I understand that chaos theory focuses on deterministic chaos, and evolutionary algorithms is stochastic. But are there techniques that apply to both? For instance, when my solution fails to converge are there ways to visualize the system and look for things like attractors that might indicate problems?
Hi Courtney,
In evolutionary algorithms, and more generally in the population based metaheuristic optimization methods, there is a stochastic component needed in order to ensure the exploratory behavior of the algorithm. Usually for this stochastic component some pseudo-random numbers generators (PRNG) are needed in order to simulate the stochastic property. There are different ways to implement the PRNGs, usually based on some recursive equations. I encountered papers where the PRNGs were implemented based on chaotic maps and the authors reported some improved results compared to the traditional PRNGs. As an example, I was able to find quicky, check this link: http://cujse.cankaya.edu.tr/archive/12_1/CUJSE14003.pdf, and also the references at the end of the paper.
For some computation formulations yes, but not in general.
I suggest reading this article:
https://www.researchgate.net/profile/Konrad_Hinsen/publication/304632399_The_Power_to_Create_Chaos/links/57bc4e2308aefea8f0f69640.pdf
Article The Power to Create Chaos
Dear Courtney,
I have worked in both fields. Although you may see some claims in literature, I think the answer is a big NO.
Regards,
Sajad
George,
Thank you. I already have a fully functional evolutionary algorithmic system. For some problems it converges on the global optimum solution. For other problems it won't reliably converge. I'm interested in ways to analyze the performance to find out why it isn't converging. I hoped that chaos theory would have some techniques.
Some global optimization problem are very difficult and cannot be solved with any methods. In my opinion the PRNGs based on chaos are not superior, despite to what other people claim. The only way to get better performance, in my opinion, is to use multi-population methods combined with the power of parallel computing. You can send to me the problems you cannot solve, maybe I can help you with some of my methods.
Look into stochastic resonance. It may not provide a chaotic (infinite period) solution but it may identify periodicities that tie up a nonlinear algorithm with noise and feedback
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