论文信息 - Constructing 1-rotational NRDFs through an Optimization Approach : New ( 46 , 9 , 8 )

Constructing 1-rotational NRDFs through an Optimization Approach : New ( 46 , 9 , 8 )

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.

Luis B. Morales | L. B. Morales

[1] Shigeyoshi Tsutsui,et al. Advances in Evolutionary Computing , 2003 .

[2] Steven Furino,et al. Existence results for near resolvable designs , 1995 .

[3] Steven Furino,et al. Frames and Resolvable Designs: Uses, Constructions and Existence , 1996 .

[4] Luis B. Morales,et al. Constructing cyclic PBIBD(2)s through an optimization approach: Thirty‐two new cyclic designs , 2005 .

[5] Carlos Velarde,et al. Enumeration of all (2k + 1;k;k 1)-NRBIBDs for 3 k 13 , 2007 .

[6] Y. Miao,et al. Constructions for rotational near resolvable block designs , 2001 .

[7] Charles J. Colbourn,et al. Resolvable and Near Resolvable Designs , 1996 .

[8] Luis B. Morales,et al. Constructing difference families through an optimization approach: Six new BIBDs , 2000 .

[9] C. Colbourn,et al. CRC Handbook of Combinatorial Designs , 1996 .