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

Huidong JIN, Kwong Sak LEUNG, Man Leung WONG, Zong Ben XU

Research output: Journal PublicationsJournal Article (refereed)

55 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)877-888
Number of pages12
JournalIEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Volume33
Issue number6
DOIs
Publication statusPublished - 1 Dec 2003

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Keywords

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

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