Abstract This paper studies the solving of fifinite-domain action planning problems with discrete action costs and soft constraints. For sequential optimal planning, a symbolic perimeter database heuristic is addressed in a bucket implementation of A*. For computing net-benefifits, we propose symbolic branch-and-bound search together with some search refifinements. The net-benefifit we optimize is the total benefifit of satisfying the goals, minus the total action cost to achieve them. This results in an objective function to be minimized that is a linear expression over the violation of the preferences added to the action cost total.