With the widespread deployment and popular usage of wireless networks, various wireless access network technologies are being developed. Taking advantages of these access network technologies will be able to offer a lot of possibilities for increasing bandwidth, accessing the Internet, and expanding the service range. For supporting interoperability between a variety of access network technologies, one of the major challenges is the creation of a new handoff protocol across heterogeneous networks. Because a mobile host with multiple network interfaces simultaneously has more than one available access network, a new handoff protocol should perform to discover RAN (Radio Access Network) and select the optimal RAN among found RANs. We present four RAN selection schemes to discover and choose the optimal RAN. These four schemes are simple, easy to implement and generic solutions for vertical and horizontal handoff. Four selection schemes discover available access networks utilizing a static/dynamic period or a CAN (Candidate Access Network) without the help of centralized servers, thereby removing unnecessary power consumption without QoS (Quality of Service) degradation. After implementing a simulator for the wireless overlay network composed of a different type of networks, we evaluated four selection schemes to observe the achieved bandwidth, number of handoffs and total amount of power consumption using our simulator. Results show that the usage of a dynamic period or a CAN reduces large amount of power consumption without degrading achieved bandwidth.