Using Swarm Intelligence to Search for Circulant Partial Hadamard Matrices

Circulant partial Hadamard matrices are useful in many scientific applications, yet the existence of such matrices is not known in general. Some Hadamard matrices of given orders are found via complete enumeration in the literature, but the searches are too computationally intensive when the orders are large. This paper introduces a search method for circulant partial Hadamard matrices by using natural heuristic algorithm. Slightly deviated from the swarm intelligence based algorithm, this method successfully generates a class of circulant partial Hadamard matrices efficiently. A table of circulant partial Hadamard matrices results are given at the end of this paper.

[1]  Mark Stamp,et al.  Unpredictable Binary Strings , 2005 .

[2]  M. Clerc,et al.  Particle Swarm Optimization , 2006 .

[3]  Yuhui Shi,et al.  Particle swarm optimization: developments, applications and resources , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[4]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[5]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

[6]  Weng Kee Wong,et al.  Recent developments in nonregular fractional factorial designs , 2008, 0812.3000.

[7]  Weng Kee Wong,et al.  The need of considering the interactions in the analysis of screening designs , 2009 .

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

[9]  Richard M. Low,et al.  Circulant partial Hadamard matrices , 2013 .

[10]  Leon G. Higley,et al.  Forensic Entomology: An Introduction , 2009 .

[11]  Weng Kee Wong,et al.  The use of nonregular fractional factorial designs in combination toxicity studies. , 2009, Food and chemical toxicology : an international journal published for the British Industrial Biological Research Association.

[12]  Weichung Wang,et al.  Optimizing Latin hypercube designs by particle swarm , 2012, Statistics and Computing.

[13]  K. Horadam.  Hadamard Matrices and Their Applications , 2006 .