  A major problem in evaluating stochastic local search algorithms for
NP-complete problems is the need for a systematic generation of hard test
instances having previously known properties of the optimal solutions. On the
basis of statistical mechanics results, we propose random generators of hard
and satisfiable instances for the 3-satisfiability problem (3SAT). The design
of the hardest problem instances is based on the existence of a first order
ferromagnetic phase transition and the glassy nature of excited states. The
analytical predictions are corroborated by numerical results obtained from
complete as well as stochastic local algorithms.
