Differing mathematical perspectives of genotype space in combinatorial problems: metric spaces vs pretopological spaces

Fitness landscapes are frequently used as an abstract view of genotype space. If the structure of this landscape can be characterized, it will be possible to extract valuable clues about the best way to search through genotype space for an optimal solution. These high-dimensional landscapes are metric spaces. But an alternative view is to treat the genotypes as part of a pretopology, which has no regular structure. This paper discusses the two representations and argues why one of them is better suited for combinatorial optimization problems.