Description: The self-organizing map (SOM) has been successfully employed to handle the Euclidean trav-eling salesman problem (TSP). By incorporating its neighborhood preserving property and the
convex-hull property ofthe TSP, we introduce a new SOM-like neural network, called the ex-panding SOM (ESOM). In each learning iteration, the ESOM draws the excited neurons close to
the input city, and in the meantime pushes them towards the convex-hull ofcities cooperatively.
The ESOM may acquire the neighborhood preserving property and the convex-hull property of
the TSP, and hence it can yield near-optimal solutions. Its feasibility is analyzed theoretically
and empirically. A series ofexperiments are conducted on both synthetic and benchmark TSPs,
whose sizes range from 50 to 2400 cities. Experimental results demonstrate the superiority of
the ESOM over several typical SOMs such as the SOM developed by Budinich, the convex
elastic net, and the KNIES algorithms. Though its solution accuracy is no
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