# A Novel Hybrid Ant Colony Optimization for a Multicast Routing Problem
###### Abstract
Simulation results show that the new algorithm gains minimal entropy. Although different versions of improved ACO for the multicast routing problems have been proposed in the literature described as above, these improved algorithms mainly include three aspects. First, path selection is a main part of ant colony algorithm, so many researchers focus on designing transition rules for ants. The effects of various transition rules on ACO algorithm were investigated in ([PERSON] et al., 2019; [PERSON] and [PERSON], 2019; [PERSON] and [PERSON], 2019). Second, the pheromone updating strategy is a deterministic factor in the performance of the ACO algorithm, as shown in references ([PERSON] and [PERSON], 2019; [PERSON] and [PERSON], 2019). The pheromone updating problem is how the ants update the pheromone intensity of their path. Third, the development of the ACO algorithm has led to considerable progress, but also has its strengths and weaknesses. Therefore, much research has tried to enhance the performance of hybrid algorithms ([PERSON] and [PERSON], 2019) and new meta-heuristics, such as a bee colony algorithm ([PERSON] and [PERSON], 2019) known as the Cuckoo Search algorithm (Cuckoo, 2019). The main weaknesses of the ACO algorithm are the slow convergence speed at the beginning of the step, and that it spends a long time on converging. While considering applying the ACO algorithm for solving the QoS multicast routing problem, the common characteristic of these algorithms is to seek the shorter paths between a source node and every destination. Then these paths are merged into a tree, and the pheromone trails on the edges of the optimal tree are updated. To improve the performance of the ACO algorithm, we present a hybrid ACO algorithm to solve the QoS multicast problem. In this study, we seek to enhance the performance of the ACO algorithm by using the cloud model (CM) ([PERSON] and [PERSON], 2019). Since high pheromone trail on some edges may lead to fast convergence and fall into local optimum, we have designed the pheromone trail updating strategy based on the CM to avoid overuse of some nodes. In this paper, the main features are different from the previous ACO-based multicast routing methods described above in the following ways. First, the primary innovative point is to combine the solution generation process of the ACO algorithm with the CM, which results in a novel hybrid algorithm, namely, ACO&CM. Within the framework structure of the ACO, we embed a cloud model in the ACO algorithm to enhance the performance of the ACO algorithm by adjusting a pheromone trail on the edges. Second, although high pheromone trail intensity on some edges may trap into local optimum, the pheromone updating strategy based on the CM is used to search for high-quality areas. To avoid the generation of loops hindering a feasible multicast path construction, we adopt a memory detection search (MDS) strategy that uses two kinds of data memory structures, that is, the current list (_CL_) and the path list (_PL_). The _CL_ records nodes which the current path routing reaches to avoid forming the self-loop, whereas the _PL_ stores all the finished routing paths to avoid the generation of the inter-loop. Finally, computational results show that the proposed algorithm has the advantages of efficient and excellent of performance for the quality of the solution. The paper is organized as follows. At first, the QoS problem description is given in Section 2. In Section 3, first, ACO algorithm is presented, and then the cloud model is introduced briefly. Section 4 introduces details of the proposed hybrid algorithm. Then, the results of numerical experiments are shown in Section 5. Finally, the Section 6 describes the conclusion remarks.