MILP taking too long to solve

Official comment

Gurobi Staff

June 23, 2025 03:09 Edited

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Jaromił Najman

Gurobi Staff

August 05, 2020 11:14 Edited

Hi,

Could you elaborate more on the problem statistics? How many variables/constraints do you add when going from days to weeks? How much time do you want/expect the optimization to take?

What exactly do you mean by "screen remains blank", does Gurobi give no output at all? Could you provide a small example to illustrate the issue?

Best regards,
Jaromił

0

Tripti Gangwar

August 06, 2020 10:00

For a day, suppose I have 24 hrs data of load, generation, and other power flow variables and it is giving output in 5 min. However, for a week it goes to 167 hours of all the variables and if I am adding the data of 167 hrs to the same, Gurobi is giving no output at all. The code for one day given below and if u add more 'tcoef' like for 167 hrs, the screen remains blank

l= [ 1 1 2 0.0922 0.0470 ; 
2 2 3 0.4930 0.2511; 
3 3 4 0.3660 0.1864; 
4 4 5 0.3811 0.1941 ; 
4 5 6 0.8190 0.7070 ; 
6 6 7 0.1872 0.6188; 
7 7 8 0.7114 0.2351; 
8 8 9 1.0300 0.7400 ; 
9 9 10 1.0440 0.7400 ; 
10 10 11 0.1966 0.0650; 
11 11 12 0.3744 0.1238; 
12 12 13 1.4680 1.1550; 
13 13 14 0.5416 0.7129; 
14 14 15 0.5910 0.5260; 
15 15 16 0.7463 0.5450 ; 
16 16 17 1.2890 1.7210 ; 
17 17 18 0.7320 0.5740; 
18 2 19 0.1640 0.1565; 
19 19 20 1.5042 1.3554 ; 
20 20 21 0.4095 0.4784; 
21 21 22 0.7089 0.9373 ; 
22 3 23 0.4512 0.3083; 
23 23 24 0.8980 0.7091; 
24 24 25 0.8960 0.7011 ; 
25 6 26 0.2030 0.1034; 
26 26 27 0.2842 0.1447 ; 
27 27 28 1.0590 0.9337 ; 
28 28 29 0.8042 0.7006 ; 
29 29 30 0.5075 0.2585; 
30 30 31 0.9744 0.9630 ; 
31 31 32 0.3105 0.3619 ;
32 32 33 0.3410 0.5302];
m= [ 1 0 0 0;
2 100 60 0;
3 90 40 0 ; 
4 120 80 0 ; 
5 60 30 0 ;
6 60 20 0 ;
7 200 100 0;
8 200 100 0 ;
9 60 20 0 ;
10 60 20 0;
11 45 30 0;
12 60 35 0 ;
13 60 35 0 ;
14 120 80 0 ;
15 60 10 0 ;
16 60 20 0 ;
17 60 20 0 ;
18 90 40 0 ;
19 90 40 0 ;
20 90 40 0 ;
21 90 40 0;
22 90 40 0 ;
23 90 50 0;
24 420 200 0;
25 420 200 0;
26 60 25 0 ; 
27 60 25 0 ;
28 60 20 0;
29 120 70 0;
30 200 600 0;
31 150 70 0 ;
32 210 100 0;
33 60 40 0 ]; 
MVAb=100;
KVb=12.66;
Zb=(KVb^2)/MVAb;
nbr=length(l);
nb=length(m);
for i=1:nbr
R(i,1)=(l(i,4))/Zb;
X(i,1)=(l(i,5))/Zb;
end
z = complex(R,X);
g = real(1./z);
b = imag(1./z);
for i=1:nb
P(i,1)=((m(i,2))/(1000*MVAb));
Q(i,1)=((m(i,3))/(1000*MVAb));
end
tcoef=[0.5409;0.5291;0.5248;0.5595;0.5446;0.5458;0.6270;0.6772;0.6933;0.7299;0.7485;0.7515;0.8625;0.9461;0.9517;0.9721;0.9994;1.0000;0.9641;0.9610;0.8674;0.8073;0.6084;0.5855];
Pt=P.*tcoef';
Qt=Q.*tcoef';
Pt=Pt';
Qt=Qt';
%%%Including solar%%%
Rsp=[0 0 0 0 0 0 91 323 547 744 892 980 1000 948 830 656 446 210 16 0 0 0 0 0];
Rstd=1000;
Rc=150;
for i=1:24
if 0<Rsp(i) && Rsp(i)<Rc
P_s(i)=0.743*(Rsp(i)^2)/150000;
elseif Rstd<=Rsp(i)
P_s(i)=0.743;
else 
P_s(i)=0.743*Rsp(i)/1000;
end 
end
P_s=P_s/(MVAb);
P_s=P_s';
% MP=xlsread('load_24.xlsx','sheet2','B2:B25');
MP=[0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11];
time=24;

