Nine selection‐survival strategies were implemented in a genetic algorithm experiment, and differences in terms of evolution were assessed. The moments of evolution (expressed as generation numbers) were recorded in a contingency of three strategies (i.e., proportional, tournament, and deterministic) for two moments (i.e., selection for crossover and mutation and survival for replacement). The experiment was conducted for the first 20,000 generations in 46 independent runs. The relative moments of evolution (where evolution was defined as a significant increase in the determination (...) coefficient relative to the previous generation) when any selection‐survival strategy was used fit a Log‐Pearson type III distribution. Moreover, when distributions were compared to one another, functional relationships were identified between the population parameters, revealing a degeneration of the Log‐Pearson type III distribution in a one‐parametrical distribution that can be assigned to the chosen variable—evolution strategy. The obtained theoretical population distribution allowed comparison of the selection‐survival strategies that were used. © 2012 Wiley Periodicals, Inc. Complexity, 2012. (shrink)

The case of ungapped alignment of two literal sequences under constrains is considered. The analysis lead to general formulas for probability mass function and cumulative distribution function for the general case of using an alphabet with a chosen number of letters in the expression of the literal sequences. Formulas for three statistics including mean, mode, and standard deviation were obtained. Distributions are depicted for three important particular cases: alignment on binary sequences, alignment of trinomial series, and alignment of genetic sequences. (...) A particular case when sequences contain each letter of the alphabet at least once in both sequences has also been analyzed and some statistics for this restricted case are given. (shrink)