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The $$\epsilon$$-Depth ANT Explorer ( $$\epsilon$$-) algorithm applied to a multiple objective optimization problem is presented in this paper. This method is a hybridization of the ant colony optimization algorithm with a depth search procedure, putting together an oriented/limited depth search. A particular design of the pheromone set of rules is suggested for these kinds of optimization problems, which are an adaptation of the single objective case. Six versions with incremental features are presented as an evolutive path, beginning in a single colony approach, where no depth search is applied, to the final $$\epsilon$$-. Versions are compared among themselves in a set of instances of the multiple objective Traveling Salesman Problem. Finally, our best version of $$\epsilon$$- is compared with several established heuristics in the field showing some promising results. [ABSTRACT FROM AUTHOR]