How to use a decision variable from optimization problem into an if else statement?

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. When I input the if else statement using Tins variable for value comparison, then the following error is shown by matlab:-

Please suggest the corrective measure. Thanks in advance

[Matt J]

We need to see a statement of the whole optimization problem.

[Paramvir Singh]

This is the constraint expression for Tins. Tins variable is not in the objective function, its an add-on variable.

Is this sufficient or I have to show the whole problem?

Because the rest of the problem is error free, only the if else condition is causing an error.

[Matt J]

We need to understand the problem, i.e., we need to know what you're trying to minimize, which variables are the design variables, and what the constraints on those variables are.

As it stands, I don't even see what makes this optimization problem linear.

[Paramvir Singh]

Thanks Matt J for your queries.

This is my Problem Formulation. You could save the images if these are not clear here on mathworks site.

Page Continued

Other data is given below:-

 Ppv=[0 0 0 0 0 0 1 1 1 2 2 3 3 2 2 1 1 1 0 0 0 0 0 0]'; % PV Generation
Pwind=[1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 ]';% Wind Generation
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]; % Grid Power Usage Cost
A=400; aref=0.5; bref=0.9; Gref=0.3;
Cewh=70;e=0.7;
u=0.7; cp=0.1;
Tout=repmat(30,24,1); Tewhcold=30;
Rewh=100; q=10;

Hope this helps you understand the problem.

My program gives me error on equations 6 to 9. If you need my whole code, please do tell me.

[Paramvir Singh]

Is the information provided regarding the problem not sufficient?

[Matt J]

It's way too much. An optimization problem has the following form

min f(x)

subject to g(x)<=0, h(x)=0

I'm looking for you to tell me, in your case, what x,f,g,and h are.

Answer 1

[Mary Fenelon]

The if-constraints (logical constraints, implication constraints) can be modeled with linear constraints and binary variables.

To see how to do this, suppose you have a binary variable y that should be 1 when x > 0. The constraint x - M*y <= 0, where M is an upper bound on x, will enforce this. When x > 0, y must be 1; the only other possible value for y is 0 and if y were 0, the constraint reduces to x <= 0, a contradiction.

To formulate constraint (6), make two constraints

• (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)

The resulting constraints are called big-M constraints or indicator constraints. The y variable is called an indicator variable.

[Paramvir Singh]

Thanks for the answer. It worked.

[Paramvir Singh]

In the code for my constraint (6), I have another doubt if for a value of Tins=27, although second constraint is being satisfied, but for the first constraint, for Tins=27,

Both BCac=0 or 1 satisfy the constraint. I think due to this reason my intlinprog solver is not giving a feasible solution.

Any help in this regard would be appreciated.

[Amir Hossein Nazeri]

@Paramvir Singh Hi Paramvir, Is your problem solved? Can you share your Matlab code with me if possible? Or if you have any Github or so...

Thanks!

Amir