A genetic algorithm for a minimization problem, has number of generations as the termination criteria. I understand that the best solution will be the one with the lowest objective function value. I also see that the objective function values of the solutions will tend to reduce with each successive generation as it approaches the best solution.
My question is:
if the raw objective function values are transformed with this fitness function
Y - x(i) / sum x(i)
where:
x(i) = individual raw objective function values
sum x(i) = sum of all the raw objective function values of the population
Y = large positive integer
How will the standard deviation of the fitness functions behave?
For the problem I am solving, the standard deviation tends to have an inverse relationship with the fitness values ie where the fitness value is an maxima, the standard deviation is a minima. and vice versa is this correct, please is there a source article where I can find details for this.
The SD is related to the genetic diversity of the population, which starts of high initially and reduces as the chromosomes get fitter and fitter and converge to a solution. So as the fitness increases, the genetic diversity decreases, as does the SD.
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