Optimizing co-existing multicast routing trees in IP network via discrete artificial fish school algorithm

Abstract

Increasingly more internet-applications require the supports of multiple multicasts, while existing multicast routing algorithms only aim to establish a single multicast routing tree (MRT). Sequentially optimizing the co-existing MRTs each is a common practice of handling the situation of multiple multicast session being concurrent, but it results in link-congestion on low-cost routes, or leads to non-optimal solution even if bandwidth reservation strategy is adopted. This paper proposes to optimize multiple co-existing MRTs as a whole via one-off optimization instead of sequentially optimizing each in isolation. To carry out the one-off optimization, a discrete artificial fish school algorithm (DAFSA) is proposed. The simulation results show that the proposed DAFSA is capable of optimally packing co-existing MRTs and exhibits remarkably better ability than several the most representative state-of-the-art algorithms in the sense of avoiding the link-congestion and minimizing the overall tree cost. The running time of the proposed DAFSA fully meets the requirements of the practical IP multicasting. Besides, Monte Carlo test proves that the convergence of the proposed DAFSA is not sensitive to its parameters.

Introduction

Many network application scenarios require the support of multicast technique, which delivers data packets from a source to multiple destinations according to a multicast routing tree (MRT). Since data packets are duplicated and forwarded on switching nodes only, the source does not have to transmit data copies to the destinations each, thus significantly reducing redundant data streams in the network. For this reason, multicast is increasingly recognized as a good solution to remedying the conflict between the limited bandwidth resources and the increasing demand for multimedia transmission. The key to implementing the multicast communication is how to establish an MRT with the least transmission-delay, that can be boiled down to the Steiner tree problem (STP) in graph theory [1], [2]. So far, many algorithms can solve the STP well [3], [4], [5], [6], [7], [8].

But, an important issue is neglected by most researchers all alone. The algorithms for solving the STP optimizes a single MRT only, while multiple multicast sessions simultaneously exist in practical IP network. The general approach to handle this situation is to optimize the MRT for each session separately. However, it is very likely to result in link-congestion. That is easy to explain. Since low-cost tree structures are more desirable, all the MRTs tend to reduce their own tree cost via occupying the low-cost links. As a result, link-congestions occur on the low-cost links. As the graphical example shown in Fig. 1, three MRTs share a common link, the capacity of which is no doubt sufficient to accommodate the data stream of each MRT, because that is the result of optimization. However, the capacity of the common link may not be sufficient to accommodate all data streams of the three MRTs. Suchlike situation would be more serious when the number of co-existing multicast sessions is large.

How to properly arrange multiple co-existing MRTs in order to avoid link-congestion in a link-capacitated network and minimize their tree cost as well is referred to as the multicast route packing problem [9]. Comparing with the original multicast routing problem of optimizing a single MRT, this problem is more significant and also far more difficult [10], [11]. So far, the reported algorithms for solving this problem are still rare and mainly heuristics. Chen et al. [12] proposed an algorithm to avoid link-congestion by minimizing the maximum congestion. Lee and Cho [13] improved the algorithm in literature [12] via maximizing the minimum residual capacity. The two algorithms cannot take the minimization of each MRT’s cost into account and thus obtain high-cost MRTs only. For avoiding link-congestion and reducing the overall tree cost as well, Jia and Wang [14] used the distance network heuristic (DNH, more often called KMB, which consists of its three proposers’ initials) [15] to construct co-existing MRTs, while Low et al. [16] used the shortest path heuristic (SPH) [17]. According to Plesník’s proof [18], the cost of a Steiner tree constructed by KMB or SPH nearly approach to (2$-$2/n) times that of the optimal one in the worst-case, where n stands for the destination number. Therefore, the overall tree cost of the co-existing MRTs is still very high, especially when each multicast session involves many destinations. Chu-Fu Wang et al. proposed two algorithms called Steiner-tree-based heuristic (STH) and cut-set-based heuristic (CSH), which possess the failure risk even if the available bandwidth is enough [19]. Obviously, the heuristics-based approaches are not promising solution to such a problem.

In contrast, intelligence algorithms are more suitable to solve this problem. Sanna et al. [20] and Ma et al. [21] separately proposed their own genetic algorithm-based approaches, which possess similar algorithmic flows with two stages, including stage-I for generating MRT-candidates of each session and stage-II for optimally combining the MRT-candidates generated in stage-I by using the genetic algorithm (GA). The main difference between the two methods lies in the stage-I, Sanna et at. developed a Dijkstra-based heuristic for generating MRT-candidates, while Ma et al. still used the GA. A drawback of such two-stage-approach is that, once one or more requisite MRT-candidates were not produced during the stage-I, the stage-II can even not find a feasible MRT-combination. A usual practice is to generate MRT-candidates for each multicast session as many as possible, which cannot fundamentally eliminate the risk of requisite MRT-candidates being absence and also makes the optimization task of the stage-II be more difficult. Ma and Liu considered the multicast route packing as a combinatorial problem of optimizing various branches and proposed a branch-based particle swarm optimization (B-PSO) [22]. As a result, it is no longer needed to generate the MRT-candidates of each session in advance, thus avoiding the problem of two-stage-approach. Nevertheless, the B-PSO is time-consumption inefficient, due to its frequent operations on eliminating redundant loops resulted from merging branches. Besides, the PSO is subjected to premature convergence. As a variant of the PSO, the B-PSO also inherits this drawback.

In this paper, we propose a one-off optimization approach for packing multiple co-existing MRTs in a link-capacitated network in order to avoid the link-congestion and minimize their overall tree cost as well. To carry out the one-off optimization, a discrete artificial fish school algorithm (DAFSA) is proposed as the optimization tool, in which the candidate solutions are encoded as the form of 0–1 matrix. Through decoding Steiner trees out from the 0–1 encoding matrix using existing minimal spanning tree algorithm, the potential co-existing MRTs can be easily obtained. For evaluating the merits of the MRT-set, a penalty function-based objective is developed. According to the characteristic of the 0–1 encoding matrix being discrete, we redesign the fish behaviors. These behaviors are performed in accordance with a predefined behavioral strategy. The simulation results show that the proposed DAFSA is capable of optimally packing co-existing MRTs and exhibits remarkably better ability than several the most representative state-of-the-art algorithms in the sense of avoiding the link-congestion and minimizing the overall tree cost. Besides, the running time of the proposed DAFSA fully meets the requirements of the practical IP multicasting and Monte Carlo test proves that the convergence of the proposed DAFSA is not sensitive to its parameters.

The rest parts of this paper are organized as follows. In Section 2, the mathematical model of the problem is formulated, and the general idea of the proposed one-off optimization is given. In Section 3, the specific algorithmic implementation is given. In Section 4, simulations are carried out to investigate the performance of the proposed approach. In Section 5, the conclusions are given.