Source-based delay-bounded multicasting in multimedia networks

GA-Based Heuristic Algorithms for QoS Based Multicast Routing

“…The creation of the initial population in this study is based on the randomized depth-first search algorithm [21,22]. We propose a modified randomized depth-first search algorithms for this purpose:…”

“…Some of them have used the traditional wellknown crossover operators, such as the following schemes: † One point crossover operator [18] † One point crossover operator, with a fixed probability P c ð< 0:6 -0:9Þ [11] † Two point crossover operator [19] † One point crossover operator plus 'and' and 'or' logic operations with a fixed probability P c [20] Unfortunately, according to the genotype representation in these papers, the above crossover operators are not suitable for recombination of two individuals (the crossover operation mostly leads to illegal individuals). However, Ravikumar et al [21] have proposed a new interesting approach for crossover of Steiner trees and Wang et al [22] have used the same scheme with some modifications. In this scheme, two multicast trees, T F ðs; MÞ and T M ðs; MÞ; are selected as parents and the crossover operation produces an offspring T O ðs; MÞ by identifying the links that are common to both parents.…”

“…First, two separate sub-trees among these sub-trees are randomly selected, and are connected them with the least-delay or the least-cost path (in Ref. [21] all sub-trees are connected to the first sub-tree). If none of the parents satisfies the delay constraint, the least-delay path is chosen.…”

“…Otherwise the least-cost path is chosen (in Ref. [21] this condition is checked for all individuals in the population). The path, which is added to join two sub-trees is selected heuristically.…”

“…However, in this encoding scheme, the transformation back and forth between genotype and phenotype space is very complicated, especially for large networks. Ravikumar et al [21] have proposed a GA-based algorithm with novel interesting approaches for crossover and mutation operators for the delay-constrained least-cost multicast routing problem. However, they have not defined their scheme for encoding and decoding of individuals.…”