Abstract
This paper discusses the utilization of the complex chaotic dynamics given by the selected time-continuous chaotic systems as well as by the discrete chaotic maps, as the chaotic pseudo-random number generators and driving maps for the chaos based optimization. Such an optimization concept is utilizing direct output iterations of chaotic system transferred into the required numerical range as the replacement of traditional and default pseudo-random number generators, or this concept uses the chaotic dynamics for mapping the search space mostly within the smart hybrid local search techniques. This paper shows totally three groups of complex chaotic dynamics given by chaotic flows, oscillators and discrete maps. Simulations of examples of chaotic dynamics as unconventional generators or mapped to the search space were performed, and related issues like parametric plots, distributions of such a systems, periodicity, and dependency on internally available parameters are brie y discussed in this paper. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Highlights
Speaking, the term "chaos" can denote anything that cannot be predicted deterministically
This paper presents the discussion about the usability of such systems, periodicity, and dependency on accessible internal parameters; the usability as chaotic pseudo random number generator (CPRNG), or for local search and metaheuristic based optimization techniques
In many research works, it was proven that chaos based optimization is very sensitive to the hidden chaotic dynamics driving the CPRNG/mapping the search space
Summary
The term "chaos" can denote anything that cannot be predicted deterministically. The deterministic chaos is a phenomenon that - as its name suggests - is not based on the presence of a random or any stochastic eects. It is evident from the structure of the equations (see the section: Chaotic Optimization) that no mathematical term expressing randomness is present. The seeming randomness in deterministic chaos is related to the extreme sensitivity to the initial conditions [1]. Systems exhibiting deterministic chaos include, for instance, weather, biological systems, many electronic circuits (Chua's circuit), mechanical systems, such as a double pendulum, magnetic pendulum, or so-called billiard problem. The idea of using chaotic systems instead of random processes (pseudo-number generators - PRNGs) has been presented in several research elds and many applications with promising results [2], [3]
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