New Bounds for Ternary Covering Arrays Using a Parallel Simulated Annealing

A covering array (CA) is a combinatorial structure specified as a matrix of N rows and k columns over an alphabet on v symbols such that for each set of t columns every t-tuple of symbols is covered at least once. Given the values of t, k, and v, the optimal covering array construction problem (CAC) consists in constructing a CA (N; t, k, v) with the minimum possible value of N. There are several reported methods to attend the CAC problem, among them are direct methods, recursive methods, greedy methods, and metaheuristics methods. In this paper, There are three parallel approaches for simulated annealing: the independent, semi-independent, and cooperative searches are applied to the CAC problem. The empirical evidence supported by statistical analysis indicates that cooperative approach offers the best execution times and the same bounds as the independent and semi-independent approaches. Extensive experimentation was carried out, using 182 well-known benchmark instances of ternary covering arrays, for assessing its performance with respect to the best-known bounds reported previously. The results show that cooperative approach attains 134 new bounds and equals the solutions for other 29 instances.