Intensification and diversification with elite tabu search solutions for the linear ordering problem

In this paper, we develop a new heuristic procedure for the linear ordering problem (LOP). This NP-hard problem has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics; In this paper, we concentrate on matrices that arise in the context of this real-world application. The proposed algorithm is based on the tabu search methodology and incorporates strategies for search intensification and diversification. For search intensification, we experiment with path relinking, a strategy proposed several years ago in connection with tabu search, which has been rarely used in actual implementations. Extensive computational experiments with input-output tables show that the proposed procedure outperforms the best heuristics reported in the literature. Furthermore, the experiments also show the merit of achieving a balance between intensification and diversification in the search.