Reservoir computing has emerged as a powerful and efficient machine learning tool especially in the reconstruction of many complex systems even for chaotic systems only based on the observational data. Though fruitful advances have been extensively studied, how to capture the art of hyper-parameter settings to construct efficient RC is still a long-standing and urgent problem. In contrast to the local manner of many works which aim to optimize one hyper-parameter while keeping others constant, in this work, we propose a global optimization framework using simulated annealing technique to find the optimal architecture of the randomly generated networks for a successful RC. Based on the optimized results, we further study several important properties of some hyper-parameters. Particularly, we find that the globally optimized reservoir network has a largest singular value significantly larger than one, which is contrary to the sufficient condition reported in the literature to guarantee the echo state property. We further reveal the mechanism of this phenomenon with a simplified model and the theory of nonlinear dynamical systems.