  The quantum approximate optimization algorithm (QAOA) has numerous promising
applications in solving the combinatorial optimization problems on near-term
Noisy Intermediate Scalable Quantum (NISQ) devices. QAOA has a
quantum-classical hybrid structure. Its quantum part consists of a
parameterized alternating operator ansatz, and its classical part comprises an
optimization algorithm, which optimizes the parameters to maximize the
expectation value of the problem Hamiltonian. This expectation value depends
highly on the parameters, this implies that a set of good parameters leads to
an accurate solution. However, at large circuit depth of QAOA, it is difficult
to achieve global optimization due to the multiple occurrences of local minima
or maxima. In this paper, we propose a parameters fixing strategy which gives
high approximation ratio on average, even at large circuit depths, by
initializing QAOA with the optimal parameters obtained from the previous
depths. We test our strategy on the Max-cut problem of certain classes of
graphs such as the 3-regular graphs and the Erd\"{o}s-R\'{e}nyi graphs.
