The minimized assumption generation has been recognized as an important improvement of the assume-guarantee verification method in order to generate minimal assumptions. The generated minimal assumptions can be used to recheck the whole component-based software at a lower computational cost. The method is not only fitted to component-based software but also has a potential to solve the state space explosion problem in model checking. However, the computational cost for generating the minimal assumption is very high so the method is difficult to be applied in practice. This paper presents an optimization as a continuous work of the minimized assumption generation method in order to reduce the complexity of the method. The key idea of this method is to find a smaller assumption in a sub-tree of the search tree containing the candidate assumptions using the depth-limited search strategy. With this approach, the improved method can generate assumptions with a lower computational cost and consumption memory than the minimized method. The generated assumptions are also effective for rechecking the systems at much lower computational cost in the context of software evolution. An implemented tool supporting the improved method and experimental results are also presented and discussed.