How can I add constraint on variable in genetic algorithm which can take both discrete and continuous values.

Hi everyone,

I am trying to solve an optimization problem using genetic algorithm. I am using the standard function "ga" for this. In the problem, the decision variable can take both discrete and continous values.

For example: Let a be the decision variable, it can take following values

a = {0, 1, 2, 6, 7,} and 45 <= a <= 85.

How can I represent this in [lb <= a <= ub]?

[Sky Sartorius]

Can you tell us more about the application? Does this decision variable represent anything physical in the real world?

[Himanshu Nagpal]

yes it does. It is the total head of a pump station, which can be zero when pump is not operating otherwise between 45 to 85.

Let me rephrase the propblem this way,

minimize

subject to

How do I formulate this problem using ga?

Answer 1

[Alan Weiss]

You can represent this 0-or-in-a-range type of constraint by using an auxiliary variable. Suppose that your variable z can be in the continuous range [1,2] or else it can be zero (this is perfectly general by scaling the range). Set y = 0 means the variable is 0, or y = 1 means the variable is in its range. Then take y as an integer binary variable and x = y*z and minimize f(x).

Alan Weiss

MATLAB mathematical toolbox documentation

[Himanshu Nagpal]

Thank you.