The aim of this paper is to introduce a general framework for preference-based search in state space graphs with a focus on the search of the preferred solutions. After introducing a formal definition of preference-based search problems, we introduce the PBA ∗ algorithm, a generalization of the A ∗ algorithm, designed to process quasi-transitive preference relations defined over the set of solutions. Then, considering a particular subclass of preference structures characterized by two axioms called Weak Preadditivity and Monotonicity, we establish termination, completeness and admissibility results for PBA ∗ . We also show that previous generalizations of A ∗ are particular instances of PBA ∗ . The interest of our algorithm is illustrated on a preference-based web access problem.