Abstract
Random mechanisms including mutations are an internal part of evolutionary algorithms, which are based on the fundamental ideas of Darwin’s theory of evolution as well as Mendel’s theory of genetic heritage. In this paper, we debate whether pseudo-random processes are needed for evolutionary algorithms or whether deterministic chaos, which is not a random process, can be suitably used instead. Specifically, we compare the performance of 10 evolutionary algorithms driven by chaotic dynamics and pseudo-random number generators using chaotic processes as a comparative study. In this study, the logistic equation is employed for generating periodical sequences of different lengths, which are used in evolutionary algorithms instead of randomness. We suggest that, instead of pseudo-random number generators, a specific class of deterministic processes (based on deterministic chaos) can be used to improve the performance of evolutionary algorithms. Finally, based on our findings, we propose new research questions.
Highlights
Chaos is a broad term that refers to dynamical phenomena showing random-like behaviors at a first glance, even if they are generated by deterministic systems
This paper focuses on using deterministic chaos to produce N periodic sequences, which are used in evolutionary algorithms instead of pseudorandom number generators or just pure deterministic chaos series
The first category examines how the existence of periodicity generated by deterministic chaos systems is influenced by computation precision, while the second one employs periodical time series generated by chaotic systems inside evolutionary algorithms (EAs) and compared with the same EAs powered by pseudo-random number generators (PRNGs)
Summary
Chaos (deterministic chaos) is a broad term that refers to dynamical phenomena showing random-like behaviors at a first glance, even if they are generated by deterministic systems. A research study, especially a theoretic one, dealing with how much the performance of different algorithms depends on different levels of chaotic dynamics has not yet been satisfactorily developed For these reasons, this work was created, which aims to point out how much the performance of the evolutionary algorithm depends on the modified chaotic dynamics, which is used inside the algorithm instead of a pseudo-random number generator. This research raises interesting research questions that suggest an interpretation of evolutionary algorithms on the level of discrete dynamic systems with feedback and allow the use of the theoretical mathematical apparatus of cybernetics to analyze and describe it This could explain why chaos has a positive effect on the performance of evolutionary algorithms. The results are discussed and summarized in the section Conclusions
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