How to optimize the run time in my optimization problem.

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naiva saeedia
naiva saeedia 2024-4-28
评论： naiva saeedia 2024-4-30
Hi guys. I have an optimization problem. The code is as follows:
Objective=@MassTransferErrors;
kL=0.5;
kH=0.5;
p0=[kL,kH];
A = [];
b = [];
Aeq = [];
beq = [];
lb=[0 ; 0];
ub=[100;100];
k = fmincon(Objective, p0, A, b, Aeq, beq, lb, ub);
disp(k)
function MTE=MassTransferErrors(p)
kL = p(1);
kH = p(2);
%% Constants
tMax=18000; % reaction duration (s)
Q0=[100 200 350 400 400 400 500]; % Q_G etylene inflow (ml/min)
T_C =[230 230 230 180 200 230 230]; %T for different cases
MTE_j=zeros(1,7);
Experiments = {[ 0.2985 0.6498 0.6147 0.43917 0.40398],[0.68662 1.6373 1.4260 1.4437 1.53169],[2.90493 5.68662 5.75704 2.65845 1.00352],[3.50352 11.3908 6.77817 3.46831 2.2007],[4.73592 10.8979 4.48944 3.01056 2.76408],[4.80634 9.45423 6.60211 4.03169 2.83451],[4.41901 10.4754 7.09507 4.13732 2.27113]};
for i=1:7
Q1=Q0(i)*1e-6/60; % Q_G ethylene inflow (m3/s)
Q2=0; % Q_G butene inflow
Q3=0; % Q_G hexene inflow
Q4=0; % Q_G octene inflow
Q5=0; % Q_G decene inflow
Q6=0; % Q_G dodecene inflow
Q7=0; % Q_G undecane inflow
P1=36e5; % ethylene inflow pressure [Pa]
T1=T_C(i)+273.15; % T_Ethylene [K]
T2=230+273.15; % T_ref [K]
R=8.314; % gas constant [J/(mol.K)]
C1=P1/(R*T1); % ethylene inlet gas concentration [mol/m^3]
VR=300e-6; % reactor volume [m^3]
VG=250e-6; % gas volume [m^3]
VL=50e-6; % liquid volume [m^3]
K=[3.24;2.23;1.72;0.2;0.1;0.08;0.09]; % solubility [nondim]
moleWt=[28;56;84;112;140;168;156]; % mole weight C2,C4,...,C12,C11 [g/mol]
wc=(0.3+0.25)*1e-3; % catalyst weight [kg]
kref=[2.224e-4;1.533e-4;3.988e-5;1.914e-7;4.328e-5;...
2.506e-7;4.036e-5;1.062e-6;6.055e-7;]; % rate at Tref=230C [mol/(s.g_cat)]
Eact=[109.5; 15.23; 7.88; 44.45; 9.438; 8.426; 10.91; 12.54; 7.127]; % activation energy [J/mol];
k=kref.*exp(-Eact*(1/T1-1/T2)/R); % rate at T=T2 [mol/(s.g)]
tauOF=5; % outflow time constant (s)
% Specify initial conditions
xinit=zeros(15,1); % initial state vector
xinit(1)=C1*VR; % initial ethylene in gas (mol)
xinit(14)=36.63/156; % initial undecane in liquid (mol)
xinit(7) = xinit(14)*VG*K(7)/VL; % initial undecane in gas (mol)
xinit(8) = xinit(1)*VL/(K(1)*VG); % initial ethylene in liquid (mol)
xinit(15)=Q1*C1; % initial outflow rate (mol/s)
