The logic relationship among equality and inequality constraints in a standard constrained optimization problem (SCOP) is only logic AND, however in a generalized constrained optimization problem (GCOP) it contains not only logic AND but also logic OR.GCOP is also known as disjunctive programming problem.The rate-monotonic (RM) optimal problem is an important instance of GCOP.Existing methods for the RM optimal problem include function transformation, mixed integer programming and linear programing search.But all these methods are not efficient enough with the increase of task volume.A linear programming based hybrid search (LPHS) method is proposed in this paper.First GCOP problem is partitioned into linear problemming sub-problems, and a linear search tree is constructed.Next, this tree is searched by the strategy of mixing depth-first-search and breadth-first-search, and an efficient pruning method is used during search progress.Then, the optimal solution is achieved.Experimental results illustrate that LPHS method is much more efficient than others.This work is related to satisfiability modulo therories (SMT), and is expected to improve the efficiency of SMT solvers and to promote applications of SMT in software verification, symbolic excecution and other fields.