Competent genetic algorithms for weighing matrices

Authors:
I. S. Kotsireas;C. Koukouvinos;P. M. Pardalos;D. E. Simos
Affiliations:
Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Canada N2L 3C5;Department of Mathematics, National Technical University of Athens, Athens, Greece 15773;Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA;Department of Mathematics, National Technical University of Athens, Athens, Greece 15773
Venue:
Journal of Combinatorial Optimization
Year:
2012

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Abstract

In this paper, we demonstrate that the search for weighing matrices constructed from two circulants can be viewed as a minimization problem together with two competent genetic algorithms to locate optima of an objective function. The motivation to deal with the messy genetic algorithm (mGA) is given from the pioneering results of Goldberg, regarding the ability of the mGA to put tight genes together in a solution which points directly to structural patterns in weighing matrices. In order to take into advantage certain properties of two ternary sequences with zero autocorrelation we use an adaptation of the fast messy GA (fmGA) where we combine mGA with advanced techniques, such as thresholding and tie-breaking. This transformation of the weighing matrices problem to an instance of a combinatorial optimization problem seems to be promising, since we resolved two open cases for weighing matrices as these are listed in the second edition of the Handbook of Combinatorial Designs.