## 1 Introduction
The G-SEP scheme altered the election probability of selecting the cluster heads by considering the distance, average distance, and residual energy of the advanced nodes. The algorithm further introduced a gateway node at the middle of the network and then installed the BS outside the field. Simulation results using MATLAB R2017a showed that the G-SEP performs better than the Zonal-Stable Election protocol (ZSEP) in terms of coverage, stability period, and extension of the lifetime of the network. Having reviewed the literature related to increasing the network lifetime of WSNs, it is important to note that selecting CHs based on their residual energy of nodes, introducing heterogeneous nodes to strengthen the ability of nodes, introducing multi-hop communication technique to reduce the energy depletion of distant nodes, and implementing energy holes removal mechanism to further conserve the energy of the nodes can remarkably improve the network lifetime. This paper proposes an energy-efficient routing scheme for wireless sensor network. The scheme selects cluster heads based on their residual energies and introduces Heterogeneous nodes to strengthen the homogeneous nodes in the existing scheme. The protocol further employs a multi-hop communication strategy, the effectiveness of which has been proven in [33], and finally implements an energy hole removal scheme to reduce the energy depletion of the nodes. These techniques are employed in this protocol to reduce energy consumption and extend the lifetime of the network. It is important to mention that this paper has been motivated by the work in [25]. Here, MGEAR has been improved using the original homogeneous nodes deployed in all the regions. In this model, the cluster heads are selected based on distance/residual energy, because they were purely homogeneous nodes. This model has been complemented by the scheme proposed in [33], where the authors only employed a gateway node to the Stable Election Protocol (SEP) so that the BS can be repositioned outside the network. Here, distance/average distance and residual energy were also considered while modifying SEP protocol. It is only the homogeneous nodes that capture data and transmit them to the heads which are heterogeneous nodes of the same energy level to the gateway node to the base. No direct transmission has been employed in any part of this network. It has nothing to do with the model used in GMEAR. The proposed model complements the work in the literature in the following four ways. Heterogeneity has been introduced in the existing MGEAR: we have introduced heterogeneous nodes of different energy levels to the existing scheme, especially in regions 3 and 4 which, to the best of our knowledge, have not been employed before. These nodes have higher energy than the homogeneous ones used in the existing scheme and therefore can transmit data effectively for a long period of time
2. Cluster heads are selected based on only residual energy, because heterogeneous nodes are deployed in Regions 3 and 4. These nodes give a better supporting role for long periods and provide a better stability period than the homogeneous nodes deployed in the case of the models in [25; 33]. This is to prevent the weak nodes from being chosen as cluster heads, as they would not transmit data effectively. 3. In the proposed scheme, both the direct and multi-hop communication technique have been employed from Region 4 to the BS, which has not happened in [25; 33]. This technique reduces the energy consumption of the nodes by preventing unnecessary data transmission by the distant nodes to the distant Base station. 4. Energy hole elimination technique has been implemented to prevent nodes from losing their entire energy during data transmission, which none of the models in [25; 33] considered. This is to prevent nodes from transmitting when their energies are below certain threshold. The remainder of the paper is organized as follows.