Dear Khadidja Belattar, 

In terms of your first question, it means that the selection does not replace the selected individuals in the population, and instead of replacing the children of the selected parents into the next generation, the two best individuals out of the two parents and two children are added back into the population.In terms of your second question, in my opinion if I understand right the question to prevent convergence to local minimum, you can improve the diversification in your algorithm  or, alternatively, adopt a different mutation operator. Also, a set of recently developed self-adaptive mechanism can be taken into account. Besides, hybridization throughout local search techniques can be helpful.

I hope my explanations be helpful to you. 

Good Luck.

Dear Khadidja

You can think about increasing a little bit the mutation probability to break the steady state (if breakable). Be carefull, a very high probability may alter the GA process and converges to rather a random search

Hi Khadidja Belattar,

As Soheila explained, the steady state in GA means that you will not replace all of your population, instead you will keep the select individuals for the next generation and replace the rest of your population with new individuals generated by the operators of crossover, mutation or another technique you are applying. About your second question, I would like to complement her answer. To prevent a local optimum, you can apply a stopping criterion that analyzes the convergence of the population and reset the population when it converges, of course, saving a percentage of the best individuals you have. There is a lot of algorithms you can implement. Also, you can insert a percentage of new individuals randomly generated in each population trying to keep the genetic variability. In few words, to prevent the optimum local you need diversity. Be creative.

I hope be helpful, good work!

Dear Khadidja Belattar,

With respect to your first question, and as it was described in the book "Introduction to Evolutionary Computing" from Eiben and Smith, in the steady state model, in each generation there is a parent population of size N, from which a mating pool of N parents are selected, usually by binary tournament. Then, M < N offspring are generated starting from the individuals in the mating pool by applying the genetic operators. Finally, those M new offspring replace M individuals belonging to the parent population. The percentage of the population that is replaced is known as the "generational gap" (M/N). One of the most analysed variants of the steady state model considers M = 1, and consequently, the generational gap can be calculated as 1/N.

Regarding your second question, there exist a wide range of approaches with different features, whose main goal is dealing with the balance between exploration and intensification of an Evolutionary Algorithm, and consequently, with the problem of premature convergence. I have attached some references.

I hope they are useful!

Best regards.

Article Exploration and Exploitation in Evolutionary Algorithms: A Survey

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