The Modified CW1 Algorithm For The Degree Restricted Minimum Spanning Tree Problem

Given edge weighted graph G (all weights are non-negative), The Degree Constrained Minimum Spanning Tree Problem is concerned with finding the minimum weight spanning tree T satisfying specified degree restrictions on the vertices. This problem arises naturally in communication networks where the degree of a vertex represents the number of line interfaces available at a terminal (center). The applications of the Degree Constrained Minimum Spanning Tree problems that may arise in real-life include: the design of telecommunication, transportation, and energy networks. It is also used as a subproblem in the design of networks for computer communication, transportation, sewage and plumbing. Since, apart from some trivial cases, the problem is computationally difficult (NP-complete), a number of heuristics have been proposed. In this paper we will discuss the modification of CW1 Algorithm that already proposed by Wamiliana and Caccetta (2003). The results on540 random table problems will be discussed

The Modified CW1 Algorithm for the Degree Restricted Minimum Spanning Tree Problem

Given edge weighted graph G (all weights are non-negative), The Degree Constrained Minimum Spanning Tree Problem is concerned with finding the minimum weight spanning tree T satisfying specified degree restrictions on the vertices. This problem arises naturally in communication networks where the degree of a vertex represents the number of line interfaces available at a terminal (center). The applications of the Degree Constrained Minimum Spanning Tree problems that may arise in real-life include: the design of telecommunication, transportation, and energy networks. It is also used as a subproblem in the design of networks for computer communication, transportation, sewage and plumbing. Since, apart from some trivial cases, the problem is computationally difficult (NP-complete), a number of heuristics have been proposed. In this paper we will discuss the modification of CW1 Algorithm that already proposed by Wamiliana and Caccetta (2003). The results on540 random table problems will be discussed

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 NP-complete multicast routing problem (MRP). The main contribution is the extension of PSO from continuous domain to the binary or discrete domain. Firstly, a novel bi-velocity strategy is developed to represent 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 while 0 stands for being otherwise. Secondly, BVDPSO updates the velocity and position according to the learning mechanism of the original PSO in 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 OR-library (Operation Research Library). The results confirm that BVDPSO can obtain optimal or near-optimal solutions rapidly as 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 GA, ACO, and PSO

QoS multicast tree construction in IP/DWDM optical internet by bio-inspired algorithms

Copyright @ Elsevier Ltd. All rights reserved.In this paper, two bio-inspired Quality of Service (QoS) multicast algorithms are proposed in IP over dense wavelength division multiplexing (DWDM) optical Internet. Given a QoS multicast request and the delay interval required by the application, both algorithms are able to find a flexible QoS-based cost suboptimal routing tree. They first construct the multicast trees based on ant colony optimization and artificial immune algorithm, respectively. Then a dedicated wavelength assignment algorithm is proposed to assign wavelengths to the trees aiming to minimize the delay of the wavelength conversion. In both algorithms, multicast routing and wavelength assignment are integrated into a single process. Therefore, they can find the multicast trees on which the least wavelength conversion delay is achieved. Load balance is also considered in both algorithms. Simulation results show that these two bio-inspired algorithms can construct high performance QoS routing trees for multicast applications in IP/DWDM optical Internet.This work was supported in part ny the Program for New Century Excellent Talents in University, the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1, the National Natural Science Foundation of China under Grant no. 60673159 and 70671020, the National High-Tech Reasearch and Development Plan of China under Grant no. 2007AA041201, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant no. 20070145017

A simulated annealing based genetic local search algorithm for multi-objective multicast routing problems

This paper presents a new hybrid evolutionary algorithm to solve multi-objective multicast routing problems in telecommunication networks. The algorithm combines simulated annealing based strategies and a genetic local search, aiming at a more flexible and effective exploration and exploitation in the search space of the complex problem to find more non-dominated solutions in the Pareto Front. Due to the complex structure of the multicast tree, crossover and mutation operators have been specifically devised concerning the features and constraints in the problem. A new adaptive mutation probability based on simulated annealing is proposed in the hybrid algorithm to adaptively adjust the mutation rate according to the fitness of the new solution against the average quality of the current population during the evolution procedure. Two simulated annealing based search direction tuning strategies are applied to improve the efficiency and effectiveness of the hybrid evolutionary algorithm. Simulations have been carried out on some benchmark multi-objective multicast routing instances and a large amount of random networks with five real world objectives including cost, delay, link utilisations, average delay and delay variation in telecommunication networks. Experimental results demonstrate that both the simulated annealing based strategies and the genetic local search within the proposed multi-objective algorithm, compared with other multi-objective evolutionary algorithms, can efficiently identify high quality non-dominated solution set for multi-objective multicast routing problems and outperform other conventional multi-objective evolutionary algorithms in the literature

An efficient null space inexact Newton method for hydraulic simulation of water distribution networks

Null space Newton algorithms are efficient in solving the nonlinear equations arising in hydraulic analysis of water distribution networks. In this article, we propose and evaluate an inexact Newton method that relies on partial updates of the network pipes' frictional headloss computations to solve the linear systems more efficiently and with numerical reliability. The update set parameters are studied to propose appropriate values. Different null space basis generation schemes are analysed to choose methods for sparse and well-conditioned null space bases resulting in a smaller update set. The Newton steps are computed in the null space by solving sparse, symmetric positive definite systems with sparse Cholesky factorizations. By using the constant structure of the null space system matrices, a single symbolic factorization in the Cholesky decomposition is used multiple times, reducing the computational cost of linear solves. The algorithms and analyses are validated using medium to large-scale water network models.Comment: 15 pages, 9 figures, Preprint extension of Abraham and Stoianov, 2015 (https://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001089), September 2015. Includes extended exposition, additional case studies and new simulations and analysi