I am trying to implement genetic algorithm for maximizing a function of n variables. However the problem is that the fitness values can be negative and I am not sure about how to handle negative values while doing selection. I read this article Linear fitness scaling in Genetic Algorithm produces negative fitness values but it's not clear to me how the negative fitness values were taken care of and how scaling factors a and b were calculated.
Also, from the article I know that roulette wheel selection only works for positive fitness value. Is it the same for tournament selection as well ?
Tournament selection is not affected by this problem. It simply compares the fitness values of a uniformly sampled subset of size n of the population and takes the one with the best value. Still of course this means that, if you sample without repetition then the worst n-1 individuals will never get selected. If you sample with repetition they have a chance of being selected.
As with proportional selection: It doesn't work with negative fitness values. You can only apply "windowing" or "scaling" of your fitness values in which case they work again.
I once programmed some sampling methods as extension methods for C#'s IEnumerable among them is a SampleProportional and SampleProportionalWithoutRepetition extension method. They're part of HeuristicLab under GPL license.