Infeasible or unbounded model

[bishal]

Hi Professor,
I am been trying to figure out the cause of infeasibility or unboundness in my programme since past few days but i couldn't take a lead. I have copied the matlab code below. Can you please look at it and say where might have i done wrong. With Objective function, the problem arises .

Thank you in advance.

%% optimzation

clc;

clear all;

load chargeLoad.mat; % load the data

stn_load1=chargeLoad(1,1:144);%per 10 minutes of load;

%% taking average of each 6 points 10 minutes to get per hour load

stn_load2=reshape(stn_load1,6,24);

temp=sum(stn_load2)./6; % average

temp1=repmat(temp,4,1);%per 15 minutes load

stn_load=reshape(temp1,1,[]); %making row vector of load per 15 minutes

P_buy_before=stn_load(1,41:64);

P_DR(5:24)=500;

%% power reduction during DR period

M_t1=zeros(1,4);

% for i=5:24

% M_t(1,i)=P_buy_before(1,i)-P_DR(1,i);

% end

M_temp=300+(450-300).*rand(1,20);

M_t=[M_t1 M_temp];

%% medium price range

M_price=[72.75 69.34 64.14 60.00 64.25 81.87 106.00 106 106 106 98.93 98.28 94.90 93.60 94.43 97.09 109.20 130.10 106.00 88.69 75.42 80.12 86.77 63.79]./1000;

price_temp=repmat(M_price,4,1);

price_temp1=reshape(price_temp,1,[]);

price_buy=price_temp1(1,41:64);

k=2; %k= 1 to 4

price_sell=price_buy*k;

price_DR(1:24)=0.2;

income_before=0;

for i=1:24;

    income_before=income_before+P_buy_before(i)*(price_sell(i)-price_buy(i));

end

income_before;

%% optimization problem formulation using yalmip tools

horizon=24;

U_d=binvar(1,horizon);

U_c=binvar(1,horizon);

P_giveup=sdpvar(1,horizon);

P_buy_after=sdpvar(1,horizon);

P_discharge=sdpvar(1,horizon);

P_charge=sdpvar(1,horizon);

soc_bes=sdpvar(1,horizon+1);

P_reduce=sdpvar(1,horizon);

%equlity constraints

F=[];

C_bes=200;

dis_min=5;

dis_max=40;

ch_min=7;

ch_max=20;

for i=1:4

    F=[F,P_buy_after(i)==P_buy_before(i),P_discharge(i)==0];   

end

for i=5:24

    F=[F,dis_min*U_d(1,i)<=P_discharge(1,i)<=dis_max*U_d(1,i)];

end

for i=1:horizon

    F=[F,ch_min*U_c(1,i)<=P_charge(1,i)<=ch_max*U_c(1,i)];

    F=[F,U_d(i)+U_c(i)==1];

end

for i=1:horizon

    F=[F,P_reduce(i)==P_giveup(i)+P_discharge(i)-P_charge(i)];

 F=[F,P_reduce(i)>=M_t(1,i)];

end

for i=1:24

 F=[F,P_buy_after(i)==P_buy_before(i)-P_giveup(i)-P_discharge(i)+P_charge(i)];

end

%% BESS constraint

F=[F,soc_bes(1,1)==0.85];

for i=1:horizon

   F=[F,soc_bes(1,i+1)==soc_bes(1,i)-1/4*(P_discharge(1,i)/(0.85*C_bes))+1/4*(P_charge(1,i)*0.85/C_bes)];

   F=[F,0.2<=soc_bes(1,i+1)<=0.85];

end

% Objective=0;

% for i=1:24

%     Objective=Objective-(1/4*(P_buy_after(i)+P_discharge(i))*price_sell(i));

% end

% for i=1:24

%     Objective=Objective-1/4*(P_reduce(i)*0.25);

% end

% for i=1:24

%     Objective=Objective+1/4*P_buy_after(i)*price_buy(i);

% end

ops=sdpsettings('solver','gurobi');

optimize(F);

% optimize(F,Objective,ops);

a=value(P_giveup)

b=value(P_buy_after)    

value(P_discharge)

value(P_charge)

value(soc_bes)

[Johan Löfberg]

Error using load

Unable to read file 'chargeLoad.mat'. No such file or directory.

 

[bishal]

Hi professor,

thank you for your response.

Here, I have attached the data file.

[Johan Löfberg]

Well, as you say, it is obviously unbounded. Adding an arbitrary lower bound on Objective and solving leads to an arbitrarily low objective, and, e.g., 

>> value(P_reduce)

ans =

   1.0e+07 *

  Columns 1 through 8

         0         0         0         0    0.0000    2.6345    0.0000    0.0000

  Columns 9 through 16

    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000

  Columns 17 through 24

    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000

https://yalmip.github.io/debuggingunbounded/

btw, you create an options structure to select solver, but you never use it

https://yalmip.github.io/tutorial/basics/

[bishal]

Hi Professor,

thank you for your quick response.

I got the same result too. I don't know what does that mean. Can you please elaborate it? How to make objective function bounded? and I have an understanding that if we create an option then "Optimize(constraint,objective,option)" yalmip will use the solver by default, isn't that true? 

Hoping for your advice

Thank you.

[Johan Löfberg]

It means that the problem formulation you have doesn't make sense, as it is missing some constraints

It's like solving the problem "build the most power generating plant possible, subject to the constraint that is generates at-least 55MW, and the color is green etc etc". Turns out that the solution generates infinite amount of energy, i.e. unbounded. Whoops, forgot the constraint that there is an upper limit on the cost and size of the plant.

To specify solver explicitly, you must send an options argument. otherwise YALMIP decides based on it's own logic