%% Parameters

Cp=54.34; Ce=81.52; %Power and energy rating cost
CRF=0.1097/365; %Capital recovery factor for r=7% and lifetime=15 yrs
eff=0.95;
a_min=0;
a_max=4;
Pc_m=1/MVAb;
Pd_m=1/MVAb;

%% Variables 
delV = sdpvar(time,nb,'full'); %voltage deviation at each bus
pfl=sdpvar(time,nbr,'full'); %power flow through a line
qfl=sdpvar(time,nbr,'full'); %power flow through a line
theta=sdpvar(time,nb,'full'); %angle difference
Pd = sdpvar(time,nb,'full'); %Char/dischar power
Pc = sdpvar(time,nb,'full');
E= sdpvar(time,nb,'full'); %stored energy
Er=sdpvar(1,nb,'full'); %Energy and power rating
Pr=sdpvar(1,nb,'full');
Ub=binvar(time,nb,'full'); %cha/dischag status
pl=sdpvar(time,nbr,'full'); %active power loss
ql=sdpvar(time,nbr,'full'); %reactive loss
p2=sdpvar(time,nbr,'full');
q2=sdpvar(time,nbr,'full');
Npc=binvar(time,nb,'full');

%% network constraints
Co = [];

for t=1:time
for i=1:nbr
Co = [Co, pfl(t,i)==((delV(t,l(i,2))-delV(t,l(i,3)))*g(i,1))-((theta(t,l(i,2))-theta(t,l(i,3)))*b(i,1))];
Co = [Co, qfl(t,i)==-((delV(t,l(i,2))-delV(t,l(i,3)))*b(i,1))-((theta(t,l(i,2))-theta(t,l(i,3)))*g(i,1))];
range=-20/MVAb:0.1/MVAb:20/MVAb;
Co=[Co,p2(t,i)==interp1(range,range.^2,pfl(t,i),'lp')];
Co=[Co,q2(t,i)==interp1(range,range.^2,qfl(t,i),'lp')];
Co = [Co,(p2(t,i)+q2(t,i))<=2*((20/MVAb)^2)];

