A bounded diameter minimum spanning tree evolutionaryalgorithm based on double chromosome

The Bounded Diameter Minimum Spanning Tree problem (BDMST) is a classical combinatorial optimization problem. In this paper,we propose a double chromosome evolutionary algorithm based on level coding and permutation coding for the BDMST problem. Double chromosome coding achieves the correspondences of the code and the solution of BDMST problem, so that the local search can be implemented more efficiently. A new crossover operator is design based on the double chromosome coding. The proposed algorithm keeps diversity and preferable convergence, because The offspring not only inherit the parent's some sub-tree, but also generate some new edges. Designed a novel decoding strategy to the level code chromosome, might find the predecessor that associated with smaller costs. The proposed algorithm is empirically compared to edge-set coded genetic algorithm and a variable neighborhood search implementation on Euclidean instances based on complete graphs with up to 1000 nodes considering either solution quality as well as computation time. It turns out that the evolutionary algorithm used double chromosome performs best the edge-set EA and the variable neighborhood search implementation concerning computation time.