nToti=sum(xinit(1:7)); % initial moles in gas (mol)
dNdt=@(t,x) [Q1*C1-x(15)*x(1)/sum(x(1:7))-VR*kL*(x(1)/VG-K(1)*x(8)/VL); % gas phase ethylene (mol/s)
Q2-x(15)*x(2)/sum(x(1:7))-VR*kL*(x(2)/VG-K(2)*x(9)/VL); % gas phase butene (mol/s)
Q3-x(15)*x(3)/sum(x(1:7))-VR*kL*(x(3)/VG-K(3)*x(10)/VL); % gas phase hexene (mol/s)
Q4-x(15)*x(4)/sum(x(1:7))-VR*kH*(x(4)/VG-K(4)*x(11)/VL); % gas phase octene (mol/s)
Q5-x(15)*x(5)/sum(x(1:7))-VR*kH*(x(5)/VG-K(5)*x(12)/VL); % gas phase decene (mol/s)
Q6-x(15)*x(6)/sum(x(1:7))-VR*kH*(x(6)/VG-K(6)*x(13)/VL); % gas phase dodecene (mol/s)
Q7-x(15)*x(7)/sum(x(1:7))-VR*kH*(x(7)/VG-K(7)*x(14)/VL); % gas phase undecane (mol/s)
VR*kL*(x(1)/VG-K(1)*x(8)/VL)+wc*(-2*k(1)*x(8)^2/VL^2-k(2)*x(8)*x(9)/VL^2-k(3)*x(8)*x(10)/VL^2-k(5)*x(8)*x(11)/VL^2-k(7)*x(8)*x(12)/VL^2);
VR*kL*(x(2)/VG-K(2)*x(9)/VL)+wc*(k(1)*x(8)^2/VL^2-k(2)*x(8)*x(9)/VL^2-2*k(4)*x(9)^2/VL.^2-k(6)*x(9)*x(10)/VL^2-k(8)*x(9)*x(11)/VL^2);
VR*kL*(x(3)/VG-K(3)*x(10)/VL)+wc*(k(2)*x(8)*x(9)/VL^2-k(3)*x(8)*x(10)/VL^2-k(6)*x(9)*x(10)/VL.^2-2*k(9)*x(10)^2/VL^2);
VR*kH*(x(4)/VG-K(4)*x(11)/VL)+wc*(k(3)*x(8)*x(10)/VL^2+k(4)*x(9)^2/VL^2-k(5)*x(8)*x(11)/VL^2-k(8)*x(9)*x(11)/VL^2);
VR*kH*(x(5)/VG-K(5)*x(12)/VL)+wc*(k(5)*x(8)*x(11)/VL^2+k(6)*x(9)*x(10)/VL^2-k(7)*x(8)*x(12)/VL^2);
VR*kH*(x(6)/VG-K(6)*x(13)/VL)+wc*(k(7)*x(8)*x(12)/VL^2+k(8)*x(9)*x(11)/VL^2+k(9)*x(10)^2/VL^2);
VR*kH*(x(7)/VG-K(7)*x(14)/VL);
(sum(x(1:7))-nToti)/tauOF]; % d(outflow rate)/dt (mol/s^2)
[t,x]=ode45(dNdt,[0,tMax],xinit);
molGend=x(end,1:7);
molLend=x(end,8:14);
massGend=molGend'.*moleWt;
massLend=molLend'.*moleWt;
%Total Product
TotalProduct = zeros(1,7);
for j=1:7
TotalProduct(j) = massGend(j) + massLend(j); %Sum of the liquid and gas phase products(g)
end
Experiment_i = cell2mat(Experiments(i)); %Converting Experiments set to matrix
MTE_i = (TotalProduct(2)-Experiment_i(1))^2+(TotalProduct(3)-Experiment_i(2))^2+(TotalProduct(4)-Experiment_i(3))^2+(TotalProduct(5)-Experiment_i(4))^2+(TotalProduct(6)-Experiment_i(5))^5; %Defining an Mass Transfer Error relation
MTE_j(i) = MTE_i; %Defines a Mass Transfer Error Vector(1*7) that contains the error for each case
end
MTE = sum(MTE_j(1:7)); %Objective function(Sum of the all arrays in MTE_j Vector) what I need to minimize is each array that is on the MTE_j Vector but since I can't return a Vector as an objective function I sum all the arrays as my objective function.
