Abstract
We eliminate the useless edges for traveling salesman problem (TSP) based on frequency \(K_5\)s. A frequency \(K_5\) is computed with ten optimal five-vertex paths with given endpoints in a corresponding \(K_5\) in \(K_n\). A binomial distribution model is built based on frequency \(K_5\)s. As the frequency of each edge is computed with N frequency \(K_5\)s, the binomial distribution demonstrates that the frequency of an optimal Hamiltonian cycle edge is bigger than 4N on average. Thus, one can eliminate the edges with frequency below 4N to reduce the number of concerned edges for resolving TSP. A heuristic algorithm is given to eliminate the useless edges. After many useless edges are cut, the computation time of algorithms for TSP will be considerably reduced.
We acknowledge W. Cook, H. Mittelmann who created the Concorde and G. Reinelt et al. who provide the TSP data to TSPLIB. The authors acknowledge the funds supported by the Fundamental Research Funds for the Central Universities (No. 2018MS039 and No. 2018ZD09).
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Wang, Y. (2020). Edges Elimination for Traveling Salesman Problem Based on Frequency \(K_5\)s. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_103
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