Does it really matter which techniques we use in the process of GA optimization? For instance, if I use the Roulette Wheel Technique instead of Tournament Method for selection, two-point crossover instead of one-point for crossover, and let’s say a single-point mutation instead of inversion method for mutation, will I still get the same optimum solutions? Why does it matter then and how do we decide on which methods to use in each step?
GA optimization is considered as a meta-heuristic algorithm and depending on the algorithms chosen for initialization, selection, mutation, and crossover and the parameters for each of the steps, a different optimum solution might be obtained in a particular run. With GA, one rarely performs it as a single-pass; unless any feasible solution (not necessarily very close to optimal) is a goal.
Though for a lot of problems, the obtained solutions will be close to each other, the GAs tend to converge to local optimums rather than the global one. Multiple techniques exist to correct/exploit this behaviour, from the choice of the methods for GA fundamental operations and their parameters to simple multiple runs of GA optimization with seeding the initial populations in different regions of likelihood optimums.
Now, the convergence of GA will be very different for different techniques; thus, the number of populations to converge, required population samples will vary quite a lot. Moreover, different techniques perform very differently for various problems and fitness function types.
A large variety of methods and parameters for GA optimization is explained by their metaheuristic nature. If there are no known studies for a performance of GA for a particular problem, one has to try those options one-by-one in order to get a feasible solution of a required quality in decent time.
For particular applications, you might find existing literature discussing different options and their performance – and with experience, one can start making connections and find similarities between different application areas. But, in general, the choice of the methods for fundamental GA steps - is trial and error, unless known otherwise.