## 2 Related Work
### ACO-Based Routing  
Ant Colony Optimisation (ACO) [6] is a swarm intelligence-based algorithm inspired by the search behaviour of an ant colony in nature. This search behaviour has the characteristics of being distributed, self-organised and having positive feedback. It has been observed in many of the existing research proposals that ACO is a widely-used technique to solve combinatorial optimisation applications due to these inherent features [16; 17].  
WSN applications require the sensor nodes to have a long network lifetime. Energy efficiency has been considered as a key issue in the design of routing protocols. In order to achieve this, it has become apparent that it is more important to route the data traffic such that the energy consumption is balanced among the nodes in proportion to their available energy instead of minimising the absolute consumed energy [18; 19]. In recent years, several ACO-based energy-efficient routing algorithms were proposed to satisfy this inherent limitation of WSNs.  
[PERSON], [PERSON] et al. [20] improved the heuristic function in ACO and considered the node communication transmission distance and residual energy to find the optimal path of data transmission. The algorithm (IACO in [20]) ignores the effects of other energy levels (e.g., average energy, minimum energy) in the heuristic and pheromone update function, which could result in the energy dissipation of the entire network to run out of balance.  
[PERSON] et al. [21] proposed a self-optimising algorithm (SensorAnt) to optimise sensor node energy. The algorithm uses ACO to enhance the best route and achieve energy consumption balance. The method uses several routing metrics including the residual energy, the number of hops and the average energy of the route and network. The results of SensorAnt show performance improvements compared to EEABR [10] in terms of energy efficiency. However, the operation of SensorAnt depletes a significant amount of energy due to the effects of overhead. This energy depletion can be considered wastage and has a significant impact on the overall performance of the network.  
[PERSON] et al. [22] proposed the Energy-Aware Ant Colony Algorithm (EAACA). The goal of EAACA is to create paths with low energy dissipation, balanced energy depletion and low transmission distance. Life Time Aware routing algorithm for Wireless Sensor Networks (LTAWSN) [23] utilised special parameters in its competency function for reducing the energy consumption of network nodes. A new pheromone update operator was designed to integrate energy consumption and hops into routing choice. However, during the route discovery and maintenance process of these two algorithms, several probe packets are sent to the destination node periodically, which results in a significant overhead and will increase the energy consumption.  
The Multilevel Minimisation and Balancing for Energy Consumption (MMBEC) [24] achieves the objectives of energy hole avoidance and network lifespan prolonging for WSNs. MMBEC adopts a short-trip moving scheme in ACO, decreases algorithm complexity and improves convergence speed. Furthermore, the algorithm presents the concept of reference transmission distance, which helps to realise local energy consumption and consumption balancing. However, MMBEC assumes that nodes are uniformly deployed in the plane. If this condition is not met, a complex computation of the data is required to calculate the energy consumption of all sub-zones.