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Also you can add that binary representation is more efficient, since the computer works that way, so at the end any other representation is only a "disguise" of a binary code.

All numerical optimization methods have computational costs. Given unlimited computing resources brute force would be the best way to optimize an objective function. However in reality this is rarely, if ever, the case.  One of the most compelling reasons of implementing GA is its being computationally cost-efficient. Binary string chromosomes where each gene represents a particular trait of the variable at hand has been proven to be a cost-effective maximum-yield aspect of GA's.

Dear Ahmed Hamed,

Thank you so much for your interesting question. All the mentioned reasons in this topic seem to be reasonable; however, the main aim here is to enhance the solution diversity. More precisely, in such representation genetic search operators can obtain more promising solutions. A detailed description has been discussed in "Practical Genetic Algorithms" Book by Randy L. Haupt and Sue Ellen Haupt