What is it about?
Finding the best solution is called optimization. We propose a new highly unconventional approach to solve this problem, which could deliver a faster and/or cheaper optimising machine than those currently available. Our approach is based on mathematics of the so-called complex systems and on the phenomenon of dynamical chaos induced by time delay.
Featured Image
Why is it important?
Traditionally, optimization has been done by digital computers, which can be insufficiently fast if the problem is too complex. More recently, much faster quantum computers have been developed, but these are based on expensive and challenging technology and are not easily available. Note that none of the existing methods can guarantee the very best solution out of all possible options, although they can considerably improve the initial guess for a good solution. To solve the same problem, we propose a very different mathematical principle, which could be implemented in faster analog (non-digital) devices, but without expensive quantum technology. Specifically, our approach would give an advantage over algorithm-based tools because it does not require making a new decision at every step based on the outcome of the previous step, where zillions of such steps are needed to achieve a solution. In contrast to algorithmic approaches, in our case almost the whole process is spontaneous, more or less like in a grandfather clock -- only with a more sophisticated design leading to much more complex behavior. This feature makes it similar to quantum computers where the behaviour is also quite spontaneous and for this reason (among others) enables much faster solution than digital computers. However, the device implementing our principle does not need to be quantum, and hence could be much cheaper to make.
Perspectives
Read the Original
This page is a summary of: Optimization with delay-induced bifurcations, Chaos An Interdisciplinary Journal of Nonlinear Science, November 2021, American Institute of Physics,
DOI: 10.1063/5.0058087.
You can read the full text:
Resources
Optimization with delay-induced bifurcations
Open Access article: Natalia B. Janson and Christopher J. Marsden , "Optimization with delay-induced bifurcations", Chaos 31, 113126 (2021) https://doi.org/10.1063/5.0058087
Delay-induced homoclinic bifurcations in modified gradient bistable systems and their relevance to optimization
Open Access article: Natalia B. Janson and Christopher J. Marsden , "Delay-induced homoclinic bifurcations in modified gradient bistable systems and their relevance to optimization", Chaos 31, 093120 (2021) https://doi.org/10.1063/5.0035959 This article explains in more detail mathematical mechanisms behind the optimization principle proposed in the "Optimization with delay-induced bifurcations".
SUPPLEMENTARY NOTE for "Delay-induced homoclinic bifurcations in modified gradient bistable systems and their relevance to optimisation"
This is Supplementary note for: Natalia B. Janson and Christopher J. Marsden , "Delay-induced homoclinic bifurcations in modified gradient bistable systems and their relevance to optimization", Chaos 31, 093120 (2021). It provides some mathematical background behind the analysis of delay-differential equations, specifically stability of fixed points and their bifurcation, and considers an additional example of a system of the same class as the one described in the main paper, only with a different kind of homoclinic bifurcation.
Contributors
The following have contributed to this page