A GRASP heuristic for the delay-constrained multicast routing problem

Abstract

The increasing development of real-time multimedia network applications, many of which require multiple participants, has created the need for efficient multicast routing algorithms. Examples of such applications include video and tele-conferencing, video-on-demand, tele-medicine, distance education, etc. Several of them require multicasting with a certain Quality of Service (QoS) with respect to elements such as delay or bandwidth. This paper deals with Delay-Constrained Multicast Routing (DCMR) where the maximum end-to-end delay in a multicast session is bounded. The DCMR problem can be reduced to the Constrained Minimum Steiner Tree Problem in Graphs (CMStTG) which has been proven to be NP-complete. As a result, several heuristics have been developed to help solve it. In this paper, we developed a GRASP heuristic for the DCMR problem. Computational experiments on medium sized problems (50-100 nodes) from literature and comparison with existing algorithms have shown that the suggested GRASP heuristic is superior in quality for this set of problems.

A Variable Neighborhood Descent Search Algorithm for Delay-Constrained Least-Cost Multicast Routing

“…In recent years, metaheuristic algorithms such as simulated annealing [17,18], genetic algorithm [19,20], tabu search [21,22,23,24], GRASP [25] and path relinking [26] have been investigated for various multicast routing problems. In the tabu search algorithm in [24], initial solutions are generated based on Dijkstra's algorithm.…”

An iterative local search approach based on fitness landscapes analysis for the delay-constrained multicast routing problem

“…As the source and all destination nodes must be included in a multicast tree, the value of their corresponding bits in the binary vector (of a feasible solution) should always be 1. This simple binary vector has been widely used in the literature and shows to be simple yet effective for representing a multicast tree [44,11].…”

“…For a multicast tree in the network of n bits with a source node and |D| destination nodes in the multicast group, the number of possible neighboring solutions of the current multicast tree is bounded by n -|D| -1. This node-based neighborhood operator has also been applied in [44,11]. It is known that higher values of fdc correlation ρ indicate that the fitness value and distance of solutions to x opt in the search space are correlated and thus the problem presents to be easier for search algorithms.…”

“…In this group of experiments, we compare ILS-VND-g with three other existing algorithms with good performance in the literature, including SSPR-VND [14], GRASP-VND [12], and GRASP-CST [11], on the 18 benchmark instances (Steinb) from the OR-library with three different delay bounds (∆ 1 = ∞, ∆ 2 = 1.1  Delay(T OPT ), and ∆ 3 = 0.9  Delay(T OPT )). SSPR-VND is a hybrid scatter search with path relinking algorithm for the DCLC-MRP, where VNDMR is applied as the local search method in it.…”

“…the Kompella-Pasquale-Polyzos (KPP) heuristic [4], has been developed in the early 1990"s, various heuristic and meta-heuristic algorithms have been proposed for solving a wide range of MRPs with different constraints. The majority of state-of-art algorithms for the DCLC-MRP are based on meta-heuristics such as simulated annealing [5,6], tabu search [7,8], genetic algorithms [9,10], greedy random adaptive search procedure (GRASP) [11,12], variable neighborhood search [13], and Scatter Search [14] etc. The rich literature of optimization algorithms for various MRPs can be found in several surveys [15][16][17][18][19].…”