I wish to solve a multi objective optimization problem with GA also I have never worked with GA before and I want to learn more about what are the packages that I can find useful? What are the pros of cons of using julia for this mission and what are the limitations ? do you have any general advice too
Have you tried NLopt.jl, Evolutionary.jl or GeneticAlgorithms.jl ?
Also BlackBoxOptim.jl might be useful to tackle your problem.
If you want to use a multi-objective problem, maybe you should better consider a real multi-objective algorithm, like NSGA-II, search https://github.com/gsoleilhac/NSGAII.jl or other similar packages.
About the pros and cons, you should decide by yourself, but in my opinion it is a great language for that, by flexibility, performance (and no license problems as Matlab).