中文摘要：

相对于标准约束优化问题，广义约束优化问题（或称析取优化问题）的等式或不等式约束条件中不仅包含逻辑“与”关系，还含有逻辑“或”关系．单调速率（RM）优化问题是广义约束优化问题的一个重要应用．目前RM优化问题已有的解法包括函数变换、混合整数规划、线性规划搜索等算法．随着任务数的增多，这些算法的求解时间较长．提出一种基于线性规划的深度广度混合搜索算法（LPHS），将广义约束优化问题拆分成若干子问题，建立线性规划搜索树，合理选择搜索顺序，利用动态剪枝算法减小子问题的规模，最终求得最优解．实验结果表明，LPHS算法比其他方法有明显的效率提升．研究成果与计算机基础理论中的可满足性模理论的研究相结合，有助于提高可满足性模理论问题的求解效率，促进该理论在程序验证、符号执行等领域的进一步应用．

英文摘要：

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.