# How to loop a objective function using the optimization toolbox?

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BOWEN LI on 5 Jul 2019
Edited: Matt J on 6 Jul 2019
Hi everyone,
I have a question that how can I put a "loop" structure in a optmization problem.
In my problem I have two binary decision variables and a objective function based on these two variables, and I am trying to use optmization toolbox to minimize the objective function.
There are 4 time periods in total, and the binary decision variables are changing(differs) in each time period. My objective function is built on the decision variable so that the objective function is for one time period as well. My goal is to minimize my objective function over all time periods.
For example, I have two binary decision variabe "y" and "s" that differs in each time period,
for n=4 %4 years in total
t=1:n
y=optimvar('y',[4,1],'Type','integer','LowerBound',0,'UpperBound',1);%binary decision variable
s=optimvar('s',[4,1],'Type','integer','LowerBound',0,'UpperBound',1);%binary decision variable
obj=optimproblem
obj.Objective = 2y+3s %minimize 2y+3s
obj.Constraints.precedence=y(t)-y(t-1)>=0 % a precedence constraint about y
[sol,fval] = solve(obj) % maybe use other method, i am supposed to use simmulated annealing

Matt J on 5 Jul 2019
Edited: Matt J on 6 Jul 2019
My objective function is built on the decision variable so that the objective function is for one time period as well.
You cannot solve this as 4 separate problems, because your precedence constraint creates a dependence between y(t) and y(t-1). The following might be what you are looking for (and it doesn't require a loop):
y=optimvar('y',[4,1],'Type','integer','LowerBound',0,'UpperBound',1);%binary decision variable
s=optimvar('s',[4,1],'Type','integer','LowerBound',0,'UpperBound',1);%binary decision variable
obj=optimproblem;
obj.Objective = 2*sum(y)+3*sum(s); %minimize
obj.Constraints.precedence=diff(eye(4))*y>=0; % a precedence constraint about y
[sol,fval] = solve(obj)

BOWEN LI on 6 Jul 2019
Thank you so much, really appreciate your help all the way!
But one question that you mentioned it does not need a loop, while my objective function: obj.Objective = 2*sum(y)+3*sum(s), which is for one time period, and I have like 4 time periods in total. Is this one can be formulated as the precedence constraint?
Thank you!
Matt J on 6 Jul 2019
obj.Objective = 2*sum(y)+3*sum(s), which is for one time period,
It's not for one time period anymore. Originally, you had
obj.Objective = 2*y(t)+3*s(t)
or at least I think that's what you meant. But in my answer, I changed it to
obj.Objective = 2*sum(y)+3*sum(s)
thus summing over all time periods. This was just a guess on my part of what objective function you really want. Only you can know what you're actually trying to solve.