A biased random-key genetic algorithm for the Steiner triple covering problem

We present a biased random-key genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used to evaluate solution procedures for this problem. The new covers for instances A(405) and A(729) have sizes 335 and 617, respectively. On all other smaller instances our algorithm consistently produces covers of optimal size.