A knowledge-based iterated local search for the weighted total domination problem

For a simple undirected weighted graph G=(V,E,w,c), the weighted total domination problem is to find a total dominating set S with the minimum weight cost. A total dominating set S is a vertex subset satisfying that for each vertex in V there is at least one neighboring vertex in S. We propose a knowledge-based iterated local search algorithm for this problem that combines a reduction procedure to reduce the input graph, a learning-based initialization to generate high-quality initial solutions and a solution-based iterated local search to conduct intensive solution examination. Experiments on 342 benchmark instances show that the algorithm outperforms state-of-the-art algorithms. In particular, it reports 93 new upper bounds and 249 same results (including 165 known optimal results). The impact of each component of the algorithm is examined.