%%losses
Co=[Co,pl(t,i)==(p2(t,i)+q2(t,i))*R(i,1)];
Co=[Co,ql(t,i)==(p2(t,i)+q2(t,i))*X(i,1)]; 
end
for i=1:nb
fr=find(l(:,2)==i);
to=find(l(:,3)==i);
if i==1
Pg(t,1)=sum(pfl(t,fr))-sum(pfl(t,to))+Pt(t,i)+0.5*sum(pl(t,fr))+(0.5*sum(pl(t,to)));
Qg(t,1)=sum(qfl(t,fr))-sum(qfl(t,to))+Qt(t,i)+0.5*sum(ql(t,fr))+(0.5*sum(ql(t,to))); 
elseif i==17
Co = [Co,Pd(t,i)+P_s(t,1)-sum(pfl(t,fr))+sum(pfl(t,to))-Pt(t,i)-Pc(t,i)-0.5*sum(pl(t,fr))-(0.5*sum(pl(t,to)))==0];
Co = [Co,-sum(qfl(t,fr))+sum(qfl(t,to))-Qt(t,i)-0.5*sum(ql(t,fr))-(0.5*sum(ql(t,to)))==0];
elseif i==18
Co = [Co,Pd(t,i)+P_s(t,1)-sum(pfl(t,fr))+sum(pfl(t,to))-Pt(t,i)-Pc(t,i)-0.5*sum(pl(t,fr))-(0.5*sum(pl(t,to)))==0];
Co = [Co,-sum(qfl(t,fr))+sum(qfl(t,to))-Qt(t,i)-0.5*sum(ql(t,fr))-(0.5*sum(ql(t,to)))==0];
elseif i==32
Co = [Co,Pd(t,i)+P_s(t,1)-sum(pfl(t,fr))+sum(pfl(t,to))-Pt(t,i)-Pc(t,i)-0.5*sum(pl(t,fr))-(0.5*sum(pl(t,to)))==0];
Co = [Co,-sum(qfl(t,fr))+sum(qfl(t,to))-Qt(t,i)-0.5*sum(ql(t,fr))-(0.5*sum(ql(t,to)))==0];
elseif i==33
Co = [Co,Pd(t,i)+P_s(t,1)-sum(pfl(t,fr))+sum(pfl(t,to))-Pt(t,i)-Pc(t,i)-0.5*sum(pl(t,fr))-(0.5*sum(pl(t,to)))==0]; 
Co = [Co,-sum(qfl(t,fr))+sum(qfl(t,to))-Qt(t,i)-0.5*sum(ql(t,fr))-(0.5*sum(ql(t,to)))==0];
elseif i==22
Co = [Co,Pd(t,i)-sum(pfl(t,fr))+sum(pfl(t,to))-Pt(t,i)-Pc(t,i)-0.5*sum(pl(t,fr))-(0.5*sum(pl(t,to)))==0]; 
Co = [Co,-sum(qfl(t,fr))+sum(qfl(t,to))-Qt(t,i)-0.5*sum(ql(t,fr))-(0.5*sum(ql(t,to)))==0];
elseif i==25
Co = [Co,Pd(t,i)-sum(pfl(t,fr))+sum(pfl(t,to))-Pt(t,i)-Pc(t,i)-0.5*sum(pl(t,fr))-(0.5*sum(pl(t,to)))==0]; 
Co = [Co,-sum(qfl(t,fr))+sum(qfl(t,to))-Qt(t,i)-0.5*sum(ql(t,fr))-(0.5*sum(ql(t,to)))==0];
else
Co = [Co,-sum(pfl(t,fr))+sum(pfl(t,to))-Pt(t,i)-0.5*sum(pl(t,fr))-(0.5*sum(pl(t,to)))==0];
Co = [Co,-sum(qfl(t,fr))+sum(qfl(t,to))-Qt(t,i)-0.5*sum(ql(t,fr))-(0.5*sum(ql(t,to)))==0]; 
end

% Co=[Co,Pd(t,i)==0];
% Co=[Co,Pc(t,i)==0];
Co = [Co, -0.05<= delV(t,i)<=0.05]; 
Co = [Co,theta(t,1) == 0]; 
Co = [Co,delV(t,1)==0];
Co = [Co,Pd(1,i)==0];
Co = [Co,Pc(1,i)==0];
Co = [Co,E(1,i)==0.5*Er(1,i)]; %Initial energy stored
Co = [Co,0.2*Er(1,i)<=E(t,i)<=0.8*Er(1,i)];
Co = [Co, 0<=Pd(t,i)<=(1/a_max)*Er(1,i)];
Co = [Co, 0<=Pc(t,i)<=(1/a_max)*Er(1,i)];
Co = [Co, 0<=Pc(t,i)<=(1-Ub(t,i))*Pc_m];
Co = [Co, 0<=Pd(t,i)<=Ub(t,i)*Pd_m]; 
if t==1
Co = [Co,E(t,i)==E(time,i)]; %Initial and final equal

else
Co = [Co,E(t,i)==E(t-1,i)-Pd(t,i)/eff+Pc(t,i)*eff]; %Energy balance

end

end 

end
for i=1:nb

Co = [Co,a_min*Pr(1,i)<=Er(1,i)<=a_max*Pr(1,i)];
Co = [Co,0<=sum(Pr)&sum(Pr)<=(1/a_max)*11/MVAb];
Co = [Co,0<=sum(Er)&sum(Er)<=11/MVAb];
end
%% Objective
Objective=sum(Ce*CRF*sum((Er*MVAb*1000))+Cp*CRF*sum((Pr*MVAb*1000)))+sum(MP*(Pg*MVAb*1000));
ops = sdpsettings('verbose',1,'debug',1,'solver','gurobi');
sol= optimize([Co,Pg,Qg],Objective,ops); %

0

Jaromił Najman

Gurobi Staff

August 07, 2020 09:58

Hi,

Could you also post the outputs of the Gurobi logs of both runs, the successful and the "blank" one so I can inspect them in more detail? In the meantime, could you try to construct a minimum working example for this issue?

