Writing Constaints for simulannealbnd

I am trying to optimize an objective using simulannealbnd function. I have constraints of upper and lower bounds on decision variable x. The constraints are: x > 0 and sum(x)< Maximum_Average_Price. I have coded as follow but the resultant sum(x) goes beyond Maximum_Average_Price. I would appreciate any help.

x0=[price(1:4), priceDash(5:28)];
lb = ones(1,28);
ub= min(sum(x0), price_avg_max);

Answer 1

[Alan Weiss]

The constraint you have is not a bound, it is a linear inequality constraint that cannot be represented by a bound.

I strongly suggest that you do not use simulannealbnd for this problem, and instead use fmincon if your objective function is smooth, and use patternsearch otherwise. If you are looking for a global solution, then start the solver from a variety of initial points

x0 = lb + rand(size(lb)).*(ub - lb);

By the way, you wrote that your lower bound is x >= 1, not x >= 0, since you said lb = ones and not zeros.

Alan Weiss

MATLAB mathematical toolbox documentation

[Saifullah Khalid]

I am grateful for the response. I have to use simulated annealing as I am trying to replicate results from a research paper. Secondly, since simulannealbnd only allow bound constraints so I tried to bound my variable between 1 and maximum average price. I do not know if my approach is right. So, please advise whether this problem can be solved using simulannealbnd in Matlab. Author in original research paper have used CVX with Matlab.

[Saifullah Khalid]

Since we know maximum average price, can we just divide it by number elements of x and set result as an upper bound on x?

[Alan Weiss]

No and no. A linear constraint is not the same as a bound constraint. Draw yourself a picture of x1 + x2 <= 1, and see if you can figure out how to get that picture as a bound constraint. The answer is no, you cannot.

You will have to do one of several things:

1. Write your own simulated annealing solver that accepts linear constraints.
2. Use a different solver.
3. Find a different problem.

Sorry, that is the set of choices.

Alan Weiss

MATLAB mathematical toolbox documentation

[Saifullah Khalid]

Alan Weiss, thank you very much for detailed comment. This is indeed a great help.