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In this paper we propose a Beam-ACO approach for a combinatorial optimization problem known as the repetition-free longest common subsequence problem. Given two input sequences and over a finite alphabet , this problem concerns to find a longest common subsequence of and in which no letter is repeated. Beam-ACO algorithms are combinations between the metaheuristic ant colony optimization and a deterministic tree search technique called beam search. The algorithm that we present is an adaptation of a previously published Beam-ACO algorithm for the classical longest common subsequence problem. The results of the proposed algorithm outperform existing heuristics from the literature.