Circulant weighing matrices: a demanding challenge for parallel optimization metaheuristics

Abstract

Circulant weighing matrices constitute a special type of combinatorial matrices that have attracted scientific interest for many years. The existence and determination of specific classes of circulant weighing matrices remains an active research area that involves both theoretical algebraic techniques as well as high-performance computational optimization approaches. The present work aims at investigating the potential of four established parallel metaheuristics as well as a special Algorithm Portfolio approach, on solving such problems. For this purpose, the algorithms are applied on a hard circulant weighing matrix existence problem. The obtained results are promising, offering insightful conclusions.