end
What I need to minimize in this problem are all the seven values in MTE_j vector but since objective function can't return a vector. I have used the sum of the all values. I doubt this is the correct way to minimize all the seven values in MTE_j vector also my code took an extremely long run time(6 hours last time I have checked with no answers yet) . I know the objective function is complicated but I guess I'm doing something wrong. I also test my objective function with an assumption for kL and kH values. my objective function code seems to work OK. Here's the test code:
%%Test Objective function
kL = 0.1; %Assumption for kL
kH = 0.1; %Assumption for kH
%% Constants
tMax=18000; % reaction duration (s)
Q0=[100 200 350 400 400 400 500]; % Q_G etylene inflow (ml/min)
T_C =[230 230 230 180 200 230 230]; %T for different cases
MTE_j=zeros(1,7);
Experiments = {[ 0.2985 0.6498 0.6147 0.43917 0.40398],[0.68662 1.6373 1.4260 1.4437 1.53169],[2.90493 5.68662 5.75704 2.65845 1.00352],[3.50352 11.3908 6.77817 3.46831 2.2007],[4.73592 10.8979 4.48944 3.01056 2.76408],[4.80634 9.45423 6.60211 4.03169 2.83451],[4.41901 10.4754 7.09507 4.13732 2.27113]};
for i=1:7
Q1=Q0(i)*1e-6/60; % Q_G ethylene inflow (m3/s)
Q2=0; % Q_G butene inflow
Q3=0; % Q_G hexene inflow
Q4=0; % Q_G octene inflow
Q5=0; % Q_G decene inflow
Q6=0; % Q_G dodecene inflow
Q7=0; % Q_G undecane inflow
P1=36e5; % ethylene inflow pressure [Pa]
T1=T_C(i)+273.15; % T_Ethylene [K]
T2=230+273.15; % T_ref [K]
R=8.314; % gas constant [J/(mol.K)]
C1=P1/(R*T1); % ethylene inlet gas concentration [mol/m^3]
VR=300e-6; % reactor volume [m^3]
VG=250e-6; % gas volume [m^3]
VL=50e-6; % liquid volume [m^3]
K=[3.24;2.23;1.72;0.2;0.1;0.08;0.09]; % solubility [nondim]
moleWt=[28;56;84;112;140;168;156]; % mole weight C2,C4,...,C12,C11 [g/mol]
wc=(0.3+0.25)*1e-3; % catalyst weight [kg]
kref=[2.224e-4;1.533e-4;3.988e-5;1.914e-7;4.328e-5;...
2.506e-7;4.036e-5;1.062e-6;6.055e-7;]; % rate at Tref=230C [mol/(s.g_cat)]
Eact=[109.5; 15.23; 7.88; 44.45; 9.438; 8.426; 10.91; 12.54; 7.127]; % activation energy [J/mol];
k=kref.*exp(-Eact*(1/T1-1/T2)/R); % rate at T=T2 [mol/(s.g)]
tauOF=5; % outflow time constant (s)
% Specify initial conditions
xinit=zeros(15,1); % initial state vector
xinit(1)=C1*VR; % initial ethylene in gas (mol)
xinit(14)=36.63/156; % initial undecane in liquid (mol)
xinit(7) = xinit(14)*VG*K(7)/VL; % initial undecane in gas (mol)
xinit(8) = xinit(1)*VL/(K(1)*VG); % initial ethylene in liquid (mol)
xinit(15)=Q1*C1; % initial outflow rate (mol/s)
