Integer Values in a Quadratic Optimization Problem

Hi everyone,

I am currently trying to solve an optimization problem with quadprog. My solution has to be an integer.

So far I have only seen options for linear programming, like the intlinprog solver.

Is it possible to set the solution to be integer values in the quadprog solver? And if not, how can I adress/sidestep this issue?

Best Regards

Sean

Answer 1

[Matt J]

You can use ga() instead of quadprog(), if you have the Global Optimization Toolbox.

[Sean Shugar]

Thanks for your quick reply Matt!

I just checked the ga() function. The examples show the ga() function giving a scalar solution for each variable.

In my case, the solution should be a trajectory/ vector with multiple values (battery state of energy over a certain amount of time).

How can I apply that to the ga() function?

Best Regards

Sean Shugar

[Matt J]

The examples show the ga() function giving a scalar solution for each variable.

So you agree that the solutions in the ga documentation examples are array-valued, but the problem is that each variable in the array is a scalar? But that is the very definition of an array... How is your problem any different?

[Sean Shugar]

Hi Matt,

I was looking for a way to formulate a vectorized form of a quadratic program in the ga() function.

At the moment my cost functions looks like this

fun = @(x) x(:)'*H*x(:) + f'*x(:)

Where H is my quadratic cost matrix and f my linear cost vector. The vector x(:) is my solution.

With equality constraits and inequality constraints defined, I set up the ga() function as following

sol = ga(fun,2*N + 1,A,b,Aeq,beq,lb,ub,[],options);

At the moment I'm trying to solve other problems but this should be the correct way to define a quadratic program in the ga() function, correct?

Best Regards

Sean Shugar

[Matt J]

It could be, except you haven't included integer constraints in the code you've shown, which was the whole point of abandoning quadprog. Note that ga() cannot directly handle both integer and equality constraints. You would have to eliminate the equality constraints for this to work, see,

https://www.mathworks.com/matlabcentral/answers/167216-genetic-algorithm-ga-with-integer-equality-and-inequality-constraint?s_tid=srchtitle