As you know choosing a genetic representation is a part of building any Genetic Algorithm (GA). A mapping can be hence defined between the genotype space (problem solving space) and the phenotype space (original problem context). The fitness function, let's called it f, can be this mapping, in case assessing individuals of GA is identical to the objective function of the original problem:
f: Genotype Space ---------> Phenotype Space
For each genotype there is one corresponding phenotype. So, f is injective. A good GA representation encodes all phenotype into genotypes. So, f is bijective. My question: is it possible to go further and assess the quality of genetic representations by just examining some analytical properties of the fitness function. Thank you.
There is not, as of yet, any set of general guidelines for assessing the quality of a fitness function.
For someone starting out on a genetic algorithm problem, the fitness function is first formulated as a heuristic which suits ones own understanding. Development of "better" measures of fitness are done progressively, with the researcher refining the fitness function as new metrics come to light.
As the Wikipedia article on fitness functions states:
Definition of the fitness function is not straightforward in many cases and often is performed iteratively if the fittest solutions produced by GA are not what is desired. In some cases, it is very hard or impossible to come up even with a guess of what fitness function definition might be.
Evaluation of the suitability of fitness function, however, is an active area of research. There has been directed research in the past towards this end, though no promising results have arisen.