# \(\epsilon\)- DANTE : an ant colony oriented depth search procedure

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## Abstract

The \(\epsilon\)-Depth ANT Explorer (\(\epsilon\)- DANTE ) 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 \(\epsilon\)- DANTE . Versions are compared among themselves in a set of instances of the multiple objective Traveling Salesman Problem. Finally, our best version of \(\epsilon\)- DANTE is compared with several established heuristics in the field showing some promising results.

## Keywords

Swarm intelligence optimization Ant colony optimization Hybrid algorithms Multiple objective optimization Depth local search## Notes

### Acknowledgments

We thank the Engineering Institute of the University of Algarve, in particular to the Department of Electrical Engineering, the Department of Civil Engineering, and the Centro de Simulação e Cálculo (CsC) for the resources, the projects Optimización de redes de interconexión (MTM2008-05866-C03-01) and Matemática Discreta en Andalucia (MaDiscA) (P06-FQM-01649), and the help for the consolidation of the research group FQM-164 (2008/FQM-164). A special thanks to the reviewers who significantly helped to improve this contribution and to the authors of García-Martínez et al. (2007) for providing us the base codes for some of the methods presented in Sect. 6.

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