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Constructing 1-rotational NRDFs through an optimization approach: new (46,9,8), (51,10,9) and (55,9,8)-NRBDs
Authors:Luis B Morales
Institution:Departamento de Métodos Matemáticos y Numéricos, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, México, DF 04510, México
Abstract:In this paper we formulate the problem of constructing 1-rotational near resolvable difference families as a combinatorial optimization problem where a global optimum corresponds to a desired difference family. Then, we develop an algorithm based on scatter search in conjunction with a tabu search to construct many of these difference families. In particular, we construct three new near resolvable difference families which lead to an equal number of new 1-rotational near resolvable block designs with parameters: (46,9,8), (51,10,9) and (55,9,8). Our results indicate that this conjunction outperforms both scatter search and tabu search.
Keywords:Difference families  Near resolvable block designs  Combinatorial optimization  Scatter and tabu search algorithms
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