How to perform the absolute value function on the output of an optimisation expression?

% Create Optimisation expressions
j = length(x);                           % is a double array
Tk = optimexpr(j);
Uk = optimexpr(j);
energyCost = optimexpr(j);
thermalCost = optimexpr(j);

%Initialise optimisation expressions
Tk(1,1) = 22;
Uk(1,1) = Tk(1,1)*K;                   % K=0.6
energyCost(1,1) = Uk(1,1)*abs(x(1,1));
thermalCost(1,1) = abs(Tk(1,1)-nominal_T); % THIS WHERE THE PROBLEM IS

% The last line always produces an error... "Undefined function 'abs' for input arguments of type 'optim.problemdef.OptimizationExpression'"
% How can I get round this?

[dpb]

call evaluate on the expression at some point or set of points.

The expression isn't a value or set of values; it's an expression for the optimizer to work on so abs() is meaningless for it.

[Akinkunmi Adegbenro]

Thanks for your response, but I am looking for a way to make sure the evaluated values of the optimisation expression is always positive.

[dpb]

That'll be under however the TB does constrained optimization, then, but certainly that wouldn't be done by calling abs() on the optimization object but has to be internal.

I'm not that familiar with the app; I've only used the direct user-called routines so not sure exactly how to set it up.

Boy, this seems to be a rat's nest of complexity to wend one's way through...but, try

https://www.mathworks.com/help/optim/ug/optim.problemdef.optimizationconstraint.html

and related links and see if can figure out how it's all supposed to work together.

[Akinkunmi Adegbenro]

Thanks, I'll check it out

Answer 1

[Matt J]

Without seeing your complete problem, it is hard to be certain, but you might find minL1lin (File Exchange download) applicable to this case. You need to enter the data into minL1lin in solver-based form, but you can still use prob2struct to extract all the relevant constraint matrices from your current problem-based code.

[Akinkunmi Adegbenro]

% Load Optimisation data from ...
load opfiles1407;
aU = 0.8;
aT = 0.8;
z = 20;
K = 0.6;
nominal_T = 22; %nominal temp (celcius)
thermalCost_Weight = 1; %thermal cost weighting
energyCost_Weight= 5; %energy cost weighting
x = optimdata.x; %copy x i.e. TOU price - avg price

%% 
% Create Optimisation variable(s)
setPoint = optimvar('setPoint',96,'LowerBound',0);
r = optimvar('absTc',96,'Lowerbound',0);


%%
% Create Optimisation expressions
j = length(x);
Tk = optimexpr(j);
Uk = optimexpr(j);
energyCost = optimexpr(j);
thermalCost = optimexpr(j);

% Formulate optimisation expressions
Tk(1,1) = 22;
Uk(1,1) = Tk(1,1)*K;
energyCost(1,1) = Uk(1,1)*abs(x(1,1));
thermalCost(1,1) = Tk(1,1)-nominal_T;

 for i=2:96
     Tk(i,1) = aT*Tk(i-1,1)+(1-aT)*(setPoint(i-1));
     Uk(i,1) = aU*Uk(i-1,1)+(K*z*(1-aU))+setPoint(i)+(K*(1-z)*(1-aU)*(setPoint(i-1)));
     energyCost(i,1) = Uk(i,1)*x(i,1);
     thermalCost(i,1) = Tk(i,1)-nominal_T;
     
             
 end


%% Code continues...
weighted_Tc = thermalCost*thermalCost_Weight;
weighted_Ec = energyCost*energyCost_Weight;
totalCost = weighted_Ec + weighted_Tc;

%% Create Optimisation problem and specify optimisation constraints
energyOpt = optimproblem('ObjectiveSense','minimize');
energyOpt.Constraints.r_upper = thermalCost<=r;
energyOpt.Constraints.r_lower = thermalCost>=-r;
energyOpt.Constraints.thermalCost = thermalCost(2:end,1) == Tk(2:end,1)-nominal_T;

%% OBJECTIVE FUNCTION
energyOpt.Objective = sum(totalCost);
energyOpt.Objective = energyOpt.Objective +sum(r);

%% Solve Optimisation problem
[sol,fval,exitflag,output] = solve(energyOpt)

[Matt J]

For me, this code returns

Problem is unbounded.

[Akinkunmi Adegbenro]

That is exactly the problem I am getting too. Not being able to evaluate thermalCost as an absolute value is what I suspect to be the cause. I have tried using linear solver on excel and got it working over there... just having problem MATLAB implementation

[Akinkunmi Adegbenro]

thermalCost can be either positive or negative depending on the value of Tk, but if I can find a way to find its absolute value then I believe the optimisation problem would be solved.

[Matt J]

OK, but if it gives the wrong result, I am not sure why you posted it.

[Akinkunmi Adegbenro]

Hoping you might be able to suggest an indirect way to implement the absolute function for the thermalCost in the context of the overall code

[Matt J]

Ah, I see. Well, any recommendations I give beyond what I mentioned above about minL1lin would require that I first see a mathematical description (not code) of the intended problem. The code you have posted does not convey the problem you are trying to solve. It conveys a problem that you are not trying to solve (clearly, since it gives the wrong result).

[dpb]

Well, perhaps naive, but why can't you just write

...
 for i=2:96
   Tk(i,1) = aT*Tk(i-1,1)+(1-aT)*(setPoint(i-1));
   Uk(i,1) = aU*Uk(i-1,1)+(K*z*(1-aU))+setPoint(i)+(K*(1-z)*(1-aU)*(setPoint(i-1)));
   energyCost(i,1) = Uk(i,1)*x(i,1);
   thermalCost(i,1) = Tk(i,1)-nominal_T;
 end
 thermalCost=abs(thermalCost);

?

Altho something seems wrong in the concept in doing so, but I don't know just what "thermalCost" really represents.

[Akinkunmi Adegbenro]

Thermal Cost is measured temperature (Tk) - nominal temperature (22°)

Thermal Cost is an optimisation expression, so putting it through abs function returns an error

[Matt J]

Should this line not be

energyCost(i,1) = Uk(i,1)*abs(x(i,1));

Without the abs, it could surely explain why the cost could be driven to -Inf.

[Akinkunmi Adegbenro]

Well spotted Matt! It was indeed the problem, it works now. Thank you very much for your help.