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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]?

  2 Comments

Sky Sartorius
Sky Sartorius on 25 Feb 2020
Can you tell us more about the application? Does this decision variable represent anything physical in the real world?
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,
minimize
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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