A New Neural Network Approach to the Traveling Salesman Problem

Siqueira, Paulo Henrique; Scheer, Sérgio; Steiner, María Teresinha Arns

doi:10.1007/11759966_59

Cited by 2 publications

(3 citation statements)

References 21 publications

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“…The results were compared with results from both the Hard Winner Takes All technique (Siqueira et al, 2008) and from similar techniques published in the literature. Table 1 and Table 2 shows the comparison between the Soft and Hard WTA techniques, where the results of applying Wang's Neural Network with Soft WTA and the 2-opt (SWTA2) route improving technique in the final solutions have mean error ranging between 0 and 4.50%.…”

Section: Resultsmentioning

confidence: 99%

“…The method proposed in this paper uses the "Winner Takes All" principle, which accelerates the convergence of Wang's Recurrent Neural Network, in addition to solve problems that appear in multiple solutions or very close solutions (Siqueira et al, 2008). The adjustment of parameter λ was done using the standard deviation between the coefficients of the rows in the problem's costs matrix and determining the vector…”

Section: Wang's Neural Network With the Soft Winner Takes All Principlementioning

confidence: 99%

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Recurrent Neural Networks with the Soft 'Winner Takes All' Principle Applied to the Traveling Salesman Problem

Siqueira¹,

Steiner²,

Scheer³

2010

Traveling Salesman Problem, Theory and Applications

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Section: Resultsmentioning

confidence: 99%

Section: Wang's Neural Network With the Soft Winner Takes All Principlementioning

confidence: 99%

Recurrent Neural Networks with the Soft 'Winner Takes All' Principle Applied to the Traveling Salesman Problem

Siqueira¹,

Steiner²,

Scheer³

2010

Traveling Salesman Problem, Theory and Applications

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“…In addition, the SA -2 Opt algorithm can find a more optimal solution than BKS (the best-known solution) in the case of Gr96. The BKS of those cases was 514 [24]. While the solution generated by the algorithm SA -2opt is 510.8863.…”

Section: A Comparison With Pure Outer and Inner Loop-based Sa Algorithmmentioning

confidence: 99%

Simulated Annealing – 2 Opt Algorithm for Solving Traveling Salesman Problem

Gunawan¹,

Iryanto²

2023

IJC

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The purpose of this article is to elaborate performance of the hybrid model of Simulated Annealing (SA) and 2 Opt algorithm for solving the traveling salesman problem (TSP). The SA algorithm used in this article is based on the outer and inner loop SA algorithm. The hybrid algorithm has promising results in solving small and medium-scale symmetric traveling salesman problem benchmark tests taken from the TSPLIB reference. Results of the optimal solution and standard deviation indicate that the hybrid algorithm shows good performance in terms of reliability and stability in finding the optimal solution from the TSP benchmark case. Values of average error and standard deviation for all simulations in the medium scale are 0.0267 and 644.12, respectively. Moreover, in some cases namely KroB100, Pr107, and Pr144, the hybrid algorithm finds a better solution compared with the best-known solution mentioned in the reference. Further, the hybrid algorithm is 1.207 – 5.692 times faster than the pure outer and inner loop-based SA algorithm. Additionally, the results show that the hybrid algorithm outperforms other hybrid algorithms such as SA – nearest neighbor (NN) and NN – 2 Opt.

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A New Neural Network Approach to the Traveling Salesman Problem

Cited by 2 publications

References 21 publications

Recurrent Neural Networks with the Soft 'Winner Takes All' Principle Applied to the Traveling Salesman Problem

Recurrent Neural Networks with the Soft 'Winner Takes All' Principle Applied to the Traveling Salesman Problem

Simulated Annealing – 2 Opt Algorithm for Solving Traveling Salesman Problem

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