A Theoretical Framework of Natural Computing - M Good Lattice Points (GLP) Method

This paper analyses several currently used computing methods inspired by the nature and concludes their common properties and their disadvantages. It then proposes a more abstract computing model inspired by the nature according to theoretical results on number theory. We also present a good lattice points method based on the number theory for problem solving, of which the discrepancy of the new method is minimized in the sense when the number of points are fixed. This method is dimensional independent and can be used to solve high dimensional problems. A typical algorithm is proposed to apply Genetic Algorithm and Immume Algorithm. Some comparable examples are given to show the advantages of our new method.

[1]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[2]  Alan F. Murray,et al.  IEEE International Conference on Neural Networks , 1997 .

[3]  Philipp Slusallek,et al.  Introduction to real-time ray tracing , 2005, SIGGRAPH Courses.

[4]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[5]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[6]  Jonathan Timmis,et al.  Artificial immune systems - a new computational intelligence paradigm , 2002 .

[7]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[8]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[9]  J. Kiefer.  On large deviations of the empiric D. F. of vector chance variables and a law of the iterated logarithm. , 1961 .

[10]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[11]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[12]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.