A Bit-Parallel Tabu Search Algorithm for Finding E(s2)-Optimal and Minimax-Optimal Supersaturated Designs

Abstract

We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, and s_max = 4t + i, where i ∈ {0, 2} and t ∈ ℤ^≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most (N + 4t + i)/4 points. Using this equivalence, we formulate the search for two-symbol E(s²)-optimal and minimax-optimal SSDs with s_max ∈ {2, 4, 6} as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found E(s²)-optimal and minimax-optimal SSDs achieving the sharpest known E(s²) lower bound with s_max ∈ {2, 4, 6} of sizes (N, m) = (16, 25), (16, 26), (16, 27), (18, 23), (18, 24), (18, 25), (18, 26), (18, 27), (18, 28), (18, 29), (20, 21), (22, 22), (22, 23), (24, 24), and (24, 25). In each of these cases, no such SSD could previously be found.