Title

An efficient self-organizing map designed by genetic algorithms for the traveling salesman problem

Document Type

Journal article

Source Publication

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Publication Date

12-1-2003

Volume

33

Issue

6

First Page

877

Last Page

888

Keywords

Convex hull, Genetic algorithms, Neural networks, Neural-evolutionary system, Self-organizing map, Traveling salesman problem

Abstract

As a typical combinatorial optimization problem, the traveling salesman problem (TSP) has attracted extensive research interest. In this paper, we develop a self-organizing map (SOM) with a novel learning rule. It is called the integrated SOM (ISOM) since its learning rule integrates the three learning mechanisms in the SOM literature. Within a single learning step, the excited neuron is first dragged toward the input city, then pushed to the convex hull of the TSP, and finally drawn toward the middle point of its two neighboring neurons. A genetic algorithm is successfully specified to determine the elaborate coordination among the three learning mechanisms as well as the suitable parameter setting. The evolved ISOM (eISOM) is examined on three sets of TSPs to demonstrate its power and efficiency. The computation complexity of the eISOM is quadratic, which is comparable to other SOM-like neural networks. Moreover, the eISOM can generate more accurate solutions than several typical approaches for TSPs including the SOM developed by Budinich, the expanding SOM, the convex elastic net, and the FLEXMAP algorithm. Though its solution accuracy is not yet comparable to some sophisticated heuristics, the eISOM is one of the most accurate neural networks for the TSP.

DOI

10.1109/TSMCB.2002.804367

Print ISSN

10834419

E-ISSN

21682275

Publisher Statement

Copyright © 2003 Institute of Electrical and Electronics Engineers

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Full-text Version

Publisher’s Version

Recommended Citation

Jin, H.-D., Leung, K.-S., Wong, M.-L., & Xu, Z.-B. (2003). An efficient self-organizing map designed by genetic algorithms for the traveling salesman problem. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 33(6), 877-888. doi: 10.1109/TSMCB.2002.804367