## 2 Related Work  
### Routing Protocols Based on Heuristic Algorithm  
Low Energy Adaptive Clustering Hierarchy (LEACH) [15] is a classic routing algorithm and it firstly introduced the idea of clustering to achieve energy efficient. In LEACH, CHs are random selected and the node chose the closest CH as its destination by single hope communication. LEACH is much more energy efficient than some flat routing protocols such as flooding, grossing, SPIN, and DD because it avoids the direct communication between sensors and the sink. However, the method of random CHs selection brings about the uneven distribution of CHs and it is not suitable for large scale WSNs. Fuzzy Logic based Hexagonal Geographical Adaptive Fidelity (FGAF-HEX) [35] is a routing method which utilizes the fuzzy logic system and geography information to achieve the target of energy efficient and energy balance. The main contributions of the work can be summarized as follows. It divides the whole sensor field into several regular hexagons in accordance with communication range and arbitrary nodes in adjacent hexagons could intercommunicate. In this way, each hexagon could only maintain one active node and keep other nodes sleeping to alleviate data redundancy and conserve energy. Fuzzy logic system is utilized to balance the energy consumption in each hexagon field. Experiment results illustrate that the presented method outperforms some traditional algorithms such as Geographical Adaptive Fidelity (GAF), Diagonal Geographical Adaptive Fidelity (DGAF), Hexagonal Geographical Adaptive Fidelity (GAF-HEX). In [36], a straight-line routing using random-walk is proposed. The main idea of this protocol is that the event and query paths are straight and they are likely to interest in a plane. In this protocol, a candidate area is ensured according to the inside and outside bands which are determined by the neighbor distance. The node with the farthest neighbor distance and biggest residual energy in the candidate area is select as the next hop. Simulation results demonstrate that it outperforms some classic random-walk routing protocols such as rnn in aspects of network lifetime. Mobile sink could further balance the network's energy consumption. In [22], a data gathering schema called Energy-Aware Path Construction (EAPC) is proposed using mobile sink for energy efficient. The schema is composed of three parts to calculate a moving path for the mobile sink. During the initial phase, a minimal spanning tree is constructed to connect all the sensor nodes. Then a set of collection points (CPs) are elected according to the benefit index during the CP selection phase and the ordinary tree is decomposed into many subtrees. Finally, a convex polygon is constructed based on the CPs. The mobile sink moves along the convex polygon to access each CP and gathers the data in each round. Simulation result proves that the presented schema owns an enhanced performance in aspects of lifetime. A hierarchical routing algorithm which based on cluster-chain is proposed in [23], the algorithm contains three steps to construct the topology of the network. During the clustering and chain formation phase, each node calculates its cluster head selection value (CHSV) in accordance with the residual energy, neighbor distance, and the amount of data generation. The node with maximal CHSV will be elected as the cluster head. Then the greedy algorithm is introduced to form chains for intracluster communication. Finally, a mobile agent (MA) is used to collect data from CH along a dynamic path which is determined by signal strength, residual energy level and path loss. Simulation results describe that they proposed algorithm outperforms some similar work such as LEACH, Energy Efficient Cluster-chain based Protocol (ECCP), and Power-Efficient Gathering in Sensor Information Systems (PEGASIS).