# Energy-Balanced Routing Algorithm Based on Ant Colony Optimization for Mobile Ad Hoc Networks
## 1 Introduction
In order to solve the problem that the basic ant colony optimization algorithm is easy to fall into the local optimum, the literature [19] proposed the Rank-Based Version of Ant System (ASRank). The algorithm is obtained by introducing the idea of sorting in the classical genetic algorithm into the ant system. The literature [20] designed an ant-swarm inspired energy-efficient ad hoc on-demand routing protocol (ACO-EEAODR) by considering the residual energy and path length of the node. The weighting factors of the two parameters in the protocol take different values according to different scenarios, and the pheromone of each node is updated according to the residual energy. Therefore, in this protocol, the selection of path is more inclined to nodes with more node energy than the shortest path, and the network energy consumption is balanced to some extent. In [21], Ant System concept is used in the mesh routing networks in order to discover the best routes while maintaining the distributed coordination between the nodes in Low-Power and Lossy network(LNNs) with low power consumption. The Ant Colony Optimization in [21] we called LNNACO improves packet transmission rate by considering energy consumption in the MMP ant colony algorithm. Because the LNNACO algorithm does not consider the impact of high mobility of nodes, it is not suitable for networks with higher mobile speeds. The literature [22] proposed an energy-aware ant-based routing (EAAR). The algorithm considers the node energy consumption based on the multipath routing protocol. In the route discovery phase, the maximum minimum residual energy (MRB) and route hop count on the path are used to update the pheromone. However, the packet delivery rate and the energy per packet in high mobile conditions are relatively inferior for EAAR. This is because energy-awareness increases the time to judge the best route for transmission. Unlike EAAR, which considers only residual energy, the literature [23] proposed an ant colony-based energy control routing protocol (ACECR). The ACECR considers the average residual energy and the minimum residual energy for each path. In the route discovery phase,the backward ant updates the pheromone table based on the minimum energy, average energy, and hop count in the statistics. However, ACER does not guarantee that the total transmission power is minimized over a chosen route. The literature [24] used the simulated annealing algorithm (SA) to find the global optimal path, combining SA with ACO. The algorithm first selects the next hop node with SA, and then updates the pheromone with the rule of ACO. The downside existing in this approach is that the time taken for determining the routing path and the distance of the routing path remains high when compared to the regular ACO algorithm. In the literature [25], by combining the firefly algorithm with ACO, the firefly algorithm is used to obtain the list of the leader nodes, the distance between the nodes, and the density of the nodes. The feature of the firefly algorithm is that the optional set of the next hop is the area with a large density of nodes. The convergence speed is faster, and then the ACO's transition probability strategy is used for routing. On the basis of the literature [26], the value of the equilibrium constant is adjusted according to the number of iterations. At the beginning of the iteration, the ant explores the new path and discovers the path to the destination node in the network topology as much as possible. After a period of time, the topology discovery in the network tends to be stable, the equilibrium constant is reduced, and the convergence speed of route discovery is accelerated. However, the algorithm ignores the fact that the pheromone concentration of some paths is significantly higher than that of other paths, which leads to more iterations to find the optimal path and reduces the convergence speed of the algorithm.