Researchers have faced numerous challenges while designing WSNs and protocols in many applications such as object tracking in military, detection of disastrous events, environment and health monitoring etc. Amongst all sustaining connectivity and capitalizing on the network lifetime is a serious deliberation. To tackle these two problems, Mobile Wireless Sensor Networks (MWSNs) is a better choice. In MWSN, Sensor nodes move freely to a target area without the need for any special infrastructure. Due to mobility, the routing process in MWSN has become more complicated as connections in the network can change dynamically. In this paper, the authors put forward an Evolutionary Mobility aware multi-objective hybrid Routing Protocol for heterogeneous wireless sensor networks (EMRP). EMRP uses two-level hierarchical clustering. EMRP selects the optimal path from source to sink using multiple metrics such as Average Energy consumption, Control Overhead, Reaction Time, LQI, and HOP Count. The authors study the influence of energy heterogeneity and mobility of sensor nodes on the performance of EMRP. The Performance of EMRP compared with Simple Hybrid Routing Protocol (SHRP) and Dynamic Multi-Objective Routing Algorithm (DyMORA) using metrics such as Average Residual Energy (ARE), Delay and Normalized Routing Load. EMRP improves AES by a factor of 4.93% as compared to SHRP and 5.15% as compared to DyMORA. EMRP has a 6% lesser delay as compared with DyMORA.