The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
OmeGA: A Competent Genetic Algorithm for Solving Permutation and Scheduling Problems
OmeGA: A Competent Genetic Algorithm for Solving Permutation and Scheduling Problems
RapidAccurate Optimization of Difficult Problems Using Fast Messy Genetic Algorithms
Proceedings of the 5th International Conference on Genetic Algorithms
An analysis of the behavior of a class of genetic adaptive systems.
An analysis of the behavior of a class of genetic adaptive systems.
Representations for Genetic and Evolutionary Algorithms
Representations for Genetic and Evolutionary Algorithms
Biased random-key genetic algorithms for combinatorial optimization
Journal of Heuristics
A modified power spectral density test applied to weighing matrices with small weight
Journal of Combinatorial Optimization
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In this paper, we demonstrate that the search for weighing matrices constructed from two circulants can be viewed as a permutation problem. To solve it a set of two competent genetic algorithms (CGAs) are used to locate common integers in two sorted arrays. 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 a recent formalism on the support of two sequences with zero autocorrelation we use an adaptation of the ordering messy GA (OmeGA) where we combine the fast mGA with random keys to represent permutations of the two sequences under investigation. This transformation of the weighing matrices problem to an instance of a combinatorial optimization problem seems to be promising since we illustrate that our framework is capable to solve open cases for weighing matrices as these are listed in the second edition of the Handbook of Combinatorial Designs.