A Hybrid Framework Combining Genetic Algorithm with Iterated Local Search for the Dominating Tree Problem

Given an undirected, connected and edge-weighted graph, the dominating tree problem consists of finding a tree with minimum total edge weight such that for each vertex is either in the tree or adjacent to a vertex in the tree. In this paper, we propose a hybrid framework combining genetic algorithm with iterated local search (GAITLS) for solving the dominating tree problem. The main components of our framework are as follows: (1) the score functions Dscore and Wscore applied in the initialization and local search phase; (2) the initialization procedure with restricted candidate list (RCL) by controlling the parameter to balance the greediness and randomness; (3) the iterated local search with three phases, which is used to intensify the individuals; (4) the mutation with high diversity proposed to perturb the population. The experimental results on the classical instances show that our method performs much better than the-state-of-art algorithms.