Hybrid GRASP with Composite Local Search And Path-Relinking for the Linear Ordering Problem with Cumulative Costs.

In this paper a GRASP algorithm hybridized with a composite local search and path-relinking is proposed to solve the linear ordering problem with cumulative costs. Our approach consists on adding a composite local search that helps to produce diverse good solutions and improve them trough a truncated path-relinking with local search. The computational results show that the GRASP algorithm finds 30 new best known solutions of the one hundred twenty three standard instances used with unknown optimal values. Also it shows that the GRASP algorithm outperforms to the best reported solution (Tabu search), when a nonparametric Wilcoxon test is applied.