A Hybrid Algorithm Based on Memetic Algorithm and Tabu Search for k-Minimum Spanning Tree Problems

A combinatorial optimization problem, namely kMinimum Spanning Tree Problem, is to find a subtree with exactly k edges in an undirected graph G , such that the sum of edges’ weights is minimal. where graph G is made up of a set of vertices and weight attached edges. Since this problem is NP-hard, heuristic and metaheuristic methods are widely adopted for solving large instances. In this paper, we propose a new hybrid algorithm to solve this problem, by using Memetic Algorithm as a diversification strategy for Tabu Search. Especially, the genetic operator in our Memetic Algorithm is based on dynamic programming algorithm, which finds the optimal subtree in a given tree efficiently. The proposed algorithm is tested on the k–Minimum Spanning Tree problems with other exiting algorithms, The experimental results show that the proposed algorithm is superior to all the exiting algorithms in precision and updates some of the best known results.