I think you need to make a clear distinction between the fitness function f and the objective function F.  These two functions do not have to be exactly the same. They can be proportional, inversely proportional, opposite, etc. depending on what suit best our needs.

Technically speaking, you can build a GA code that works with negative fitness..  However, for ease of implementation, the fitness is usually defined in GA as a non-negative function so that, even in the case of a minimization, the higher the fitness, the better the member of the population. For example, if you want to minimize an objective function F which varies between M to 35 where M is some unknown real value, then you can define the fitness function as f = 35 - F so that the best individual (that minimizes F) will have the maximum fitness f.

I think you need to make a clear distinction between the fitness function f and the objective function F.  These two functions do not have to be exactly the same. They can be proportional, inversely proportional, opposite, etc. depending on what suit best our needs.

Technically speaking, you can build a GA code that works with negative fitness..  However, for ease of implementation, the fitness is usually defined in GA as a non-negative function so that, even in the case of a minimization, the higher the fitness, the better the member of the population. For example, if you want to minimize an objective function F which varies between M to 35 where M is some unknown real value, then you can define the fitness function as f = 35 - F so that the best individual (that minimizes F) will have the maximum fitness f.

I think it is better to check the fitness function formula, normalization (if necessary), and the range of the parameters to optimize

Dear Nnene,

First of all please correct your argument "why negative fitness values are not used in genetic algorithm." GA  uses both  positive and negative values depending on the problem. 

Whether fitness function takes negative, positive or both  it completely depends on the problem itself and designing of fitness function. Designer is the one who have to decide whether function will take negative or not. It is not that GA does not use negative values so you have to suppress negative. You have to decide on your own what kind of values will suitable for your GA utilized problem.

Anupam Biswas , from your explanation I understood that whatever the sign the GA gives, if you want to maximize a function, (and you multiply your function with minus sign to get max value) and then GA gives a value, that value must be considered as positive even if it has a negative sign due to the modified Obj function? is it true or my statement is incorrect?

This is beacuse if you use the roulette method as selection strategy. You need possitive numbers from calculate their respective probabilities.

The roulette wheel selection procedure requires non-negative fitness values if it is the procedure used. Therefore negative fitness value needs to be normalized/re-scale. some literature suggests the offsetting technique. However, since GA is flexible in the selection procedure and generally. Any appropriate normalization procedure may be employed to adjust the negative value without affecting each chromosome ranking and randomness of the fitness function away from each other.

Alternatively, depending on the problem at hand, the fitness function's objective can be adjusted with a positive constant i.e intercept wrt to the mathematical advantage available for the transformation of the function without losing generalism and realism. Also, note to avoid the Function transposition problem.

@ Erik Cuevas RIGHTLY said if need to calculate fitness probability you need ono-negative fitness values