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It has been a big challenge to develop a routing protocol that can meet different application needs and optimize routing paths according to the topology changes in mobile ad hoc networks. Basing their forwarding decisions only on local topology, geographic routing protocols have drawn a lot of attentions in recent years. However, there is a lack of holistic design for geographic routing to be more efficient and robust in a dynamic environment. Inaccurate local and destination position information can lead to inefficient geographic forwarding and even routing failure. The use of proactive fixed-interval beaconing to distribute local positions introduces high overhead when there is no traffic and cannot capture the topology changes under high mobility. It is also difficult to preset protocol parameters correctly to fit in different environments. In this work, we propose two self-adaptive on-demand geographic routing schemes which build efficient paths based on the need of user applications and adapt to various scenarios to provide efficient and reliable routing. To alleviate the impact due to inaccurate local topology knowledge, the topology information is updated at a node in a timely manner according to network dynamics and traffic demand. On-demand routing mechanism in both protocols reduces control overhead compared to the proactive schemes which are normally adopted in current geographic routing protocols. Additionally, our route optimization scheme adapts the routing path according to both topology changes and actual data traffic requirements. Furthermore, adaptive parameter setting scheme is introduced to allow each node to determine and adjust the protocol parameter values independently according to different network environments, data traffic conditions, and node's own conditions. Our simulation studies demonstrate that the proposed routing protocols are more robust and outperform the existing geographic routing protocol and conventional on-demand routing p- otocols under various conditions including different mobilities, node densities, traffic loads, and destination position inaccuracies. Specifically, the proposed protocols could reduce the packet delivery latency up to 80 percent as compared to GPSR at high mobility. Both routing protocols could achieve about 98 percent delivery ratios, avoid incurring unnecessary control overhead, have very low forwarding overhead and transmission delay in all test scenarios.