Abstract
We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.
Highlights
Philosophy of determinism comes from the development of classic mechanic that was originally established and studied by Isaac Newton, Pierre-Simon Laplace, Gottfried Wilhelm Leibniz, and so forth
We propose using CE algorithm framework to implement a new interactive evolutionary computation (EC) (IEC) algorithm, interactive chaotic evolution (ICE)
The population size of the algorithms is 20 and we evaluate them with 20 generations to simulate the characteristic of IEC algorithms, that is, with less population size and less generation
Summary
Philosophy of determinism comes from the development of classic mechanic that was originally established and studied by Isaac Newton, Pierre-Simon Laplace, Gottfried Wilhelm Leibniz, and so forth. Inspired from chaotic motion of nonlinear system that has an ergodicity property, a chaotic ergodicity based EC algorithm, chaotic evolution, was proposed and studied recently [6] It simulates the chaotic motion in a search space for implementing optimization. If the ICE algorithm can present significantly optimization performance compared to other paired comparison-based IEC algorithms, such as interactive differential evolution (IDE) [12] or its variations [13], ICE can be a practical algorithm implementation in IEC framework and enrich IEC algorithm family. We will investigate this subject in this paper.
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