How can i implement a second decision variable which is not in the objective function?

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Azime Beyza Ari 2022-3-27

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编辑： Torsten 2022-3-28

hello everyone,

I am working on an optimization problem where i have 2 decision variable. One of the variable is xij, which is directly in the objective function, other one is yj, which is not in the objective function, it is in my constraints. yj is dependent to xij.

xij is an binary variable where i want solver to decide if xij is 1 or 0, and yj is the row summation of xij. here is an example;

lets say that the solver gave me a solution for xij like this;

x = [ 1 0 1 1; 0 0 1 0; 1 1 0 0]

i want yj to be column or a row vector it does not matter (preferably column)

yj = [ (1 +0 +1=) 2 ; (0 + 0+ 1=) 1; (1+1+0=)2 ; (1+0+0=)1]

I have other constraints where i use yj.

here is my model; (p=67) (M is some large number like 1000)

My first question is that; can i do this kind of an operation?

second Q : how can i do this?

Ps: I am using genetic algorithm solver!

thak you in advance!

Best,

Beyza.

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Torsten 2022-3-28

编辑：Torsten 2022-3-28

Isn't there a much easier way to do this? Since I and J has 36 elements each.

You can use a loop to build the matrices if you know where the "ones" have to be placed.

Another question is ; I have 4 constraints so what i need to do is i need to write them all in open form and left sides will be Aeq and right sides will be Beq.

You must create two big matrices A and Aeq. The number of rows of A and Aeq gives the total number of inequality and equality constraints. The number of columns is equal to the total number of unknowns.

Another Question is since the ga solver only allows to input 1 linear constraint i should write each of my constriants in that matrix right?

Yes, all in two big matrices and two big vectors.

finally where should i write this; in the constraints section of the live editor or where?

[1 1 0 0 0 0; 0 0 1 1 0 0;0 0 0 0 1 1]*[x11; x12 ;x21; x22 ;x31 ;x32] <= [1;1;1]

You don't write the inequalities as I did above. You only write a script in which you specify the matrices and vectors just as you specify other variables. But you will have to put all variables in one vector. So for your case the vector could be arranged as

x = [x11; x21;...;x36,1;x12;x22;...,x36,2,...,x1,36, x2,36, ..., x36,36, y1,y2,...,y36]

with a size of (36*36 + 36,1).

Azime Beyza Ari 2022-3-28

I understood what you are saying. Thank you this is the answer.

i do not have equality constraints so Aeq and Beq will be empty. However, A and b, will be very big matrix and vector.

A will have an dimension of approxiametly 125x1332, so this is very unlogical to write manuelly. I will try to write them with a for loop if i can.

Again thank you!

Torsten 2022-3-28

编辑：Torsten 2022-3-28

My pleasure.

And use "intlinprog" instead of "ga" if the problem remains unchanged.

Setting up the matrix A and the vector b is the same for both solvers.

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How can i implement a second decision variable which is not in the objective function?

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