# Decomposition Tehniques for Solving Frequency Assigment Problems (FAP) - A Top-Down Approach

### Lamia Sadeg-Belkacem, Zineb Habbas, Fatima Benbouzid-Si Tayeb, Daniel Singer

#### Abstract

This paper deals with solving MI-FAP problem. Because of the NP-hardness of the problem, it is difficult to cope with real FAP instances with exact or even with heuristic methods. This paper aims at solving MI-FAP using a decomposition approach and mainly proposes a generic Top-Down approach. The key idea behind the generic aspect of our approach is to link the decomposition and the resolution steps. More precisely, two generic algorithms called Top-Down and Iterative Top-Down algorithms are proposed. To validate this approach two decomposition techniques and one efficient Adaptive Genetic Algorithm (AGA-MI-FAP) are proposed. The first results demonstrate good trade-off between the quality of solutions and the execution time.

#### References

- Aardal, K., Van Hoessel, S., Koster, A., Mannino, C., and Sassano, A. (2003). Models and solution techniques for frequency assignment problems. 4OR, Quaterly Journal of the Belgian, French and Italian Operations Research Sciences, 1:261-317.
- Allouche, D., Givry, S., and Schiex, T. (2010). Towards parallel non serial dynamic programming for solving hard weighted csp. In Proc. CP'2010, pages 53-60.
- CALMA-website (1995). Euclid Calma project. ftp://ftp.win.tue.nl/pub/techreports/CALMA/.
- Colombo, G. and Allen, S. M. (2007). Problem decomposition for minimum interference frequency assignment. In Proc. of the IEEE Congress in and Evolutionary Computation, Singapor.
- Fontaine, M., Loudni, M., and Boizumault, S. (2013). Exploiting tree decomposition for guiding neighborhoods exploration for vns. RAIRO-Operations Research, 47/2:91-123.
- Hale, W. K. (1980). Frequency assignment: Theory and applications. 68/12:1497-1514.
- Kolen, A. (2007). A genetic algorithm for the partial binary constraint satisfaction problem: an application to a frequency assignment problem. Statistica Neerlandica, 61/1:4-15.
- Koster, A., Van Hoessel, S., and Kolen, A. (1998). The partial constraint satisfaction problems: Facets and lifting theorem. O. R. Letters, 23(3-5):89-97.
- Maniezzo, V. and Carbonaro, A. (2000). An ants heuristic for the frequency assignment problem. Computer and Information Science, 16:259-288.
- Stoer, M. and Wagner, F. (1997). A simple min-cut algorithm. Journal of the ACM, 44/4:585-591.
- Voudouris, C. and Tsang, E. (1995). Partial constraint satisfaction problems and guided local search. Technical report, Department of Computer Science,University of Essex. Technical Report CSM-25.

#### Paper Citation

#### in Harvard Style

Sadeg-Belkacem L., Habbas Z., Benbouzid-Si Tayeb F. and Singer D. (2014). **Decomposition Tehniques for Solving Frequency Assigment Problems (FAP) - A Top-Down Approach** . In *Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-758-015-4, pages 477-484. DOI: 10.5220/0004820204770484

#### in Bibtex Style

@conference{icaart14,

author={Lamia Sadeg-Belkacem and Zineb Habbas and Fatima Benbouzid-Si Tayeb and Daniel Singer},

title={Decomposition Tehniques for Solving Frequency Assigment Problems (FAP) - A Top-Down Approach},

booktitle={Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2014},

pages={477-484},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004820204770484},

isbn={978-989-758-015-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - Decomposition Tehniques for Solving Frequency Assigment Problems (FAP) - A Top-Down Approach

SN - 978-989-758-015-4

AU - Sadeg-Belkacem L.

AU - Habbas Z.

AU - Benbouzid-Si Tayeb F.

AU - Singer D.

PY - 2014

SP - 477

EP - 484

DO - 10.5220/0004820204770484