A simulation study for the distribution law of relative moments of evolution

Abstract

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.

Supervised Evolution: Research Concerning the Number of Evolutions that Occur Under Certain Constraints

“…In this research, the maximum likelihood estimation (MLE) was applied to obtain population's parameter for the Weibull distribution. Verify the linearity between parameters of Weibull distribution. This step was introduced as dependence between parameters of probability distribution function was previously identified . Optimize the parameters and test the agreement between the new models and observation using Kolmogorov‐Smirnov , Anderson‐Darling , and Chi‐squared statistics, whenever linearity exists. Evaluate the overall agreement of linearity with F‐C‐S . Compare selection strategies, survival strategies, and selection‐survival strategies in terms of differences between speciation produced by a certain strategy and speciation produced by another strategy.…”

“…Generally, the algorithm effectiveness (speed required to achieve the imposed objective function), mutation, and cross‐operators have been investigated and reported , besides identification of the optimum solution . Furthermore, some studies related to genetic algorithms were conducted regarding the correlation coefficient , evolution , validation of number of genotypes present in the generations when an evolution occurred , and assessment of the distribution law for the relative moments of evolution .…”