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

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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]?
Himanshu Nagpal
Himanshu Nagpal on 25 Feb 2020
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,
subject to
How do I formulate this problem using ga?

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Accepted Answer

Alan Weiss
Alan Weiss on 25 Feb 2020
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
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