# An Equilibrium Strategy-Based Routing Optimization Algorithm for Wireless Sensor Networks
## 1 Introduction
### Related Works  
In some traditional routing algorithms that extend the network lifetime by reducing network energy consumption [15; 16], the energy consumption is saved mainly by reducing the hop counts of the transmission paths. Among them, the GBR algorithm [15] finds the path with the least hops from source node to the sink by calculating the parameter \"node height\"; Min-Hop [16] chooses a node among the neighbors as the relay, which has the least hops from source node to the sinknode, and when there are multiple paths with the fewest hop counts, the residual energy of the nodes will be taken as a decisive factor. This type of algorithms based on the minimum hops is equivalent to the minimum energy consumption routing [17]. Generally, it can reduce the path energy consumption, but it is easy to cause some nodes to exhaust prematurely due to overuse, bringing about an uneven distribution of residual energy and a short network lifetime. In addition, there are some routing algorithms that consider the sleep strategies [18; 19; 20]. These algorithms lessen the energy consumption rate by adjusting the \"sleeping\" and \"awake\" working modes of nodes, thus prolonging the lifetime of the entire network. However, there always exists a trade-off between energy efficiency and other performances.  
For the above problems, some routing algorithms that consider the load balancing are proposed in [21; 22; 23; 24; 25; 26]. Among them, SLDD [21] uses the evaluation function to select a super-link to redistribute network load through nodes with large energy and communication capacity on the super-link. However, since only a single metric is considered in the routing decision, this strategy can only be locally optimal, which may make other nodes exceed the load capacity [27]. In order to avoid the nodes in hot spot from taking too many forwarding tasks, in [22], the transmission power is controlled to balance the load, which can shrink the difference of residual energy of each node and achieve the purpose of extending the network lifetime, but for the network performance optimization, such as the network throughput and transmission delay, it is irrationally overlooked. DECOR [23] proposes a degree-limited routing, in which the load-balanced routing tree is established by limiting the degree of each node, but the required overhead of the computation and communication in this algorithm are large. To ensure the load balancing of node communication, a heuristic multi-path algorithm is proposed in [24], but it ignores the energy consumption caused by the distance factor. In [25], the FAF-EBRM adopts an energy balancing routing protocol based on a forward sensing factor, and utilizes the energy density of the forward region and the link data traffic to make routing decisions, which can alleviate data congestion in some way, similarly, due to the energy loss of detours, it is hard to minimize the path energy consumption. In [26], FLEOR can reduce the energy waste caused by the detours on the basis of the fuzzy theory, it selects the next hop by considering the transmission distance, hop counts and energy balance of the path, which can reduce the transmission energy consumption and prioritize the nodes with higher residual energy. Nevertheless, the fuzzy rules are formulated artificially, which lead to the lack of objectivity of next hop selecting, so the final path may not be the optimal.  
Therefore, in order to maximize the network lifetime, we both consider reducing the energy consumption of the whole network and balancing the node load, proposing an equilibrium strategy-based routing optimization algorithm for wireless sensor networks (ESRA).