2 research outputs found
A Heuristic Procedure with Guided Reproduction for Constructing Cocyclic Hadamard Matrices
A genetic algorithm for constructing cocyclic Hadamard matrices
over a given group is described. The novelty of this algorithm is
the guided heuristic procedure for reproduction, instead of the classical
crossover and mutation operators. We include some runs of the algorithm
for dihedral groups, which are known to give rise to a large amount of
cocyclic Hadamard matrices.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM–296Junta de Andalucía P07-FQM-0298
Searching for partial Hadamard matrices
Three algorithms looking for pretty large partial Hadamard ma-
trices are described. Here “large” means that hopefully about a third of a
Hadamard matrix (which is the best asymptotic result known so far, [8]) is
achieved. The first one performs some kind of local exhaustive search, and
consequently is expensive from the time consuming point of view. The second
one comes from the adaptation of the best genetic algorithm known so far
searching for cliques in a graph, due to Singh and Gupta [21]. The last one
consists in another heuristic search, which prioritizes the required processing
time better than the final size of the partial Hadamard matrix to be obtained. In
all cases, the key idea is characterizing the adjacency properties of vertices in a
particular subgraph Gt of Ito’s Hadamard Graph (4t) [18], since cliques of
order m in Gt can be seen as (m + 3) × 4t partial Hadamard matrices.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM-016Junta de Andalucía P07-FQM-0298