Rediscovery of the Cauer (Elliptic) Topology for Filters
(A Human-Competitive Result Produced by Genetic Programming)
Genetic programming evolved the topology for a Cauer (elliptic) filter circuit as described in Section 27.3.7 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999).
The evolved circuit has the elliptic topology that was invented and patented by Wilhelm Cauer.
Wilhelm Cauer of Gottingen, Germany, received three U.S. patents (Cauer 1934, 1935, 1936).
As Cauer explained in U.S. patent 1,989,545 (Cauer 1935),
“One of the objects of this invention is to provide new and improved electric-wave filters, some of them of new types, never known before …“
“It is further an object of my invention to improve upon filters of types already known, to the ends that their efficiency may be improved, their cost of manufacture lessened, and the number of elements, of which they are composed, reduced.”
The Cauer filter was a significant advance (both theoretically and commercially) over the previously known Campbell, Zobel, Johnson, Butterworth, and Chebychev filters. For example, for one commercially important set of specifications for telephones, a fifth-order elliptic filter matches the behavior of a 17th-order Butterworth filter or an eighth-order Chebychev filter. Most pertinently, the fifth-order elliptic filter has one less inductor than the eighth-order Chebychev filter. As Van Valkenburg (1982, page 379) relates in connection with the history of the elliptic filter,
“Cauer first used his new theory in solving a filter problem for the German telephone industry. His new design achieved specifications with one less inductor than had ever been done before. The world first learned of the Cauer method not through scholarly publication but through a patent disclosure, which eventually reached the Bell Laboratories. Legend has it that the entire Mathematics Department of Bell Laboratories spent the next two weeks at the New York Public Library studying elliptic functions. Cauer had studied mathematics under Hilbert at Goettingen, and so elliptic functions and their applications were familiar to him.”
Genetic programming did not, of course, study mathematics under Hilbert or anybody else. The elliptic topology emerged during this run of genetic programming as a natural consequence of the problem's fitness measure and natural selection—not because the run was primed with domain knowledge about elliptic functions. That is, genetic programming opportunistically reinvented the elliptic topology in this run because, as they say, necessity is the mother of invention.
Cauer received a patent for his invention of the elliptic filter because it satisfied the legal criteria for obtaining a U.S. patent, namely, that his filter was "new and useful" and
“…the differences between the subject matter sought to be patented and the prior art are such that the subject matter as a whole would [not] have been obvious at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains. (35 United States Code 103a.)
Referring to the eight criteria in chapter 1 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999) for establishing that an automatically created result is competitive with a human-produced result, the automatic synthesis of the topology for a Cauer (elliptic) filter circuit satisfies the following two 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.
(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.
Cauer, Wilhelm. 1934. Artificial Network. U.S. Patent 1,958,742. Filed June 8, 1928, in Germany. Filed December 1, 1930, in United States. Issued May 15, 1934.
Cauer, Wilhelm.. 1935. Electric Wave Filter. U.S. Patent 1,989,545. Filed June 8, 1928, in Germany. Filed December 6, 1930, in United States. Issued January 29, 1935.
Cauer, Wilhelm.. 1936. Unsymmetrical Electric Wave Filter. U.S. Patent 2,048,426. Filed November 10, 1932, in Germany. Filed November 23, 1933 in United States. Issued July 21, 1936.
Koza, John R., Bennett III, Forrest H, Andre, David, and Keane, Martin A. 1999a. Genetic Programming III: Darwinian Invention and Problem Solving. San Francisco, CA: Morgan Kaufmann.
Van Valkenburg, M. E. 1982. Analog Filter Design. Fort Worth, TX: Harcourt Brace Jovanovich.
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Last updated on December 28, 2003