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An ACO-RFD hybrid method to solve NP-complete problems

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Abstract

In this paper we hybridize ant colony optimization (ACO) and river formation dynamics (RFD), two related swarm intelligence methods. In ACO, ants form paths (problem solutions) by following each other’s pheromone trails and reinforcing trails at best paths until eventually a single path is followed. On the other hand, RFD is based on copying how drops form rivers by eroding the ground and depositing sediments. In a rough sense, RFD can be seen as a gradient-oriented version of ACO. Several previous experiments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACO. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACO in the first execution steps in general, though RFD solutions surpass ACO solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACO. We use a kind of ant-drop hybrid and consider both pheromone trails and altitudes in the environment. We apply the hybrid method, as well as ACO and RFD, to solve two NP-hard problems where ACO and RFD fit in a different manner: the traveling salesman problem (TSP) and the problem of the minimum distances tree in a variable-cost graph (MDV). We compare the results of each method and we analyze the advantages of using the hybrid approach in each case.

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Authors and Affiliations

  1. Dept. Sistemas Informáticos y Computación, Facultad de Informática, Universidad Complutense de Madrid, Madrid, 28040, Spain

    Pablo Rabanal, Ismael Rodríguez & Fernando Rubio

Authors
  1. Pablo Rabanal
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  2. Ismael Rodríguez
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  3. Fernando Rubio
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Corresponding author

Correspondence to Pablo Rabanal.

Additional information

Dr. Pablo Rabanal is an assistant professor in the Computer Systems and Computation Department, Complutense University of Madrid (Spain). He obtained his MS in Computer Science in 2004 and his PhD in the same subject in 2010, devoted to the development of nature-inspired techniques to solve NP-complete problems. Dr. Rabanal has published more than 20 papers in international refereed conferences and journals. His research interests cover heuristic methods, formal methods, testing techniques, and web services.

Dr. Ismael Rodríguez is an associate professor in the Computer Systems and Computation Department, Complutense University of Madrid (Spain). He obtained his MS in Computer Science in 2001 and his PhD in the same subject in 2004. Dr. Rodríguez received the Best Thesis Award of his faculty in 2004. He also received the Best Paper Award in the IFIP WG 6.1 FORTE 2001 conference. Dr. Rodríguez has published more than 70 papers in international refereed conferences and journals. His research interests cover formal methods, testing techniques, e-learning environments, and heuristic methods.

Dr. Fernando Rubio is an associate professor in the Computer Systems and Computation Department, Complutense University of Madrid (Spain). He obtained his MS in Computer Science in 1997 and his PhD in the same subject in 2001. Dr. Rubio received the National Degree Award on the subject of Computer Science from the Spanish Ministry of Education in 1997, as well as the Best Thesis Award of his faculty in 2001. Dr. Rubio has published more than 60 papers in international refereed conferences and journals. His research interests cover functional programming, testing techniques, e-learning environments, and heuristic methods.

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Rabanal, P., Rodríguez, I. & Rubio, F. An ACO-RFD hybrid method to solve NP-complete problems. Front. Comput. Sci. 7, 729–744 (2013). https://doi.org/10.1007/s11704-013-2302-4

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