Creation of a Sorting Network for Seven Items Using Only 16 Steps
(A Human-Competitive Result Produced by Genetic Programming)
Genetic programming evolved sorting network for seven items using only 16 steps as described in Sections 21.4.4, 23.6, and 57.8.1 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999).
The sorting network evolved in chapter 21 of Genetic Programming III: Darwinian Invention and Problem Solving (Koza, Bennett, Andre, and Keane 1999) using the Genetic Programming Problem Solver (GPPS 1.0), the solution evolved in Chapter 23 using GPPS 2.0, and the solution evolved in Chapter 57 using field-programmable gate arrays are all superior to that presented by the inventors of sorting networks in their 1962 patent (O'Connor and Nelson 1962). Specifically, the 16-step seven-sorter evolved using GPPS has two fewer steps than the sorting network described in the 1962 patent. In fact, GPPS rediscovered what Floyd and Knuth (Knuth 1973) discovered several years after the 1962 patent, namely, that 16 steps are sufficient for a sorting network for seven items. That is, genetic programming evolved a solution here that is better than that devised by the inventors of sorting networks (O'Connor and Nelson) and equal to that devised by two well-known subsequent human researchers of computer algorithms (Floyd and Knuth).
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 sorting network for seven items using only 16 steps 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 publishable in its own right as a new scientific result (independent of the fact that the result was mechanically created).
Knuth, Donald E. 1973. The Art of Computer Programming. Vol.3. Reading, MA: Addison-Wesley.
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.
O'Connor, Daniel G.; and Nelson, Raymond J. 1962. Sorting System with N-Line Sorting Switch. U.S. Patent 3,029,413. Issued April 10, 1962.
· The home page of Genetic Programming Inc. at www.genetic-programming.com.
· For information about the field of genetic programming and the field of genetic and evolutionary computation, visit www.genetic-programming.org
· For information about John Koza’s course on genetic algorithms and genetic programming at Stanford University
· Information about the 1992 book Genetic Programming: On the Programming of Computers by Means of Natural Selection, the 1994 book Genetic Programming II: Automatic Discovery of Reusable Programs, the 1999 book Genetic Programming III: Darwinian Invention and Problem Solving, and the 2003 book Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Click here to read chapter 1 of Genetic Programming IV book in PDF format.
· 3,440 published papers on genetic programming (as of November 28, 2003) in a searchable bibliography (with many on-line versions of papers) by over 880 authors maintained by William Langdon’s and Steven M. Gustafson.
· For information on the Genetic Programming and Evolvable Machines journal published by Kluwer Academic Publishers
· For information on the Genetic Programming book series from Kluwer Academic Publishers, see the Call For Book Proposals
· For information about the annual Genetic and Evolutionary Computation (GECCO) conference (which includes the annual GP conference) to be held on June 26–30, 2004 (Saturday – Wednesday) in Seattle and its sponsoring organization, the International Society for Genetic and Evolutionary Computation (ISGEC). For information about the annual Euro-Genetic-Programming Conference to be held on April 5-7, 2004 (Monday – Wednesday) at the University of Coimbra in Coimbra Portugal. For information about the 2003 and 2004 Genetic Programming Theory and Practice (GPTP) workshops held at the University of Michigan in Ann Arbor. For information about Asia-Pacific Workshop on Genetic Programming (ASPGP03) held in Canberra, Australia on December 8, 2003. For information about the annual NASA/DoD Conference on Evolvable Hardware Conference (EH) to be held on June 24-26 (Thursday-Saturday), 2004 in Seattle.
Last updated on December 28, 2003