Spanning Trees---Short or Small
SIAM Journal on Discrete Mathematics
Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms
Decomposing Matrices into Blocks
SIAM Journal on Optimization
Local search algorithms for the k-cardinality tree problem
Discrete Applied Mathematics
Variable neighborhood decomposition search for the edge weighted k-cardinality tree problem
Computers and Operations Research
New metaheuristic approaches for the edge-weighted k-cardinality tree problem
Computers and Operations Research
IWINAC'05 Proceedings of the First international work-conference on the Interplay Between Natural and Artificial Computation conference on Artificial Intelligence and Knowledge Engineering Applications: a bioinspired approach - Volume Part II
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
Obtaining optimal k-cardinality trees fast
Journal of Experimental Algorithmics (JEA)
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In recent years it has been shown that an intelligent combination of metaheuristics with other optimization techniques can significantly improve over the application of a pure metaheuristic. In this paper, we combine the evolutionary computation paradigm with dynamic programming for the application to the NP-hard k-cardinality tree problem. Given an undirected graph G with node and edge weights, this problem consists of finding a tree in G with exactly k edges such that the sum of the weights is minimal. The genetic operators of our algorithm are based on an existing dynamic programming algorithm from the literature for finding optimal subtrees in a given tree. The simulation results show that our algorithm is able to improve the best known results for benchmark problems from the literature in 60 cases.