genetic algorithm handling negative fitness values

When you have negative values, you could try to find the smallest fitness value in your population and add its opposite to every value. This way you will no longer have negative values, while the differences between fitness values will remain the same.

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.