A Memetic Algorithm for the Minimum Weighted k-Cardinality Tree Subgraph Problem

The minimum weighted k-cardinality tree subgraph problem consists in finding, in a given undirected weighted graph G(V,E,W ), a tree T ⊆ E of k edges having minimal total weight among all of k-trees that are subgraphs of G. We will refer this problem as the Min W-k-Tree. This is combinatorial optimization problem first described by Hamacher, Jörnsten, and Maffioli in [HJM91] who also proved to be strongly NP-hard. This said, it is unlikely to be solved efficiently. Given this observation, researchers have focused on heuristic and metaheuristic algorithms to find suboptimal feasible solutions for the problem, as a good way to cope with most practical setting applications. The problem is of relevance to both theory and industrial applications. In the latter group we can cite field leasing [HJ93] were it has arisen. Other applications of this problem can be found in diverse areas such as facility layout and graph partitioning [FH92, FHW98], open pit mining [FHW97], quorum-cast routing [TCK94], telecommunications [GH97] and matrix decomposition [BFM98, BFM97]. We refer the reader to [JL97] for a general complete mathematical formulation of the problem as well as [EFHM97].