如何解决使用 GEKKO 求解热集成优化模型
我正在尝试解决有关换热器网络综合的优化问题（基于下面提供的参考资料的方程）。为此，我使用 GEKKO 并创建了本文中提供的模型。
不幸的是，我的模型无法找到解决方案。它给出了模型具有负数自由度（确切地说是 -28）的警告。有人可以帮我在我的代码中分配确切的问题吗？
感谢您阅读我的帖子。
from gekko import GEKKO
m = GEKKO() # Initialize gekko
m.options.soLVER=1 # APOPT is an MINLP solver
m.options.IMODE=3 # Steady state optimization
# optional solver settings with APOPT
m.solver_options = ['minlp_maximum_iterations 500',\
# minlp iterations with integer solution
'minlp_max_iter_with_int_sol 10',\
# treat minlp as nlp
'minlp_as_nlp 0',\
# nlp sub-problem max iterations
'nlp_maximum_iterations 50',\
# 1 = depth first,2 = breadth first
'minlp_branch_method 1',\
# maximum deviation from whole number
'minlp_integer_tol 0.05',\
# covergence tolerance
'minlp_gap_tol 0.01']
"Defining constants and variables"
# Size of the problem
I = 2 # 2 hot streams
J = 2 # 2 cold streams
K = 3 # 3 temperature nodes
HP = range(I) #Set of hot streams
CP = range(J) #Set of cold streams
HU = range(1) #Set of hot utility (only 1)
CU = range(1) #set of cold utility (only 1)
ST = range(K-1) #set of stages: number = k - 1
TIN_i = [443,423] #Inlet temperatures hot streams
TIN_j = [293,353] #Inlet temperatures cold streams
TIN_HU = 450 #Inlet temperature hot utility
TIN_CU = 293 #Inlet temperature cold utility
TOUT_i = [333,303] #Outlet temperatures hot streams
TOUT_j = [408,413] #Outlet temperatures cold streams
TOUT_HU = 450 #Outlet temperatures hot utility
TOUT_CU = 313 #Outlet temperatures cold utility
F_i = [30,15] #Heat capacity hot streams
F_j = [20,40] #Heat capacity cold streams
#Constants mostly for cost calculations in objective function
U = m.Const(1)
CCU = m.Const(20)
CHU = m.Const(80)
CF = m.Const(1000)
CF_CU = m.Const(1000)
CF_HU = m.Const(1000)
C = m.Const(1000)
B = m.Const(0.6)
#Constans to apply big M formulation
OMEGA = m.Const(10000) #Max heat transfer in a single connection
TAU = m.Const(1000) #Max temperature difference in a single connection
#Defining variables
dT = m.Array(m.Var,(I,J,K-1),value = 1,lb = None,ub = None) #Approach temperature difference
dT1 = m.Array(m.Var,ub = None) #Approach temperature difference k+1
dTcu = m.Array(m.Var,(I),ub = None) #Approach temperature difference cold utility
dThu = m.Array(m.Var,(J),ub = None) #Approach temperature difference hot utility
Q = m.Array(m.Var,ub = None) #Amount of heat transfer between hot/cold streams in stage k
Qcu = m.Array(m.Var,ub = None) #Amount of heat transer with hot stream i and cold utility
Qhu = m.Array(m.Var,ub = None) #Amount of heat transer with cold stream j and hot utility
Ti = m.Array(m.Var,K),ub = None ) #Temperature of hot streams at node k
Tj = m.Array(m.Var,(J,ub = None ) #Temperature of cold streams at node k
z = m.Array(m.Var,integer = True ) #Decision veriables (is there a match for heat integration)
zcu = m.Array(m.Var,integer = True )
zhu = m.Array(m.Var,integer = True )
#Some variables for objective function calculation
Utility_cost = m.Var()
HXfixed_cost = m.Var()
CUfixed_cost = m.Var()
HUfixed_cost = m.Var()
HXarea_cost = m.Var()
cuarea_cost = m.Var()
HUarea_cost = m.Var()
