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In this paper we introduce ACOP, a novel ACO algorithm for solving permutation based optimization problems. The main novelty is in how ACOP ants construct a permutation by navigating the space of partial orders and considering precedence relations as solution components. Indeed, a permutation is built up by iteratively adding precedence relations to a partial order of items until it becomes a total order, thus the corresponding permutation is obtained. The pheromone model and the heuristic function assign desirability values to precedence relations. An ACOP implementation for the Linear Ordering Problem (LOP) is proposed. Experiments have been held on a large set of widely adopted LOP benchmark instances. The experimental results show that the approach is very competitive and it clearly outperforms previous ACO proposals for LOP.