Dear Denio Junior,

The following are some key Selection methods in Genetic Algorithm: 

1. Stochastic uniform

2. Remainder

3. Uniform 

4. Roulette 

5. Tournament , and

6. Custom 

I would suggest you try all the above selection methods and compare their results in order to determine the best among them with respect to your research.

I this information will be helpful for you.

Good luck.

The selection process mentioned by Oluwarotimi Williams Samuel is mostly adopted in standard genetic algorithm. In MATLAB these options for selection process is also available. As per my experience, selection process is not so responsible to improve quality of the solution. However, if you are getting good results then its really nice. It will be good if you test the same with different type of problems of different size. 

Which version of GA are you using? How big a population size you have, what is the objective function, what are you using for crossover, are you using adaptable or fixed mutation rate? All these things will affect the speed of convergence (and, where applicable, may affect quality of the solution e.g. in terms of local minima/maxima etc.). So, my main advice is to not look at selection mechanism in isolation. And if you do want to specifically isolate/compare different selection mechanisms to each other, then you need to ensure that all these other parameters that affect GA performance are the same / fixed (across your own work and that of others, so that's in general hard and often impossible). So, if you cannot guarantee a truly 'apple to apple' comparisons, be careful not to attribute to (presumed superiority of) your selection mechanism, as it may well be that you see e.g. faster convergence of your algo, than what you've seen in the literature, due to other things (such as very different population sizes, different mutation rates/mechanisms, different crossovers,...)

Although GA selection method least contributes to the performance of GAs yet I believe that your work can be published if it is easy to implement compared to some or other selection approaches; it is more intuitive and so on.

With metaheuristics, I have found that having a small population of parents and offspring often help finding better solutions. With encompasses, GAs, ES, ILS, MA and other hybrids. 

Through my observations and the algorithms generated by CGP hyper-heuristics frameworks, the best selection methods and replacement heuristics are the hillclimbing ones. For example, select the best parents and replace the least fit.

Case by case, the results can be different, why dont you test all selection and have better understand 

Stochastic uniform

Remainder

Uniform

Roulette

Tournament

Stochastic uniform