"Defining the equations and objective"
#Heat balance for each stream
m.Equations( (TIN_i[i] - TOUT_i[i] ) * F_i[i] == sum([sum([Q[i,j,k] for j in CP]) for k in ST]) + Qcu[i] for i in HP)
m.Equations( (TOUT_j[j] - TIN_j[j] ) * F_i[j] == sum([sum([Q[i,k] for i in HP]) for k in ST]) + Qhu[j] for j in CP)
#Heat balance for each stage
m.Equations( (Ti[i,k] - Ti[i,k+1] ) * F_i[i] == sum([Q[i,k] for j in CP]) for k in ST for i in HP)
m.Equations( (Tj[j,k] - Ti[j,k+1] ) * F_i[j] == sum([Q[i,k] for i in HP]) for k in ST for j in CP)
#Assignment of inlet temperatures
m.Equations( TIN_i[i] == Ti[i,0] for i in HP)
m.Equations( TIN_j[j] == Tj[j,K-1] for j in CP)
#Feasibility of temperatures
m.Equations( Ti[i,k] >= Ti[i,k+1] for k in ST for i in HP)
m.Equations( Tj[j,k] >= Tj[j,k+1] for k in ST for j in CP)
m.Equations( TOUT_i[i] <= Ti[i,K-1] for i in HP)
m.Equations( TOUT_j[j] >= Tj[j,0] for j in CP)
#Hot and cold uttility load
m.Equations( ( Ti[i,K-1] - TOUT_i[i] ) * F_i[i] == Qcu[i] for i in HP)
m.Equations( ( TOUT_j[j] - Tj[j,0] ) * F_j[j] == Qhu[j] for j in CP)
#Logical constrains
m.Equations( Q[i,k] - OMEGA * z[i,k] <= 0 for i in HP for j in CP for k in ST)
m.Equations( Qcu[i] - OMEGA * zcu[i] <= 0 for i in HP)
m.Equations( Qhu[j] - OMEGA * zhu[j] <= 0 for j in CP)
#Approach temperature calculations
m.Equations( dT[i,k] <= Ti[i,k] - Tj[j,k] + TAU * (1 - z[i,k] ) for k in ST for i in HP for j in CP )
m.Equations( dT1[i,k+1] - Tj[j,k+1] + TAU * (1 - z[i,k] ) for k in ST for i in HP for j in CP )
m.Equations( dTcu[i] <= Ti[i,K-1] - TOUT_CU + TAU * (1 - zcu[i]) for i in HP)
m.Equations( dThu[j] <= TOUT_HU - Tj[j,0] + TAU * (1 - zhu[j]) for j in CP)
#Avoiding infinite areas
m.Equations( dT[i,k] >= 0.1 for i in HP for j in CP for k in ST)
m.Equations( dT1[i,k] >= 0.1 for i in HP for j in CP for k in ST)
m.Equations( dTcu[i] >= 0.1 for i in HP)
m.Equations( dThu[j] >= 0.1 for j in CP)
#Objective deFinitions
m.Equation( Utility_cost == sum([ CCU * Qcu[i] for i in HP ]) + sum([ CHU * Qhu[j] for j in CP ]) )
m.Equation( HXfixed_cost == sum([ sum([ sum([ CF * z[i,k] for k in ST ]) for j in CP ]) for i in HP ]) )
m.Equation( CUfixed_cost == sum([ CF_CU * zcu[i] for i in HP ]) )
m.Equation( HUfixed_cost == sum([ CF_HU * zhu[j] for j in CP ]) )
m.Equation( HXarea_cost == sum([ sum([ sum([ C* ( Q[i,k] / ( (U * ( dT[i,k] * dT1[i,k] * (dT[i,k] + dT1[i,k]) / 2) )**(0.33) ) ) ** B for k in ST ]) for j in CP ]) for i in HP ]) )
m.Equation( cuarea_cost == sum([ C * (Qcu[i] / ( U * (dTcu[i] * (TOUT_i[i] - TIN_CU) * (dTcu[i] + ( TOUT_i[i] - TIN_CU ) ) / 2) ** (0.33) ) ) ** B for i in HP ]) )
m.Equation( HUarea_cost == sum([ C * ( Qhu[j] / (U * (dThu[j] * (TIN_HU - TOUT_j[j]) * (dThu[j] + (TIN_HU - TOUT_j[j]) ) / 2) ** (0.33) )) ** B for j in CP ]) )
m.Minimize(Utility_cost + HXfixed_cost + CUfixed_cost + HUfixed_cost + HXarea_cost + cuarea_cost + HUarea_cost)
m.solve()
方程来源：“Yee,T. F. & Grossmann,I. E. (1990)。同时优化 热集成模型/II。换热网络综合。 计算机与化学工程 1,1165."
版权声明：本文内容由互联网用户自发贡献，该文观点与技术仅代表作者本人。本站仅提供信息存储空间服务，不拥有所有权，不承担相关法律责任。如发现本站有涉嫌侵权/违法违规的内容， 请发送邮件至 dio@foxmail.com 举报，一经查实，本站将立刻删除。
