## 2 Related Works  
Recently, most of the energy efficient protocols designed for heterogeneous networks are based on the clustering technique [7], which is effective for scalability and energy saving in WSNs. With special advantages related to scalability and efficient communication, clustering provides an efficient and scalable way to design and organize large-scale WSNs for data communication energy efficiency [8]. In a hierarchical architecture, higher energy nodes can be used to process and send the information while low energy nodes can be used to perform the sensing in the proximity of the target. Some of routing protocols in this group include low energy adaptive clustering hierarchy (LEACH) [9], LEACH-C [9], LEACH-M [10], energy-efficient improvement heterogeneous networks protocol (EEIHN) [11], approximate dynamic programming algorithm (ADP) [12] and efficient cluster head selection approach for collaborative data processing (CHSCDP) [13]. In those protocols, the nodes are equipped with the same energy at the beginning, but the networks cannot evolve equally for each node in expending energy, due to the radio communication characteristics, random events such as short-term link failures or the morphological characteristics of the field [14]. However, deployment of sensors in a WSN can be deterministic or random depending on the application. They can be stationary or location-aware, homogeneous or heterogeneous in nature. WSNs are more typically heterogeneous networks than homogeneous ones. The protocols should be fit for the characteristics of heterogeneous wireless sensor networks. Currently, due to the construction of a simple mathematic mode for analyzing the energy consumption and data aggregation, most clustering algorithms assume that the sensor networks are homogeneous, so these algorithms often perform poorly in heterogeneous environments. According to the initial energy, [PERSON] _et al._ proposed a SEP scheme [15] for a two-level heterogeneous wireless sensor network composed of two types of nodes. The advanced nodes were equipped with more energy than the normal nodes at the beginning. SEP prolonged the stability period, which was defined as the time interval before the death of the first node. However, it was not fit for the widely used multi-level heterogeneous wireless sensor networks which include more than two types of nodes. In [16], [PERSON] _et al._ considered an event detection heterogeneous network with two types of nodes that included type-1 and type-0 node. Type-1 nodes had more battery energy than type-0 nodes. The key design features were that the energy supply was built into the nodes and the network lifetime was analyzed. [PERSON] _et al._ proposed a distributed energy efficient clustering algorithm (DEEC) [17] for multi-level and two level energy heterogeneous wireless sensor networks. In this scheme, the cluster heads were selected using the probability derived from the ratio between the residual energy of each node and the average energy of the network. The nodes with high initial and residual energy had more chances of the becoming cluster heads compared to nodes with low energy. The DEEC protocol considered both two-level and multi-level heterogeneous networks. However, each node needed to possess global knowledge of the network along with its initial and residual energy in the DEEC protocol. There are three common types of resource heterogeneity in sensor nodes: computational heterogeneity, link heterogeneity, and energy heterogeneity [18]. Computational heterogeneity means that the heterogeneous nodes have more powerful microprocessors and more memory than normal nodes. With these powerful computational resources, the heterogeneous nodes can provide complex data processing and longer-term storage features. Link heterogeneity means that the heterogeneous nodes have high-bandwidth and long-distance network transceiver than normal nodes. Link heterogeneity can provide more reliable data transmission.