1. Title:
PRIMARY ENTRY
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Evolving Chua's Circuit Topology Using Genetic Algorithm
BACKGROUND AND SUPPORTING PAPERS
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A. Rak, G. Gandhi, and Gy. Cserey, "Chua's circuit topology evolution using genetic algorithm," International Journal of Bifurcation and Chaos, vol. 20, no. 3, pp. 687-696, 2010.
2. Authors:
AUTHORS FOR PRIMARY ENTRY
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Adam Rak:
Physical Address:
Faculty of Information Technology, Pazmany Peter Catholic University, Budapest, Prater u. 50/a. 1083, Hungary.
E-mail: rakad@itk.ppke.hu
Gaurav Gandhi:
Physical Address:
A-1/283, Janakpuri, New Delhi, India -110058.
Email: respondgaurav@gmail.com
Gyorgy Cserey:
Physical Address:
Faculty of Information Technology, Pazmany Peter Catholic University, Budapest, Prater u. 50/a. 1083, Hungary.
Email : cserey@itk.ppke.hu
3. Corresponding author:
AUTHOR FOR CORRESPONDENCE
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Gaurav Gandhi (Email: respondgaurav@gmail.com)
4. Abstract for Primary entry
ABSTRACT
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In this paper, a novel approach of using genetic algorithm towards realization of Chua's circuit is presented. The paper demonstrates the use of genetic algorithm to evolve Chua's circuit from a set of given passive and active components. More than a dozen of the evolved designs are demonstrated to work satisfactorily in simulation. The evolved designs are found to be human competitive and are also demonstrated to work in a laboratory set up.
5. Criteria
CRITERIA THAT THE WORK SATISFIES
(A) The result was patented, as an invention in the past, is an improvement over a patented invention, or would qualify today as a patentable new invention.
(B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal.
(D) The result is publishable in its own right as a new scientific result independent of the fact that the result was mechanically created.
(E) The result is equal to or better than the most recent human-created solution to a long-standing problem for which there has been a succession of increasingly better human-created solutions.
(F) The result is equal to or better than a result that was considered an achievement in its field at the time it was first discovered.
6. A statement stating why the result satisfies the criteria
Analog circuit designing follows the approach of "Linearize and Analyze" which isn't true in the realms of non-linear system design. Chaotic systems work in non-linear and chaotic regime, a state where the dynamical system is highly sensitive to initial conditions, making them much harder to design and humanly comprehend. This makes the problem of designing chaotic circuits as a whole an even more complex problem than that of analog design.
In circuit theory, Chua's circuit, invented by Prof. Leon Chua in 1983, has been described as a paradigm for chaos. With applications ranging from cryptography to chaotic music, Chua's circuit has attracted the attention of circuit designers as well. However, since its inception 27 years ago, there are only around a dozen and half different implementations of Chua's circuit reported in the literature. Most of these designs have similar topologies because Chua's diode, a key element of Chua's circuit, is nonlinear and does not have a set recipe to design.
Till now all the Chua's circuits reported so far were made by humans and no one thought of automating the task by a machine. One reason for this can be that in order to evolve Chua's circuit, a rigorous analysis of its time series is required and the lack of necessary and sufficient condition for a system to exhibit chaos might have stopped researchers to attempt the same. Thus designing a novel topology for a chaotic circuit, including a highly studied Chua's circuit (http://www.eecs.berkeley.edu/~chua/circuitrefs.html) is a very difficult problem for humans.
In our work SPICE based software that uses Genetic Algorithm (GA) has been used to invent a series of Chua's circuit topologies. It is the largest family of different Chua's circuit designed using discrete passive and active elements. Almost all the invented designs were unique and were topologically patentable. These topologies are findings of evolutionary algorithm and some of them are not even anticipated by human intuitive thinking.
All the evolved designs were simulated on SPICE and their results were found to be in agreement with the theory. Some of them were even breadboarded and results of chaotic simulations were seen on Oscilloscope, thereby proving the validity of evolutionary approach to Chua's circuit designing.
Further in comparison to human ways of thinking which at times takes days to implement, the presented algorithm has evolved more than a dozen novel topologies for Chua's circuit in less than 24 hours on a single (Intel Xeon HyperThread, 3.4 GHz, 2 GB RAM) machine.
