Some links which are useful for your this study may be : Chapter Offspring Selection Genetic Algorithm Revisited: Improvement...

Also Chapter Offspring Selection: A New Self-Adaptive Selection Scheme fo...

Certainly there are many selection methods that you can use to find the best solution to the issue used in your work The attached file contains many selection methods for chromosomes that give the best solution

Article Using enhanced genetic programming techniques for evolving c...

Article Advanced Genetic Programming Based Machine Learning

Article On the Reliability of Nonlinear Modeling Using Enhanced Gene...

Conference Paper On Crossover Success Rate in Genetic Programming with Offspr...

Article System for EEG/ERP data and metadata storage and management

https://pdfs.semanticscholar.org/aa76/b73b476f122ec75d6937fd3aaa9c77cd97e5.pdf

Chapter Offspring Selection Genetic Algorithm Revisited: Improvement...

Muhammad Ali Thank you so much.

Shahbaa I. Khaleel Thank you so much.

Thank you so much, Cristian Ramos-Vera .

Usually, implementations are to maximize the objective function. In your case, the goal is to minimize the cost. Then, you must correct the calculation of each individual's fitness so that a High Cost produces a Low Fitness

Nestor H. Caceres A. Thank you so much, sir. you are right, I found the solution by deducting the fitness value from the maximum fitness value in the strings (fitness function for each chromosome = D-O.F.), where D is a constant number (maximum fitness value), and O.F. is the Objective Function for the selected string)) when the O.F is maximized, the fitness function will be minimized, So for selecting the survived chromosomes, the high F.F value will be selected by using roulette wheel selection method, in a result the minimum O.F value will be selected, for crossover and mutation.

You said "The selection of chromosomes start with dividing the fitness function of the chromosome by total fitness function...".

Do you mean: The selection of chromosomes start with dividing the fitness value of each chromosome by the summation of the fitness values of all chromosomes ?

Because this last is the way to assign to each chromosome a probability for selection that is proportional to his fitness.

Nestor H. Caceres A. , I meant, after randomly initial population generated, the roulette wheel selection method will start for discarding some chromosomes and duplicating some others where they have more probability to be selected, the calculation is by dividing fitness value of each chromosome by average fitness value, but unfortunately, I don't know how to control the population size fluctuation, after discarding some chromosome and duplicating some others, but still, some chromosomes be missed. I want the population size for each iteration to remain constant..

I'm confused. The roulette wheel is used for the Selection operator, but keeping the population constant is handled with the Crossover operator.

Could you tell me what tools (programming languages, libraries, applications) are you working on?

Nestor H. Caceres A. ,well, I am working on C# programming language, actually in roulette wheel selection, as you know, when the weight of the fitness function found the selection will discard some chromosomes and some other will duplicated, for my project which is about time cost trade-off using genetic algorithm, I have another evaluation for selecting better solution after crossover, the outcome of the offspring from the crossover may be accepted if the fitness function value is better than the worst fitness value of the selected chromosomes by roulette wheel, I believe in the crossover step it is not guarantee the calibration of the population size, because when you accept the good crossover offspring the new chromosome takes place of the worst chromosome which have minimum fitness value. I think I need to fill the discarded chromosomes in the roulette wheel stage with the other better chromosomes in this way I guarantee to remain population size constant,

As I can see, you are developing a genetic algorithm from the scratch.

I have done this using C++ and C# but, I am not sure your requirements are the same than mine.

Next, a brief pseudocode showing the way I build a genetic algorithm.

If this way agree with your requirements, I can send to you some examples of the source code.

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- create a random population with 20 chromosomes or individuals.This populatios is called OldPopulation

- calculate the fitness of each individual (fitness is inversely proportional to cost)

- choose the "bestIndividual" (the individual with the best fistness) from OldPopulation

repeart for 100 generations

repeat 10 times

- select parent1 from OldPopulation using roulette wheel

- select parent2 from OldPopulation using roulette wheel

- create child1 and child2 by crossing parent1 and parent2

- calculate the fitness of child1 and child2

- add child1 and child2 to NewPopulation

end_repeat

- Apply Mutation Operator (Changing randomly some values into some individuals)

- Copy NewPopulation to OldPopulation

- Empty the NewPopulation

- choose the best individual from OldPopulation

end_repeat

/* "bestIndividual" contains the solution */

Nestor H. Caceres A. Sir, thank you so much for your help, yes actually I want to adapt the algorithm with my problem, but I have a lack of information, I am trying to collect more opinions and recommendations to drive me to the target. Anyway, for now, I want to calibrate the population size in the crossover operation while the reproduction will start from this stage, and I will be very grateful if you send your example, maybe it's not the same but I will get the concept and modified some steps or calculations to match with my model.

Ary H. Ahmed , the file SourceCode.zip contains an example of GA developed in C#. In the file Population.cs you can find the implementation of selection, crossover and mutation operators. Genome and Individual class must be customized to agree your model variables. Let me know if I can help you in any way.