Jin, Hui-DongHui-DongJinProf. LEUNG Kwong SakWong, Man-LeungMan-LeungWongXu, Zong-BenZong-BenXu2023-03-282023-03-282003IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2003, Vol. 33 (6), pp. 877 - 8881083-44191941-0492http://hdl.handle.net/20.500.11861/7624As 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.enSelf-Organizing MapTraveling Salesman ProblemNeural NetworkHeuristicComputational ComplexityExcitatory NeuronsLearning MechanismsConvex HullLearning RuleElastic NetNeighboring NeuronsLearning RateLearning StrategiesUnsupervised LearningLocal OptimumLearnable ParametersOutput NeuronsEffective WidthTopological StatesFirst Set of ExperimentsSimulated Annealing ApproachSynaptic WeightsValues of CitiesAverage Relative DeviationTheoretical BoundIterative LearningMedium ScaleUnit SquareGood CoordinationPeer Reviewed Journal Article10.1109/TSMCB.2002.804367