A GPU accelerated Genetic Algorithm for the Construction of Hadamard Matrices

TL;DR

This paper presents a GPU-accelerated genetic algorithm that efficiently constructs Hadamard matrices by leveraging parallel processing capabilities of GPUs with CuPy, enabling handling of large populations and complex matrix operations.

Contribution

It introduces a novel GPU-based genetic algorithm framework for constructing Hadamard matrices, optimizing fitness functions, and utilizing parallel processing for large-scale matrix evolution.

Findings

Successfully constructed Hadamard matrices using GPU acceleration

Achieved large population handling with parallel matrix operations

Demonstrated improved efficiency over traditional methods

Abstract

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 CuPy library in Python on graphics processing units enables us to handle populations of thousands of matrices and matrix operations in parallel.