而呈指数级增长，因此您需要确保不会开始需要 30 年才能完成的问题。检查这一点的一个好方法是依次解决更大的问题，以了解扩大规模。