Thank you,
Jaromił

0

Tripti Gangwar

August 08, 2020 06:29

Dear Sir,

Please find the logs of both runs attached. Please note that the blank log screenshot is taken after 1 hour of the run and is still the same. The problem occurs when the 'tcoef' size is changed from 24 (hours of a day) to 167 (hours of a week)

Thankyou

0

Tripti Gangwar

August 08, 2020 06:29

0

Tripti Gangwar

August 08, 2020 09:24

Dear Sir,

Below is the log when 'tcoef' size is increased to 167 and the log is after three hours of run. A memory error appears

------------------------------------------------------------------------------------------------

Warning: YALMIP has detected that your drive or network is unusually slow.
This causes a severe delay in OPTIMIZE when I try to find available solvers.
To avoid this, use the options CACHESOLVERS in SDPSETTINGS.
See the FAQ for more information.
Academic license - for non-commercial use only
Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (win64)
Optimize a model with 4466051 rows, 4361772 columns and 17536907 nonzeros
Model fingerprint: 0x46d7dc40
Model has 10688 SOS constraints
Variable types: 4356261 continuous, 5511 integer (5511 binary)
Coefficient statistics:
Matrix range [1e-06, 1e+01]
Objective range [6e+03, 4e+05]
Bounds range [1e+00, 1e+00]
RHS range [1e-05, 1e+00]
Presolve removed 0 rows and 0 columns (presolve time = 9s) ...
Presolve removed 4319521 rows and 400 columns (presolve time = 47s) ...
Presolve removed 4331577 rows and 12324 columns (presolve time = 78s) ...
Presolve removed 4331581 rows and 12357 columns (presolve time = 94s) ...
Presolve removed 4331581 rows and 12357 columns (presolve time = 122s) ...
Presolve removed 4359200 rows and 12357 columns (presolve time = 135s) ...
Presolve removed 4359200 rows and 12357 columns (presolve time = 136s) ...
Presolve removed 4359200 rows and 12357 columns (presolve time = 143s) ...
Presolve removed 4366843 rows and 20000 columns (presolve time = 153s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 155s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 162s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 285s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 297s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 301s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 307s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 310s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 316s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 320s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 325s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 330s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 335s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 341s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 345s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 350s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 355s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 361s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 366s) ...
Presolve removed 4380392 rows and 33549 columns (presolve time = 370s) ...
Presolve removed 4380562 rows and 33549 columns (presolve time = 401s) ...
Presolve removed 4385739 rows and 33718 columns (presolve time = 415s) ...
Presolve removed 4389865 rows and 37844 columns (presolve time = 427s) ...
Presolve removed 4389865 rows and 37844 columns (presolve time = 443s) ...
Presolve removed 4389865 rows and 37844 columns (presolve time = 490s) ...
Presolve removed 4389865 rows and 37844 columns (presolve time = 502s) ...
Presolve removed 4389865 rows and 37844 columns (presolve time = 505s) ...
Presolve removed 4389865 rows and 37844 columns (presolve time = 510s) ...
Presolve removed 4390631 rows and 38610 columns (presolve time = 515s) ...
Presolve removed 4390631 rows and 38610 columns (presolve time = 520s) ...
Presolve removed 4390871 rows and 64381 columns (presolve time = 543s) ...
Presolve removed 4390871 rows and 64381 columns
Presolve time: 542.82s
Presolved: 75180 rows, 4297391 columns, 12995433 nonzeros
Presolved model has 10624 SOS constraint(s)
Variable types: 4291913 continuous, 5478 integer (5478 binary)

Deterministic concurrent LP optimizer: dual simplex and barrier
Showing barrier log only...

Explored 0 nodes (0 simplex iterations) in 1081.02 seconds
Thread count was 1 (of 4 available processors)

Solution count 0

Solve interrupted (error code 10001)
Best objective -, best bound -, gap -
Error using gurobi
Gurobi error 10001: Out of memory

Error in callgurobi (line 13)
result = gurobi(model,model.params);

Error in solvesdp (line 361)
eval(['output = ' solver.call '(interfacedata);']);

Error in optimize (line 31)
[varargout{1:nargout}] = solvesdp(varargin{:});

Error in thirtythreeinterpmo (line 246)
sol= optimize([Co,Pg,Qg],Objective,ops); %

>>

0

Jaromił Najman

Gurobi Staff

August 10, 2020 12:46

Hi,

This is a fairly large problem!

In order to tackle this out-of-memory issue, you could try using the Simplex method only, by setting the Method parameter to 1 or 0.

Is it possible for you to get a machine with more memory or to upgrade your current machine?

Please also have a look at our knowledge base article What can be done to avoid an out-of-memory condition?

Best regards,
Jaromił

0

MILP taking too long to solve

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