Genetic algorithms for the construction of Hadamard matrices with two circulant cores

Abstract Genetic Algorithms are a class of powerful combinatorial optimization methods that exploit algorithmic analogs of concepts from the Theory of Evolution. Genetic Algorithms have been applied successfully to a wide range of difficult optimization problems across many areas of scientific research. In this paper we apply for the first time Genetic Algorithms to the construction of Hadamard matrices with two circulant cores. An important novel aspect of our approach is the choice of the objective functions, which is done based on an algebraic formalism of the two circulant core construction. We implemented several Genetic Algorithms based on these objective functions and constructed Hadamard matrices of orders 52, 56, 60 and 64.