The proper representation of the search space is the fundamental step in every optimization task, because it has a decisive impact on the quality of potential solutions. In particular, this problem appears when the search spaces are nonstandard and complex, with the large number of candidate solutions that differ from classical forms usually investigated. One of such spaces is the set of continuous-time, homogenous, and stationary Markov processes. They are commonly used to describe biological phenomena, for example, mutations in DNA sequences and their evolution. Because of the complexity of these processes, the representation of their search space is not an easy task but it is important for effective solving of the biological problems. One of them is optimality of mutational pressure acting on protein-coding sequences. Therefore, we described three representations of the search spaces and proposed several specific evolutionary operators that are used in evolutionary-based optimization algorithms to solve the biological problem of mutational pressure optimality. In addition, we gave a general formula for the fitness function, which can be used to measure the quality of potential solutions. The structures of these solutions are based on two models of DNA evolution described by substitution-rate matrices, which are commonly used in phylogenetic analyzes. The proposed representations have been successfully utilized in various issues, and the obtained results are very interesting from a biological point of view. For example, they show that mutational pressures are, to some extent, optimized to minimize cost of amino acid substitutions in proteins.
Keywords: DNA; Markov processes; algorithms; evolutionary optimization; mutation; substitution rate matrix.