# A Novel Hybrid Ant Colony Optimization for a Multicast Routing Problem
###### Abstract
Many researchers have concentrated on adopting meta-heuristic algorithms [8] such as simulated annealing (SA) [9], genetic algorithms (GA) [10; 11], bee colony algorithm [12], Cuckoo Search algorithm [13] and particle swarm optimization (PSO) [14] for solving the constrained routing problem. The ant colony algorithm (ACO) is widely used among these meta-heuristic algorithms. [PERSON], [PERSON] and [PERSON] [15] proposed the first ACO algorithm, and they successfully applied it to solve the traveling salesman problem by finding the shortest path capabilities of ants. The ACO algorithm simulates the foraging behavior of ants in nature. The ants should be able to find the shortest possible route from a given food source to their nest. At the same time, these ants can adapt to changes of the surrounding environment. When they encounter new obstructions on the old shortest route path, the ants can seek the next shortest route path. This is the primary reason information is transferred among ants through pheromone trail. It is remarkable to notice that some ants by choosing the shorter route path can more quickly reconstruct the pheromone trail than those selecting the longer one. Thus, there are a greater deal of pheromone trails on the shorter paths, which can attract more ants to choose. Therefore, the Ant's foraging behavior indicates the positive feedback pheromones. The more the ants choose a specific path, the more likely that other ants choose this path later. Because of the complexity of the multicast routing problem, the basic algorithms can't meet more requirements. Some researchers have adopted different strategies to enhance basic ACO algorithm performance. [PERSON] et al. [16] present an ACO algorithm for solving the delay-constrained broadcasting problem, and they verify the efficiency of the algorithm by a series of experiments. [PERSON] et al. [17] also present an ACO algorithm with consideration of the orientation factor to solve the multicast routing delay problem. Compared with the basic ACO, the solution quality and convergence rate of the improved algorithm are all enhanced. [PERSON] et al. [18] proposed an adaptive multi-QoS routing algorithm combining ant quantity system with ACO and improving the ACO algorithm based on a routing strategy by concentrating on a dynamic topology network graph and concave metric QoSconstraint to avoid networks congestion. [PERSON] et al. (2019) adopt a hybrid updating strategy based on iteration and global optimal solutions to improve the performance of ACO algorithm. [PERSON] and [PERSON] (2000) [PERSON] and [PERSON] (2000) presented an algorithm that paid attention to the applications of the basic ACO algorithm to solve the multicast routing problem under the delay constraint. A routing table which records routings from a source node to destination nodes is built for every pair of source-destination nodes. Each ant chooses a route for one destination node. Then combine all the destination node routes and remove the overlapped edges. A tree connecting all the source and destination nodes should be built, and this tree satisfies the delay constraint simultaneously. The pheromone trail intensity on edges of the multicast tree is updated. [PERSON] et al. (2018) presented a niched ACO algorithm for solving the QoS multicast routing problem with respect to the delay and bandwidth requirements. The niched ACO algorithm first constructs a QoS constrained tree, which guarantees feasible searches with consideration of QoS requirements. The computational results show that the niched ACO algorithm outperforms the genetic algorithm on the cost. However, the algorithm only takes into account delay-and-bandwidth constraints, without considering delay jitter constraint, packet loss rate constraints, etc. [PERSON] et al. (2018) present a difference-elite ant colony algorithm, which can optimize the parameters of ACO algorithm by differential evolution algorithm so as to increase the convergence speed of the ACO algorithm.