Routing Problem In Communication Networks Research Articles

Multicast Routing Problem in Communication Networks: State of the Art

Multicast Routing Problem in Communication Networks: State of the Art

Bi-Velocity Discrete Particle Swarm Optimization and Its Application to Multicast Routing Problem in Communication Networks

This paper proposes a novel bi-velocity discrete particle swarm optimization (BVDPSO) approach and extends its application to the nondeterministic polynomial (NP) complete multicast routing problem (MRP). The main contribution is the extension of particle swarm optimization (PSO) from the continuous domain to the binary or discrete domain. First, a novel bi-velocity strategy is developed to represent the possibilities of each dimension being 1 and 0. This strategy is suitable to describe the binary characteristic of the MRP, where 1 stands for a node being selected to construct the multicast tree, whereas 0 stands for being otherwise. Second, BVDPSO updates the velocity and position according to the learning mechanism of the original PSO in the continuous domain. This maintains the fast convergence speed and global search ability of the original PSO. Experiments are comprehensively conducted on all of the 58 instances with small, medium, and large scales in the Operation Research Library (OR-library). The results confirm that BVDPSO can obtain optimal or near-optimal solutions rapidly since it only needs to generate a few multicast trees. BVDPSO outperforms not only several state-of-the-art and recent heuristic algorithms for the MRP problems, but also algorithms based on genetic algorithms, ant colony optimization, and PSO.

The extended Ritz method for functional optimization: overview and applications to single-person and team optimal decision problems

Functional optimization problems entail minimization of functionals with respect to admissible solutions belonging to infinite-dimensional spaces of functions. The extended Ritz method (ERIM) searches for suboptimal solutions expressed as linear combinations of basis functions with ‘free’ parameters that are optimized, together with the coefficients of the linear combinations, by solving finite-dimensional nonlinear programming problems and exploiting stochastic approximation techniques. The first part of the paper gives an overview of the ERIM and introduces the concept of polynomially complex optimizing sequences. Their elements are given by the solutions of the nonlinear programming problems obtained using an increasing number of basis functions. Under some conditions, the optimizing sequences epi-converge to the optimal solution and for a given approximation accuracy, the number of free parameters increases moderately (e.g. polynomially) with the number of variables in the admissible solutions. Therefore, the ERIM may avoid the curse of dimensionality, i.e. an exponential growth of the number of parameters. In the second and third parts of the paper, the ERIM and the stochastic approximation algorithms are specialized to the solution of stochastic T-stage single-person and stochastic team decision problems, respectively. Numerical results are given for the optimal management of systems of water reservoirs and for the dynamic routing problem in communication networks. In the reservoirs management application, the ERIM is compared with dynamic programming (DP) using random sampling of the state space. The dynamic routing application considers the presence of several destinations and classes of traffic, which are useful to address quality of service requirements. Here, the ERIM is compared with an algorithm based on the open shortest path first protocol.

On routing in VLSI design and communication networks

In this paper, we study the global routing problem in VLSI design and the multicast routing problem in communication networks. First we propose new and realistic models for both problems. In the global routing problem in VLSI design, we are given a lattice graph and subsets of the vertex set. The goal is to generate trees spanning these vertices in the subsets to minimize a linear combination of overall wirelength (edge length) and the number of bends of trees with respect to edge capacity constraints. In the multicast routing problem in communication networks, a graph is given to represent the network, together with subsets of the vertex set. We are required to find trees to span the given subsets and the overall edge length is minimized with respect to capacity constraints. Both problems are APX -hard. We present the integer linear programming (LP) formulation of both problems and solve the LP relaxations by the fast approximation algorithms for min–max resource-sharing problems in [K. Jansen, H. Zhang, Approximation algorithms for general packing problems and their application to the multicast congestion problem, Math. Programming, to appear, doi: 10.1007/s10107-007-0106-8] (which is a generalization of the approximation algorithm proposed by Grigoriadis and Khachiyan [Coordination complexity of parallel price-directive decomposition, Math. Oper. Res. 2 (1996) 321–340]). For the global routing problem, we investigate the particular property of lattice graphs and propose a combinatorial technique to overcome the hardness due to the bend-dependent vertex cost. Finally, we develop asymptotic approximation algorithms for both problems with ratios depending on the best known approximation ratio for the minimum Steiner tree problem. They are the first known theoretical approximation bound results for the problems of minimizing the total costs (including both the edge and the bend costs) while spanning all given subsets of vertices.