A novel particle swarm optimization for the Steiner tree problem in graphs

The Steiner tree problem (STP) in graphs is a special but essential case of multiple destination routing (MDR) problems, which focuses on finding a minimal spanning tree (MST) that connecting the source and destinations. It has been proved to be an NP-hard problem. Particle swarm optimization (PSO) is an important swarm intelligent algorithm with fast convergence speed and easy implementation. In this paper, a novel discrete PSO for the STP (DPSO-STP), with the concept that the particle is guided by social and self cognition, is proposed. Different from the standard PSO, the DPSO-STP includes four parts: 1. two preprocessing operations are introduced, which are to construct a complete graph and to calculate each nodepsilas total distance from itself to the source and destination nodes; 2.the position of a particle is represented as a binary string, where 1 stands for the selected nodes and 0 denotes the opposite; 3. several novel update operations, including new mutation factor c3, are adopted for the binary string; 4. when generating a MST from a binary string, a modified Primpsilas algorithm and a trimming strategy are employed. The experiments based on the benchmarks from category B, C of STP in the OR-library have been carried out to demonstrate the effectiveness of the proposed algorithm. Compared with traditional heuristic algorithms, such as shortest path heuristic (SPH), average distance heuristic (ADH), etc, the DPSO obtains more promising results. And it also performs better than the other iteration based algorithm, with much less computation. The discussion to extend the algorithm to other MDR problems is also given.

[1]  Hwa-Chun Lin,et al.  VTDM-a dynamic multicast routing algorithm , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[2]  N. Franken,et al.  Combining particle swarm optimisation with angle modulation to solve binary problems , 2005, 2005 IEEE Congress on Evolutionary Computation.

[3]  Stefan Voß,et al.  Steiner's Problem in Graphs: Heuristic Methods , 1992, Discret. Appl. Math..

[4]  Gurdip Singh,et al.  Ant Colony Algorithms for Steiner Trees: An Application to Routing in Sensor Networks , 2005 .

[5]  Min Huang,et al.  An Intelligent QoS Multicast Routing Algorithm under Inaccurate Information , 2006, 2006 International Conference on Computational Intelligence and Security.

[6]  Henrik Esbensen,et al.  Computing near-optimal solutions to the steiner problem in a graph using a genetic algorithm , 1995, Networks.

[7]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[8]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[9]  Anujan Varma,et al.  Distributed algorithms for multicast path setup in data networks , 1996, TNET.

[10]  Yangyang Zhang,et al.  Optimal multicast routing in wireless ad hoc sensor networks , 2004, IEEE International Conference on Networking, Sensing and Control, 2004.

[11]  Shampa Chakraverty,et al.  Directed Convergence Heuristic: A fast & novel approach to Steiner Tree Construction , 2006, 2006 IFIP International Conference on Very Large Scale Integration.

[12]  Victor J. Rayward-Smith,et al.  On finding steiner vertices , 1986, Networks.

[13]  B. Al-kazemi,et al.  Discrete Multi-Phase Particle Swarm Optimization , 2005 .

[14]  George Markowsky,et al.  A fast algorithm for Steiner trees , 1981, Acta Informatica.

[15]  K. Dowsland.  HILL-CLIMBING, SIMULATED ANNEALING AND THE STEINER PROBLEM IN GRAPHS , 1991 .

[16]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[17]  R. Eberhart,et al.  Fuzzy adaptive particle swarm optimization , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[18]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[19]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[20]  Yee Leung,et al.  A genetic algorithm for the multiple destination routing problems , 1998, IEEE Trans. Evol. Comput..

[21]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).