big M constraints bringing an infeasinle solution

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Paramvir Singh 2018-5-5

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https://ww2.mathworks.cn/matlabcentral/answers/399200-big-m-constraints-bringing-an-infeasinle-solution

评论： Nicola Blasuttigh 2021-1-17

Here Tins is a decision variable of size=(24,1) in my optimization problem. The value of Tins(min_des) =20 while value of Tins(max_des) = 23.

I have tried using the following constraints for the above equation in MILP problem.

(Tmin - Tins) - M1*(1-BCac) <= 0 where M1 is an upper bound on (Tmin - Tins)

(Tins - Tmax) - M2*BCac <= 0 where M2 is an upper bound on (Tins - Tmax)

But if its supposed that Tins=27

then my first constraint gets satisfied with both BCac=1 and BCac=0

although the second constraint is satisfied at BCac=1 only, which is correct.

But due to the first constraint, my program is getting an infeasible solution.

Any help would be deeply appreciated.

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Paramvir Singh 2018-5-6

在 MATLAB Online 中打开

This is giving me an infeasible solution

powerprob=optimproblem;
% Continous Variables
Pgrid=optimvar('Pgrid',24,1,'LowerBound',0,'UpperBound',7); % for grid power
Tins=optimvar('Tins',24,1,'LowerBound',20,'UpperBound',23); % Inside Temperature of room
% Binary Variables
BCac = optimvar('BCac',24,1,'Type','integer','LowerBound',0,'UpperBound',1);
BHac = optimvar('BHac',24,1,'Type','integer','LowerBound',0,'UpperBound',1);
% Parameters
Hr2end=2:24; Time=1:24;
Cgrid=[0.033 0.027 0.020 0.017 0.017 0.029 0.033 0.054 0.215...
0.572 0.572 0.572 0.215 0.572 0.286 0.279 0.086 0.059 0.050 0.061...
0.181 0.077 0.043 0.037];
A=200;e=0.9;u=0.5;Tout=repmat(35,24,1);
Pac=1.15;
%
gridCost = sum(Pgrid.*Cgrid');
Dth=(Pac*(BCac+BHac));
% Objective
powerprob.Objective= gridCost;
% Equality Constraints
powerprob.Constraints.PowerBalance = Pgrid == Dth; % Power Balance equation
powerprob.Constraints.C22 = Tins(Hr2end) == (e*Tins(Hr2end-1)) + (1-e)*(Tout(Hr2end) - ((u*BCac(Hr2end)*Pac)/A));
powerprob.Constraints.C23 = Tins(Hr2end) == (e*Tins(Hr2end-1)) + (1-e)*(Tout(Hr2end) + ((u*BHac(Hr2end)*Pac)/A));
% Inequality Constraints
powerprob.Constraints.C13 = BCac + BHac <=1;
powerprob.Constraints.C14 = (20-Tins(Time))-20*(1-BCac(Time))<=0;
powerprob.Constraints.C15 = (Tins(Time)-23)-23*(BCac(Time))<=0;
powerprob.Constraints.C16 = (Tins(Time)-20)-20*(BHac(Time)-1)<=0;
powerprob.Constraints.C17 = (23-Tins(Time))-23*(BHac(Time))<=0;
%
% Options for the optimization algorithm, here we set the max time it can run for
options=optimoptions('intlinprog','Maxtime',1000);
% Call the optimization solver to find the best solution
[sol,TotalCost,exitflag,output]=solve(powerprob,'options',options);

Paramvir Singh 2018-5-6

Sorry, the code is running in my software. But the result is no feasible solution. Here, check it out in the pic below:

Mary Fenelon 2018-5-9

Paramvir is using the new syntax for specifying solve options introduced in 18a.

Paramvir, here a couple of suggestions to diagnose the infeasibility:

Write a text version of the problem with writeproblem and make sure your constraints are as you expect
Often, it's one group of constraints that lead to infeasibility. Try to identify that group by commenting out groups of constraints.

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Answer 1

Paramvir Singh 2018-5-10

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https://ww2.mathworks.cn/matlabcentral/answers/399200-big-m-constraints-bringing-an-infeasinle-solution#answer_319575

Thanks a lot Mam, I too figured it out that solve options is introduced recently in the 2018a version of Matlab. I was giving out of bounds initial value to the Tins variable. Moreover, one of the big M constraint in my main program was given a wrong form. Also there were two equality constraints of Tins variable(both containing its formula for cooling and heating version), I edited that formula and now my program is giving satisfactory results.

Thanks a lot to Matt J for helping me out.