ART-Based Parallel Learning of Growing SOMs and Its Application to TSP
This paper studies parallel learning of growing self-organizing maps ( GSOMs ) and its application to traveling sales person problems ( TSPs ). Input space of city positions are divided into subspaces automatically through adaptive resonance theory ( ART ) map. One GSOM is allocated to each subspace and grows following input data. After all the GSOMs grow sufficiently they are fused and we obtain a tour. The algorithm performance can be controlled by four parameters: the number of subspaces, insertion interval, learning coefficient and final number of cells. In basic experiments for a data-set of 929 cities we can find semi-optimal solution much faster than serial methods although there exist trade-off between tour length and execution time.
KeywordsInput Space Travel Salesman Problem Adaptive Resonance Theory Tour Length Fuzzy Adaptive Resonance Theory
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- 3.Fritzke, B.: Growing neural gas network learns topologies. In: Advances in Neural Information Processing Systems, vol. 7, pp. 625–632 (1995)Google Scholar
- 4.Kawahara, S., Saito, T.: An adaptive self-organizing algorithm with virtual connection. J. Advanced Comput. Intelli. 2, 203–207 (1998)Google Scholar
- 6.Ohta, R., Saito, T.: A growing self-organizing algorithm for dynamic clustering. In: Proc. of IJCNN, pp. 469–473 (2001)Google Scholar
- 8.Ohki, M., Torikai, H., Saito, T.: A simple radial basis ART network: basic learning characteristics and application to area measurement. In: Proc. NOLTA, pp. 262–265 (2005)Google Scholar
- 10.Fujimura, K., Tokutaka, H., Ishikawa, M.: Performance of improved SOM-TSP algorithm for traveling salesman problem of many cities. Trans. IEE Japan 119- C, 875–882 (1997)Google Scholar
- 11.Durbin, R., Szeliski, R., Yuille, A.: An analysis of the elastic net approach to the traveling salesman problem. In: Obermayer, K., Sejnowski, T.J. (eds.) Self-organization map formation, pp. 407–417. MIT press, Cambridge (2001)Google Scholar
- 12.Sasamura, H., Ohta, R., Saito, T.: A simple learning algorithm for growing ring SOM and its application to TSP. In: Proc. ICONIP, CD-ROM#1508 (2002)Google Scholar
- 13.Ehara, T., Sasamura, H., Saito, T.: An Approach to the TSP based on Growing Self-Organizing Maps. In: Proc. NOLTA, pp. 709–712 (2004)Google Scholar
- 15.Sasamura, H., Saito, T.: A Simple learning algorithm for growing self-organizing maps and its application to the skeletonization. In: Proc. of IJCNN, pp. 787–790 (2003)Google Scholar
- 16.Sasamura, H., Saito, T., Ohta, R.: A simple learning algorithm for network formation based on growing self organizing maps. IEICE Trans. Fundamentals E87-A, 2807–2810 (2004)Google Scholar
- 17.Matsushita, H., Nishio, Y.: Competing Behavior of Two Kinds of SOMs and its Application to Clustering. In: Proc. of WSOM, pp. 355–362 (2005)Google Scholar
- 18.Matsushita, H., Nishio, Y.: Competing and Accommodating Behaviors of Peace SOM. In: Proc. of IEEE/ISCAS, pp. 3642–3645 (2006)Google Scholar