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A Gpu Accelerated Genetic Algorithm For The Construction Of Hadamard Matrices, Andras Balogh, Raven Ruiz
A Gpu Accelerated Genetic Algorithm For The Construction Of Hadamard Matrices, Andras Balogh, Raven Ruiz
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
We use a genetic algorithm to construct Hadamard Matrices. The initial population of random matrices is generated to have a balanced number of +1 and −1 entries in each column except the first column with all +1. Several fitness functions are implemented in order to find the most effective one. The crossover process creates offspring matrix population by exchanging columns of the parent matrix population. The mutation process flips +1 and −1 entry pairs in random columns. The use of CuPylibrary in Python on graphics processing units enables us to handle populations of thousands of matrices and matrix operations in …
A Gpu Accelerated Genetic Algorithm For The Construction Of Hadamard Matrices, Raven I. Ruiz
A Gpu Accelerated Genetic Algorithm For The Construction Of Hadamard Matrices, Raven I. Ruiz
Theses and Dissertations
Hadamard matrices are square matrices with +1 and -1 entries and with columns that are mutually orthogonal. The applications include signal processing and quantum computing. There are several methods for constructing Hadamard matrices of order 2k for every positive integer k. The Hadamard conjecture proposes that there are also Hadamard matrices of order 4k for every positive integer k. We use a genetic algorithm to construct (search for) Hadamard Matrices. The initial population of random matrices is generated to have a balanced number of +1 and -1 entries in each column. Several fitness functions are implemented exploiting …