## 2 Related Works
### Cluster-Based Energy Consumption Optimization Approaches  
A large number of cluster-based energy consumption optimization approaches have been proposed for energy consumption balance, and they can be categorized into two types: meta-heuristic approaches and nature-inspired approaches. Meta-heuristic approaches are proposed on the basis of intuitive or empirical construction, and they usually have some randomness and uncertainty. The classic LEACH (Low-Energy Adaptive ClusteringHierarchy) is proposed in Ref. [23]. LEACH can effectively reduce energy consumption to some extent, but it may select a cluster head with low residual energy and shorten the network lifetime. Therefore, many approaches have made some improvement on the basis of LEACH. HEED in Ref. [24] selects cluster heads according to a hybrid of the node residual energy and a secondary parameter such as node proximity to its neighbors or node degree. PEGASIS in Ref. [25] makes sensor node communicate only with a close neighbor and takes turns transmitting to the base station. In Ref. [26], TL-LEACH saves energy consumption by using random rotation of local cluster base station. DL-LEACH in Ref. [27] increases the energy efficiency of sensor node by reducing the transmission distance and simplifying the transmission routine for short-range transmission. In Ref. [28; 29; 30], the authors propose energy efficient cluster based routing schemes for reliable networks. In Ref. [31], E-LEACH uses homomorphic encryption to provide secure data aggregation and reduce energy consumption. According to Ref. [32], M-LEACH is better than the TL-LEACH, and E-LEACH is better than M-LEAC. Although these approaches have better performance than LEACH, they cannot guarantee the energy consumption balance of sensor nodes when the size of the network is large. Other approaches are proposed in the literature based on application of nature-inspired approaches. Among them, some are the improved LEACH. For example, LEACH-C in Ref. [33] has better performance than LEACH because it considers the intra-cluster distance and residual energy of sensor nodes in the phase of cluster head selection. In Ref. [34], a PSO based approach is proposed to select the optimal location of cluster head. Although these two approaches can guarantee the energy consumption balance of cluster head, they ignore the sink distance which is also an important factor to improve energy efficiency for direct communication of data to the base station. LEACH-FL takes battery level, distance and node density into consideration [35], and it easily raises complexity and the accuracy problem in the fuzzification and defuzzification process. As nature-inspired approaches which only utilize approximation algorithm to achieve energy consumption balance. PSO is utilized to achieve cluster head selection in Refs. [36; 37; 38]. The authors in Ref. [36] increase the network lifetime by reducing the total communication distance, and the authors in Ref. [37] consider the intra-cluster distance and the residual energy of cluster head candidates. In Ref. [38], the proposed approach considers the residual energy, intra-cluster distance, node degree and head count of the probable cluster heads. However, these three approaches cannot guarantee the performance with the size of the network verifying because they ignore the sink distance. In Ref. [39], the authors propose an energy efficient clustering scheme based on recent variable population based chemo-inspired approach. To prolong the network lifetime, a PSO-based multiple-sink placement algorithm is proposed in Ref. [40]. However, it ignores the fault-tolerance of a network. Our proposed cluster-based approach belongs to a nature-inspired approaches.