A mathematical programming approach to the construction of BIBDs

Daisuke Yokoya, Takeo Yamada
2011 International Journal of Computer Mathematics  
BIBD (balanced incomplete block design) is instrumental in design of experiments. This is usually constructed using algebraic tools such as finite projective (or affine) algebra or difference sets. Recently, heuristic algorithms have been tried, including artificial neural networks, simulated annealing, and various local search methods. In this paper, we present a novel approach to construct BIBDs that makes use of MIP (mixed integer programming) solvers. Based on this, branch-and-bound and
more » ... search algorithms are given, and these are compared against the local search method presented by a previous researcher. Keywords: BIBD (balanced incomplete block design); MIP (mixed integer programming problem); branch-and-bound method; tabu search
doi:10.1080/00207160.2010.492869 fatcat:eq4libfdxfh4liizczrf57qn6i