The role of crossover operator in evolutionary-based approach to the problem of genetic code optimization

One of theories explaining the present structure of canonical genetic code assumes that it was optimized to minimize harmful effects of amino acid replacements resulting from nucleotide substitutions and translational errors. A way to testify this concept is to find the optimal code under given criteria and compare it with the canonical genetic code. Unfortunately, the huge number of possible alternatives makes it impossible to find the optimal code using exhaustive methods in sensible time. Therefore, heuristic methods should be applied to search the space of possible solutions. Evolutionary algorithms (EA) seem to be ones of such promising approaches. This class of methods is founded both on mutation and crossover operators, which are responsible for creating and maintaining the diversity of candidate solutions. These operators possess dissimilar characteristics and consequently play different roles in the process of finding the best solutions under given criteria. Therefore, the effective searching for the potential solutions can be improved by applying both of them, especially when these operators are devised specifically for a given problem. To study this subject, we analyze the effectiveness of algorithms for various combinations of mutation and crossover probabilities under three models of the genetic code assuming different restrictions on its structure. To achieve that, we adapt the position based crossover operator for the most restricted model and develop a new type of crossover operator for the more general models. The applied fitness function describes costs of amino acid replacement regarding their polarity. Our results indicate that the usage of crossover operators can significantly improve the quality of the solutions. Moreover, the simulations with the crossover operator optimize the fitness function in the smaller number of generations than simulations without this operator. The optimal genetic codes without restrictions on their structure minimize the costs about 2.7 times better than the canonical genetic code. Interestingly, the optimal codes are dominated by amino acids characterized by polarity close to its average value for all amino acids.