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The objective space Y is the space spanned by the codomains of the objective functions. F = {fi : X → Yi : 0 < i ≤ n, Yi ⊆ R} ⇒ Y = Y1 × Y2 × .. 32) The set F maps the elements x of the problem space X to the objective space Y and, by doing so, gives the optimizer information about their qualities as solutions for a given problem. 34 (Optimization Problem). An optimization problem is defined by a fivetuple (X, F, G, Op, gpm) specifying the problem space X, the objective functions F , the search space G, the set of search operations Op, and the genotype-phenotype mapping gpm.
14. Simply put, the DNA is a string of base pairs that encodes the phenotypical characteristics of the creature it belongs to. 22 (Genotype). The elements g ∈ G of the search space G of a given problem are called the genotypes. The elements of the search space rarely are unstructured aggregations. Instead, they often consist of distinguishable parts, hierarchical units, or well-typed data structures. The same goes for the DNA in biology. It consists of genes, segments of nucleic acid, that contain the information necessary to produce RNA strings in a controlled manner26 .
Such an approach would not only be error-prone, it would also make it very hard to formulate general laws or consolidated findings. It therefore makes sense to distinguish between the search space G and the problem space X. 21 (Search Space). The search space G of a certain optimization problem is the set of elements g on which the search operations of an optimization algorithm work. In dependence on genetic algorithms, we often refer to the search space synonymously as genome 24 , a term coined by the German biologist Winkler [39] as a portmanteau of the words gene and chromosome [40].