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
Ant system: optimization by a colony of cooperating agents
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A new hybrid evolutionary algorithm for the huge k-cardinality tree problem
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Obtaining optimal k-cardinality trees fast
Journal of Experimental Algorithmics (JEA)
Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers
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Research efforts in metaheuristics have shown that an intelligent incorporation of more classical optimization techniques in metaheuristics can be very beneficial. In this paper, we combine the metaheuristic ant colony optimization with dynamic programming for the application to the NP – hard k-cardinality tree problem. Given an undirected graph G with node and/or edge weights, the problem consists of finding a tree in G with exactly k edges such that the sum of the weights is minimal. In a standard ant colony optimization algorithm, ants construct trees with exactly k edges. In our algorithm, ants may construct trees that have more than k edges, in which case we use a recent dynamic programming algorithm to find—in polynomial time—the best k-cardinality tree embedded in the bigger tree constructed by the ants. We show that our hybrid algorithm improves over the standard ant colony optimization algorithm and, for node-weighted grid graph instances, is a current state-of-the-art method.