The linear ordering problem (LOP) is one of the classical NP-Hard combinatorial optimization problems. Motivated by the difficulty of solving it up to optimality, in recent decades a great number of heuristic and meta-heuristic algorithms have been proposed. Despite the continuous work on this problem, there is still room nowadays for designing strategies that beat the state-of-the-art algorithms, and take a step forward in terms of the quality of the obtained solutions.In this paper, two novel schemes are presented. The first algorithm consists of an iterated local search algorithm that carries out an organized exploration of the search space. The second scheme is an extension of the previous algorithm that, based on the properties of the LOP, proposes an exact procedure that allows us to improve the quality of the solutions systematically. Conducted experiments on one of the hardest LOP benchmarks (xLOLIB) show that 77 new best results were found out of 78 instances. The described strategies also provide innovative ideas for developing more advanced algorithms for solving the LOP.