nToti=sum(xinit(1:7)); % initial moles in gas (mol)
dNdt=@(t,x) [Q1*C1-x(15)*x(1)/sum(x(1:7))-VR*kL*(x(1)/VG-K(1)*x(8)/VL); % gas phase ethylene (mol/s)
Q2-x(15)*x(2)/sum(x(1:7))-VR*kL*(x(2)/VG-K(2)*x(9)/VL); % gas phase butene (mol/s)
Q3-x(15)*x(3)/sum(x(1:7))-VR*kL*(x(3)/VG-K(3)*x(10)/VL); % gas phase hexene (mol/s)
Q4-x(15)*x(4)/sum(x(1:7))-VR*kH*(x(4)/VG-K(4)*x(11)/VL); % gas phase octene (mol/s)
Q5-x(15)*x(5)/sum(x(1:7))-VR*kH*(x(5)/VG-K(5)*x(12)/VL); % gas phase decene (mol/s)
Q6-x(15)*x(6)/sum(x(1:7))-VR*kH*(x(6)/VG-K(6)*x(13)/VL); % gas phase dodecene (mol/s)
Q7-x(15)*x(7)/sum(x(1:7))-VR*kH*(x(7)/VG-K(7)*x(14)/VL); % gas phase undecane (mol/s)
VR*kL*(x(1)/VG-K(1)*x(8)/VL)+wc*(-2*k(1)*x(8)^2/VL^2-k(2)*x(8)*x(9)/VL^2-k(3)*x(8)*x(10)/VL^2-k(5)*x(8)*x(11)/VL^2-k(7)*x(8)*x(12)/VL^2);
VR*kL*(x(2)/VG-K(2)*x(9)/VL)+wc*(k(1)*x(8)^2/VL^2-k(2)*x(8)*x(9)/VL^2-2*k(4)*x(9)^2/VL.^2-k(6)*x(9)*x(10)/VL^2-k(8)*x(9)*x(11)/VL^2);
VR*kL*(x(3)/VG-K(3)*x(10)/VL)+wc*(k(2)*x(8)*x(9)/VL^2-k(3)*x(8)*x(10)/VL^2-k(6)*x(9)*x(10)/VL.^2-2*k(9)*x(10)^2/VL^2);
VR*kH*(x(4)/VG-K(4)*x(11)/VL)+wc*(k(3)*x(8)*x(10)/VL^2+k(4)*x(9)^2/VL^2-k(5)*x(8)*x(11)/VL^2-k(8)*x(9)*x(11)/VL^2);
VR*kH*(x(5)/VG-K(5)*x(12)/VL)+wc*(k(5)*x(8)*x(11)/VL^2+k(6)*x(9)*x(10)/VL^2-k(7)*x(8)*x(12)/VL^2);
VR*kH*(x(6)/VG-K(6)*x(13)/VL)+wc*(k(7)*x(8)*x(12)/VL^2+k(8)*x(9)*x(11)/VL^2+k(9)*x(10)^2/VL^2);
VR*kH*(x(7)/VG-K(7)*x(14)/VL);
(sum(x(1:7))-nToti)/tauOF]; % d(outflow rate)/dt (mol/s^2)
[t,x]=ode45(dNdt,[0,tMax],xinit);
molGend=x(end,1:7);
molLend=x(end,8:14);
massGend=molGend'.*moleWt;
massLend=molLend'.*moleWt;
%Total Product
TotalProduct = zeros(1,7);
for j=1:7
TotalProduct(j) = massGend(j) + massLend(j); %Sum of the liquid and gas phase products(g)
end
Experiment_i = cell2mat(Experiments(i));
MTE_i = (TotalProduct(2)-Experiment_i(1))^2+(TotalProduct(3)-Experiment_i(2))^2+(TotalProduct(4)-Experiment_i(3))^2+(TotalProduct(5)-Experiment_i(4))^2+(TotalProduct(6)-Experiment_i(5))^2;
MTE_j(i) = MTE_i;
end
MTE = sum(MTE_j(1:7));
I just want the kL and kH values that minimize each value on MTE_j vector and I want a code to actually give me these values. My code take an extremely long run time with no answers.

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采纳的回答

Torsten
Torsten 2024-4-28
I don't see anything obviously wrong in your coding - except for the last term in MTE_i which should be
(TotalProduct(6)-Experiment_i(5))^2
instead of
(TotalProduct(6)-Experiment_i(5))^5
Try whether switching to ode15s from ode45 will reduce the runtime.
