Chaotic populations in genetic algorithms

We set two objectives for this study: one is to emulate chaotic natural populations in GA (Genetic Algorithms) populations by utilizing the Logistic Chaos map model, and the other is to analyze the population fitness distribution by utilizing insect spatial distribution theory. Natural populations are so dynamic that one of the first experimental evidences of Chaos in nature was discovered by a theoretical ecologist, May (1976, Nature, 261,459–467) [30], in his analysis of insect population dynamics. In evolutionary computing, perhaps influenced by the stable or infinite population concepts in population genetics, the status quo of population settings has dominantly been the fixed-size populations. In this paper, we propose to introduce dynamic populations controlled by the Logistic Chaos map model to Genetic Algorithms (GA), and test the hypothesis – whether or not the dynamic populations that emulate chaotic populations in nature will have an advantage over traditional fixed-size populations.The Logistic Chaos map model, arguably the simplest nonlinear dynamics model, has surprisingly rich dynamic behaviors, ranging from exponential, sigmoid growth, periodic oscillations, and aperiodic oscillations, to complete Chaos. What is even more favorable is that, unlike many other population dynamics models, this model can be expressed as a single parameter recursion equation, which makes it very convenient to control the dynamic behaviors and therefore easy to apply to evolutionary computing. The experiments show result values in terms of the fitness evaluations and memory storage requirements. We further conjecture that Chaos may be helpful in breaking neutral space in the fitness landscape, similar to the argument in ecology that Chaos may help the exploration and/or exploitation of environment heterogeneity and therefore enhance a species’ survival or fitness.

Graphical abstractMean Fitness vs. Population Size- and Mean Fitness Crowding for a Chaotic Population, Z. S. Ma, Applied Soft Computing.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Natural populations are dynamic, should the populations in evolutionary computing be dynamic too? ► We introduced ecological population dynamics theory to evolutionary computing. ► Logistic chaos map model was used to control the population size in genetic algorithms. ► Chaotic populations were found to outperform fixed-size populations significantly (approximately half search time). ► Fitness distribution was found to follow Taylor's power law.