The current work is a perfect example of how evolutionary machine approach can aid human designers in designing systems limited by their intuitive ways of thinking.
Future work:
The designed SPICE based software is a general tool to evolve nonlinear resistor using any linear building block. In the present research, it has only been used to design a specific non-linearity of Chua's diode. It can be created as a push-button invention tool to invent topologies with defined nonlinear V-I characteristics.
Interestingly, the current work can be easily clubbed with the following mentioned work (which incidentally won HUMIES - 2006) to evolve a whole new set of patentable novel topologies of Chua's circuit
V. Aggarwal, "Evolving Sinusoidal Oscillators Using Genetic Algorithms", in Proc., The 2003 NASA/DoD Conference on Evolvable Hardware, Chicago, USA, 2003, pp. 67-76.
Another direction for future work can be in the field of nonlinear analog circuits, which are difficult to achieve using human way of thinking.
Why the result satisfies the criteria that the contestant claims
In view of the preceding assertions, the result satisfies the following criteria:
(A) The result was patented, as an invention in the past, is an improvement over a patented invention, or would qualify today as a patentable new invention.
(The significance of the results is evident by the fact that a topology of Chua's circuit using human intuitive way of thinking has been patented in the past by one of the authors (refer US Patent No. 7119640). In present case all the evolved topologies were novel and some of them are like improvement on the patented design and are themselves patentable.)
(B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal.
(The significance of the result is evident by the fact that invention of different Chua's circuits with the features mentioned has been published in International Journal of Bifurcation and Chaos.)
(D) The result is publishable in its own right as a new scientific result ¾ independent of the fact that the result was mechanically created.
(This paper has been accepted in International Journal of Bifurcation and Chaos, which is not concerned with the method of synthesizing chaotic circuits, but for its value in enhancing the state-of-art in chaotic systems and circuit designs.)
(E) The result is equal to or better than the most recent human-created solution to a long-standing problem for which there has been a succession of increasingly better human-created solutions.
(Chaotic circuit design is one of the hardest problems in circuit design and requires a complete different mindset. Chua's circuit, considered as a paradigm of chaos, has attracted circuit designers in recent past. However the limitations of human intuitive ways of thinking lead to almost similar circuit topologies for designed Chua's circuit.
Invention of several Chua's circuits using evolutionary algorithm is a significant leap in the field. There is no other larger catalogue of topologically patentable Chua's circuit designs using evolutionary approach. The development of some of these designs on breadboard and observing the behavior on oscilloscope proves the validity of evolved designs. )
(F) The result is equal to or better than a result that was considered an achievement in its field at the time it was first discovered.
(Evident in the points mentioned above)
7. Full citation of paper
A. Rak, G. Gandhi, and Gy. Cserey, "Chua's circuit topology evolution using genetic algorithm," International Journal of Bifurcation and Chaos, vol. 20, no. 3, pp. 687-696, 2010.
8. Prize Money Division:
The prize money, if any, is to be divided equally among the co-authors.
9. Why 'best' in comparison of other entries:
Even a simple nonlinear effect in a circuit sometimes gives jitters to the people skilled in the art of designing circuits. People skilled in the art understand that the evolution of several Chua's circuits in few hours using automation is an achievement in itself. However, we would like to mention the following points to prove why is our work 'best' in comparison to other entries.
(a) The entry solves the problem of Chua's circuit design, which was considered an art by designers and has never been automated. It makes a first attempt to automate the task and is able to evolve several novel Chua's circuit designs using different discrete active and passive blocks in few hours. Note that the literature has reported an equal number of novel designs topologies of Chua's circuit in last two decades as what has been achieved in few hours using automation.
(b) All the inventions are completely new, state-of-art and are topologically patentable.
(c) Rigorous simulations and practical design in the lab back the results, thereby making them useful for both academic study as well as industrial use.
(d) Many of these designs are interpretable and comprehensible and yet do not follow the set approach described in literature to design Chua's diode. This makes the present entry as a perfect case of how evolutionary machine approach can aid circuit designers in designing systems limited by their intuitive ways of thinking.