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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 glassydoi:10.1103/physrevlett.88.188701 pmid:12005728 fatcat:lbqrp62sgjhlrjf5bhnamgzgyi