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Torsten
Torsten 2024-4-29
Load it into the editor and click the "Run" button under "Octave".
But now with 1 min runtime, I'd prefer MATLAB ...
function main
pkg load "optim"
Objective=@MassTransferErrors;
kL=0.5;
kH=0.5;
p0=[kL,kH];
A = [];
b = [];
Aeq = [];
beq = [];
lb=[0 ; 0];
ub=[100;100];
k = fmincon(Objective, p0, A, b, Aeq, beq, lb, ub);
disp(k)
end
function MTE=MassTransferErrors(p)
kL = p(1)
kH = p(2)
%% Constants
tMax=18000; % reaction duration (s)
Q0=[100 200 350 400 400 400 500]; % Q_G etylene inflow (ml/min)
T_C =[230 230 230 180 200 230 230]; %T for different cases
MTE_j=zeros(1,7);
Experiments = {[ 0.2985 0.6498 0.6147 0.43917 0.40398],[0.68662 1.6373 1.4260 1.4437 1.53169],[2.90493 5.68662 5.75704 2.65845 1.00352],[3.50352 11.3908 6.77817 3.46831 2.2007],[4.73592 10.8979 4.48944 3.01056 2.76408],[4.80634 9.45423 6.60211 4.03169 2.83451],[4.41901 10.4754 7.09507 4.13732 2.27113]};
for i=1:7
Q1=Q0(i)*1e-6/60; % Q_G ethylene inflow (m3/s)
Q2=0; % Q_G butene inflow
Q3=0; % Q_G hexene inflow
Q4=0; % Q_G octene inflow
Q5=0; % Q_G decene inflow
Q6=0; % Q_G dodecene inflow
Q7=0; % Q_G undecane inflow
P1=36e5; % ethylene inflow pressure [Pa]
T1=T_C(i)+273.15; % T_Ethylene [K]
T2=230+273.15; % T_ref [K]
R=8.314; % gas constant [J/(mol.K)]
C1=P1/(R*T1); % ethylene inlet gas concentration [mol/m^3]
VR=300e-6; % reactor volume [m^3]
VG=250e-6; % gas volume [m^3]
VL=50e-6; % liquid volume [m^3]
K=[3.24;2.23;1.72;0.2;0.1;0.08;0.09]; % solubility [nondim]
moleWt=[28;56;84;112;140;168;156]; % mole weight C2,C4,...,C12,C11 [g/mol]
wc=(0.3+0.25)*1e-3; % catalyst weight [kg]
kref=[2.224e-4;1.533e-4;3.988e-5;1.914e-7;4.328e-5;...
2.506e-7;4.036e-5;1.062e-6;6.055e-7;]; % rate at Tref=230C [mol/(s.g_cat)]
Eact=[109.5; 15.23; 7.88; 44.45; 9.438; 8.426; 10.91; 12.54; 7.127]; % activation energy [J/mol];
k=kref.*exp(-Eact*(1/T1-1/T2)/R); % rate at T=T2 [mol/(s.g)]
tauOF=5; % outflow time constant (s)
% Specify initial conditions
xinit=zeros(15,1); % initial state vector
xinit(1)=C1*VR; % initial ethylene in gas (mol)
xinit(14)=36.63/156; % initial undecane in liquid (mol)
xinit(7) = xinit(14)*VG*K(7)/VL; % initial undecane in gas (mol)
xinit(8) = xinit(1)*VL/(K(1)*VG); % initial ethylene in liquid (mol)
xinit(15)=Q1*C1; % initial outflow rate (mol/s)
nToti=sum(xinit(1:7)); % initial moles in gas (mol)
