## 1 Introduction  
In recent years, the increased performance of the microminiature sensor in terms of memory capability and sensitivity and the decreased price have caused the widespread use of the self-organized wireless sensor networks (WSNs) [1; 2; 3; 4]. They commonly consist of plenty of sensors monitoring the area of interest (AoI) and use special routing protocols to realize the information exchange. The sensors are usually randomly deployed in tough environment using aircraft and organize networks by themselves. Due to the advantages of WSNs such as convenient deployment, self-organization, and low price, they have been employed in forest fire detection [5; 6], environment monitoring [7; 8], medical systems and healthcare [9; 10; 11], and smart homes [12; 13; 14].  
Because of the harsh environment of the deployed sensors in some applications, it is impossible for people to change the batteries of sensors. Therefore, energy efficiency is an important factor for us to design routing protocols. Much researches have been focused in energy conservation and many routing schemas have been proposed. Two-tier [15; 16; 17; 18; 19; 20; 21] routing schema usually divides the sensors into two types, member nodes and CHs by clustering. In a two-tier WSN, member nodes transmit their sensor data to the corresponding CH by single or multiple hop communication, and the CHs take the responsibility to process the data fusion and forward the data to the sink. The benefit of clustering can be summarized as follows: (1) Data fusion can be conducted in CHs to fuse the data from their members. Therefore, redundant data can be filtered and the transmission burden of CHs is relieved. (2) It simplifies the topology of the network and reduce the control messages because local nodes only need to know its corresponding CH. Meanwhile, it enhances the scalability of the network. (3) Communication bandwidth is conserved because the intracluster communication usually uses a time division multiple access (TDMA) schema.  
However, in the two-tier schema, nodes close to the CHs will consume more energy and cause energy holes because they relay the data for the outer nodes [15; 16]. Unbalanced energy consumption may cause premature death of nodes and cut down the network's lifetime. In order to achieve the goal of energy balancing, one valid method is to utilize the mobile sink for energy balancing [18; 22; 23; 24; 25; 26]. As the energy efficient routing problem in WSNs has been proved to be a NP-hard problem [27], some biologically inspired algorithms [28; 29; 30; 31; 32; 33; 34] are also introduced to solve it. Some work combines ant-colony algorithm and aims to find an optimal path for data transmission to save and balance the energy [28; 29]. In this paper, we propose an improved routing schema utilizing energy center-based clustering to achieve the goal of energy efficient and energy balance. The protocol was conducted by rounds and during the first several rounds, CHs were elected in accordance with the location of nodes using geometric partitioning. We calculated the optimal communication distance for multi-hop communication. Then we used the PSO algorithm to search the energy centers of the network and chose the nodes closest to the energy centers as the CHs. A low energy protection mechanism was also used to avoid weak nodes becoming relay nodes. Extensive simulations were conducted and the result proved that our presented protocol owns a better performance in several metrics such as lifetime and energy consumption of the network. We could summarize our contribution as follows:  
* We explored the optimal communication distance for multi-hop transmission.
* PSO algorithm was utilized for the energy centers searching to select the CHs.
* A protection mechanism is proposed to avoid low energy nodes becoming relay nodes.
* Plenty of simulations were performed and we compared them with some similar work such as [PERSON] et al. [32], Variable Dimension based Particle Swarm Optimization (VD-PSO) [34].