More and more wireless mobile sensor networks are employed by robotics to perform harsh tasks such as disaster rescue, emission sources localization or hazardous contaminants localization. There are a lot of network optimization problems to be solved in the protocol design of wireless mobile sensor networks (WMSN), such as rate control, flow control, congestion control, medium access control, queue management, power control and topology control etc. These issues involve several layers of the network protocol stack so that it's quite difficult to consider every single optimization problem of them in a holistic view. The majority of contemporary research works mainly deal with one or some of them in terms of certain applications or objectives. However, most of the proposed protocols are based on simulations or experiments which lack of sufficient mathematical or theoretical analysis to fully understand the convergence or stability. In order to study the theoretical basis of network algorithms, this paper briefly outlines the current methodologies exploited to design and optimize the performance of sensor networks. In addition, the paper investigates the theoretical aspects to make sense of the network optimization algorithms and give a survey mainly in terms of convex optimization, game theory and artificial intelligence