dNdt=@(t,x) [Q1*C1-x(15)*x(1)/sum(x(1:7))-VR*kL*(x(1)/VG-K(1)*x(8)/VL); % gas phase ethylene (mol/s)
Q2-x(15)*x(2)/sum(x(1:7))-VR*kL*(x(2)/VG-K(2)*x(9)/VL); % gas phase butene (mol/s)
Q3-x(15)*x(3)/sum(x(1:7))-VR*kL*(x(3)/VG-K(3)*x(10)/VL); % gas phase hexene (mol/s)
Q4-x(15)*x(4)/sum(x(1:7))-VR*kH*(x(4)/VG-K(4)*x(11)/VL); % gas phase octene (mol/s)
Q5-x(15)*x(5)/sum(x(1:7))-VR*kH*(x(5)/VG-K(5)*x(12)/VL); % gas phase decene (mol/s)
Q6-x(15)*x(6)/sum(x(1:7))-VR*kH*(x(6)/VG-K(6)*x(13)/VL); % gas phase dodecene (mol/s)
Q7-x(15)*x(7)/sum(x(1:7))-VR*kH*(x(7)/VG-K(7)*x(14)/VL); % gas phase undecane (mol/s)
VR*kL*(x(1)/VG-K(1)*x(8)/VL)+wc*(-2*k(1)*x(8)^2/VL^2-k(2)*x(8)*x(9)/VL^2-k(3)*x(8)*x(10)/VL^2-k(5)*x(8)*x(11)/VL^2-k(7)*x(8)*x(12)/VL^2);
VR*kL*(x(2)/VG-K(2)*x(9)/VL)+wc*(k(1)*x(8)^2/VL^2-k(2)*x(8)*x(9)/VL^2-2*k(4)*x(9)^2/VL.^2-k(6)*x(9)*x(10)/VL^2-k(8)*x(9)*x(11)/VL^2);
VR*kL*(x(3)/VG-K(3)*x(10)/VL)+wc*(k(2)*x(8)*x(9)/VL^2-k(3)*x(8)*x(10)/VL^2-k(6)*x(9)*x(10)/VL.^2-2*k(9)*x(10)^2/VL^2);
VR*kH*(x(4)/VG-K(4)*x(11)/VL)+wc*(k(3)*x(8)*x(10)/VL^2+k(4)*x(9)^2/VL^2-k(5)*x(8)*x(11)/VL^2-k(8)*x(9)*x(11)/VL^2);
VR*kH*(x(5)/VG-K(5)*x(12)/VL)+wc*(k(5)*x(8)*x(11)/VL^2+k(6)*x(9)*x(10)/VL^2-k(7)*x(8)*x(12)/VL^2);
VR*kH*(x(6)/VG-K(6)*x(13)/VL)+wc*(k(7)*x(8)*x(12)/VL^2+k(8)*x(9)*x(11)/VL^2+k(9)*x(10)^2/VL^2);
VR*kH*(x(7)/VG-K(7)*x(14)/VL);
(sum(x(1:7))-nToti)/tauOF]; % d(outflow rate)/dt (mol/s^2)
[t,x]=ode15s(dNdt,[0,tMax],xinit);
molGend=x(end,1:7);
molLend=x(end,8:14);
massGend=molGend'.*moleWt;
massLend=molLend'.*moleWt;
%Total Product
TotalProduct = zeros(1,7);
for j=1:7
TotalProduct(j) = massGend(j) + massLend(j); %Sum of the liquid and gas phase products(g)
end
Experiment_i = cell2mat(Experiments(i)); %Converting Experiments set to matrix
MTE_i = (TotalProduct(2)-Experiment_i(1))^2+(TotalProduct(3)-Experiment_i(2))^2+(TotalProduct(4)-Experiment_i(3))^2+(TotalProduct(5)-Experiment_i(4))^2+(TotalProduct(6)-Experiment_i(5))^5; %Defining an Mass Transfer Error relation
MTE_j(i) = MTE_i; %Defines a Mass Transfer Error Vector(1*7) that contains the error for each case
end
MTE = sum(MTE_j(1:7)) %Objective function(Sum of the all arrays in MTE_j Vector) what I need to minimize is each array that is on the MTE_j Vector but since I can't return a Vector as an objective function I sum all the arrays as my objective function.
end

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