The limited energy source used in wireless sensor networks (WSNs) is a crucial aspect when designing a routing protocol. Developing a routing protocol that tries to maximize energy utilization can significantly improve the system's lifetime and balance energy consumption. A novel geometrical-based energy-efficient routing protocol called "EVRP" is presented in this paper. The Cluster generation process is based on the k-means algorithm for nodes grouping. To choose a cluster head (CH) for each cluster, a cost function is calculated for each node considering factors such as remaining energy level for the node, and the mean distance between the node and its neighbors. In the inter-cluster routing phase, a novel geometrical-based routing protocol is introduced considering factors such as the distance to a base station (BS), remaining energy level, and distance between CHs to find the optimal path between BS and CH. The cluster structure is integrated with direct communication in addition to a dynamic clustering mechanism based on the optimum number of CHs and a load balancing mechanism to reduce the load on CHs near BS. The simulation results demonstrate that in different scenarios, the proposed protocol can significantly increase the network lifetime, network throughput, and network stability by 52 %, 45 %, and 30 % respectively compared with the EECRAIFA protocol and by 100 %, 97.6 %, 64.3 % respectively compared with D2CRP protocol.
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