I want to include the voltage limits of each bus of a 30 bus system as an objective using multi-objective genetic algorithm and minimize power loss as main objective. How can I write the voltage limits as an objective function?
Most of the objectives in a multi-objective (MO) GA are real numbers. But that is perhaps not necessary... For the voltage limit problem, the objective can be a pair of numbers (think of it physically as a line from Vmax to Vmin). So, effectively you'll have 60 variables (if you think in terms of real numbers) to optimize, along with the voltage loss !
If you are coding this problem yourself then:
You could set the problem in terms of chromosomes with 30 bases which take on real values between your voltage limits which you set. Then you implement arithmetic crossover. see http://www.ijarcsse.com/docs/papers/Volume_4/3_March2014/V4I3-0330.pdf.
For mutation you add a small random number to a randomly selected genes in each chromosome. see http://www.obitko.com/tutorials/genetic-algorithms/crossover-mutation.php. Then you do a correction to ensure that you have not breeched the voltage limits you have set.
The fitness function to maximise then will be 1/power1+1/power2+.....+1/power29+1/power30, which will ensure that the powers lost are minimised within the limits you set for the voltages. To maximise the powers lost then the fitness function to maximise is power1+power2+....+power29+power30, which will maximise the powers lost within the limits you set for the voltages. The total power lost =power1+power2+....+power3+power4. I am assuming that power.n lost is some function of voltage.n for n=1 to 30.
So, what you need is real value encoding with arithmetic crossover and real value mutation, with correction applied to ensure that the voltage limits which you set are not breeched. see http://www.geatbx.com/docu/algindex-04.html
It's sometimes easy to programatically handle parameters when they are real-coded, because we don't need to go to the bit level to crossover or mutate, but just select functions to create offsprings. I think the link below to be a really simple overview of that.
But what I think is important is how to take the "voltage limits"-- whether binary or real coded is perhaps a secondary issue.
I just came across this article... maybe they have done something very similar to what Mr. Ritesh is asking (though using Bee Colony instead of GA), taking voltage limits as one of the constraints.
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