Setting Linear constraints GA

Using the optimization toolbox with the GA solver. My variables are such that they cannot be within a certain range [g,f], i.e must be:

y(i)<g
OR
y(i)>f

where f is larger than g. I then put this in the standard LMI form with:

A.y<b

The toolbox returns an in-feasibility error; which is no surprise, as no single point can satisfy both of the above inequalities simultaneously.

Is there an OR or similar function so I can implement the constraints in the toolbox?

[José-Luis]

LMI?

Answer 1

[Alan Weiss]

There is documentation about OR constraints here.

That said, it seems to me that you really have a binary kind of problem here, where you need to optimize over a decision variable x(i) that can be 0 or 1, and when it is 0 you have y(i) < g, and when 1 you have y(i) > f. You might have better luck after reformulating your problem this way, or by making an exhaustive search over all binary choices.

Alan Weiss

MATLAB mathematical toolbox documentation

[Mo]

The OR documentation looks promising.

But I don't immediately see how the problem can be reformulated to the binary type.

Need to find an optimal sensor placement on a plate, with a fitness function based on the coverage performance of the sensors. The coverage performance is quite complex and takes a while to compute for the entire plate. There's a region on which the sensors can't be located on, hence the constraint.

Answer 2

[Matt J]

You could express this using nonlinear constraints

(y(i)-f)*(g-y(i))<=0

However, your feasible region is highly non-connected, which will make it hard for GA to find a solution.