Abstract
Take a complete weighted graph \(K_n\). We want to find a weighted tree on which the path length between any two vertices is as close as possible to their corresponding distance in \(K_n\). The optimality criterion we have chosen for this problem is the residual sum of squares (RSS). To find the optimal tree, we face two challenges: finding the optimal edge weights on a given tree and finding the optimal tree structure. For the former, we make use of the Cholesky decomposition, and for the latter, we use two metaheuristics: Simulated Annealing (SA) and Iterated Local Search (ILS). Our results suggest that SA and ILS both perform well at finding the optimal tree structure when the dispersion of distances in the complete graph is large. However, when the dispersion of distances is small, ILS has a much better performance.
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Soheil Hosseini, S., Wormald, N., Tian, T. (2022). Optimal Tree of a Complete Weighted Graph. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. WCO 2020. Studies in Computational Intelligence, vol 986. Springer, Cham. https://doi.org/10.1007/978-3-030-82397-9_10
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DOI: https://doi.org/10.1007/978-3-030-82397-9_10
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