A self-organising model for the travelling salesman problem

A self-organizing neural network using ideas from the immune system to solve the traveling salesman problem

“…This section makes a brief review of self-organized neural nets to solve TSP problems, focusing on the main differences between the proposals and describing in greater detail the works of Angeniol et al [1] and Somhom et al [40], which were re-implemented and used for direct performance comparisons.…”

“…In the work of Somhom et al [40], a SOM-like neural network is proposed with a number of neurons fixed as twice the number of cities in the problem. To guarantee the convergence of the algorithm to feasible solutions, no neuron is allowed to win twice within the same epoch.…”

“…The algorithm allows one neuron to map more than one city and, in this case, a heuristics has to be used to determine the proposed route. The performance of their algorithm is compared to that of [3,16,31,40] with very good results.…”

“…Another instance with 64 cities symmetrically distributed, ncit64, proposed in [34] was also employed. To compare the performance of the modified RABNET-TSP, the following algorithms were implemented: (1) the original algorithm oRABNET-TSP [34]; (2) Angeniol's algorithm [1], named here AVT; (3) Somhom's algorithm [40], named here SME. The reason why we chose Angeniol's algorithm for comparison is because it is one of the pioneers in the literature and it also incorporates a growing mechanism in the network.…”

“…5 we observe that after some epochs the h value is considerably small for large neighborhoods d, thus suggesting that the updating procedure could be constrained so as to avoid unnecessary computational effort. Some authors restrict the adaptation, decreasing the effective neighborhood of the winner neuron by performing the adaptation only to values of d lower than a pre-determined threshold [8,40]. This approach does not consider that, at the beginning of the learning process, some neighbors far from the winner neuron carry out a significant adaptation to the network and that, at the end of the adaptive process, neighbors close to the winner neuron no longer carry out significant adaptations.…”