This paper considers the problem of computing an optimal trajectory for an\nautonomous system that is subject to a set of potentially conflicting rules.\nFirst, we introduce the concept of prioritized safety specifications, where\neach rule is expressed as a temporal logic formula with its associated weight\nand priority. The optimality is defined based on the violation of such\nprioritized safety specifications. We then introduce a class of temporal logic\nformulas called $\\textrm{si-FLTL}_{\\mathsf{G_X}}$ and develop an efficient,\nincremental sampling-based approach to solve this minimum-violation planning\nproblem with guarantees on asymptotic optimality. We illustrate the application\nof the proposed approach in autonomous vehicles, showing that\n$\\textrm{si-FLTL}_{\\mathsf{G_X}}$ formulas are sufficiently expressive to\ndescribe many traffic rules. Finally, we discuss practical considerations and\npresent simulation results for a vehicle overtaking scenario.\n