The sensor network localization (SNL) problem is to reconstruct the positions of all the sensors in a network with the given distance between pairs of sensors and within the radio range between them. It is proved that the computational complexity of the SNL problem is NP-hard, and semi-definite programming or second-order cone programming relaxation methods are only able to solve some special problems of this kind. In this study, a stochastic global optimization method called the state transition algorithm is introduced to solve the SNL problem without additional assumptions and conditions of the problem structure. To transcend local optimality, a novel dynamic adjustment strategy called "risk and restoration in probability" is incorporated into the state transition algorithm. An empirical study is investigated to appropriately choose the "risk probability" and "restoration probability", yielding the dynamic state transition algorithm, which is further improved by gradient-based refinement. The dynamic state transition algorithm with refinement is applied to the SNL problem, and satisfactory experimental results have testified the effectiveness of the proposed approach.