Constructing cyclic PBIBD(2)s through an optimization approach: Thirty‐two new cyclic designs

Abstract

Abstract:We formulate the construction of cyclic partially balanced incomplete block designs with two associate classes (PBIBD(2)s) as a combinatorial optimization problem. We propose an algorithm based on tabu search to tackle the problem. Our algorithm constructed 32 new cyclic PBIBD(2)s. #

Complete Mixed Doubles Round Robin Tournaments

“…Most of the examples were found using an Embarcadero Delphi XE program, available from the second author. The program fixes the partnerships and then exchanges them between games in a tabu search algorithm that seeks to optimize the opposition pairs incidence matrix (see [14]). The examples will be used in the next section as the basis of our recursive construction.…”

“…Finally we can use Theorems 3.4 and 3.6 to handle special cases for n < 32 and give our main result. Theorem 3.8 There exists a CMDRR(n, k) for each n ≥ 2, k ≤ n, and n−k even, except for (n, k) = (2, 2), (3, 3), (4, 2), (6,6) and possibly excepting the following 31 values: (n, k) = (5, 3), (6, 2), (12, 2), (12,6), (12,8), (13,3), (13, 7), (14, 2), (14,6), (15,3), (15,7), (15,9), (16,2), (16,10) Resolvability of a CMDRR is more difficult to ensure. By filling holes in an HSOLSSOM we can construct resolvable CMDRR.…”