![](bg8.png)
Table 6: Comparing direct and decomposition approaches.
Instance Direct Via decomposition σ cost(%) σ cpu
cost cpu cost cpu
CELAR06 3389 37 3389 13 0.00 2.84
CELAR07 343691 312 343592 120 -0.02 2.60
GRAPH05 221 35 221 21 0.00 1.66
GRAPH06 4124 222 4126 160 0.04 1.38
GRAPH11 3119 1946 3256 677 4.39 2.87
GRAPH13 10392 3700 10796 1810 3.88 2.04
ecution times of direct approach and that via decom-
position respectively . The row σ
cost shows clearly
that the results are comparable with the quality of the
solutions on all instances. However, the row σ
cpu
outlines clearly the benefit of approaches via decom-
position in term of cpu time. this corresponds to our
first objective aiming to solve large problems in short
time near to optimality.
Table 7: Comparison with recent decomposition algo-
rithms.
Instance Our approach All 10 Fon 13
cost cpu(s) cost cpu(s) cost cpu(s)
CELAR06 3389 13 3389 212 3389 93
CELAR07 343592 120 343592 607 343592 317
GRAPH05 221 21 - - 221 10
GRAPH06 4126 160 - - 4123 240
GRAPH11 3256 677 - - 3080 2762
GRAPH13 10796 1810 - - 10110 3196
6.6 Comparison with Related Works
Table 7 compare the best results we obtained by our
algorithms based on decomposition and the best re-
sults of (Allouche et al., 2010) and (Fontaine et al.,
2013)) which both exploit Tree Decomposition of
problems to be solved.
Our results are comparable to those presented in
(Fontaine et al., 2013) in terms of quality of the solu-
tion but are better in terms of CPU-time.
7 CONCLUSIONS
In this paper, a Top-Down approach is developed for
solving hard instances of MI-FAP problem near to op-
timality in short time.
To validate experimentally this approach:
• Two decomposition methods based on a Min-Cut
algorithm were implemented. The first one called
BMCWD aims to minimize the global weight of
the cut. The second one called BMCCD aims to
minimize the number of edges of the cut.
• An adaptive genetic algorithm (AGA-MI-FAP)
was proposed to solve the initial problem without
decomposition or for solving the sub-problems.
• The 1-opt local search heuristic was used to im-
prove the global solution.
The quality of the solutions and the runtime of the
different approaches, with and without decomposi-
tion, were compared on instances of CALMA project.
Almost instances were solved using AGA-MI-FAP.
When solving decomposed MI-FAP, optimal or near-
optimal solutions were obtained in a short time with
the proposed method. The Iterative Top-Down algo-
rithm have good performances even when the number
of clusters increases. This promising result leads to
investigate further this decomposition approach. The
first results obtained in this work indicate that the best
strategy proposed can significantly improve the com-
putation time without any significant loss of quality
of the solution.
Several perspectives to this work will be investi-
gated: different decomposition methods and criteria,
other exact or heuristic algorithms to solve the clus-
ters.
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 decomposi-
tion 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 neighbor-
hoods exploration for vns. RAIRO-Operations Re-
search, 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 bi-
nary constraint satisfaction problem: an application
to a frequency assignment problem. Statistica Neer-
landica, 61/1:4–15.
Koster, A., Van Hoessel, S., and Kolen, A. (1998). The par-
tial 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 algo-
rithm. Journal of the ACM, 44/4:585–591.
Voudouris, C. and Tsang, E. (1995). Partial constraint sat-
isfaction problems and guided local search. Technical
report, Department of Computer Science,University
of Essex. Technical Report CSM-25.
ICAART2014-InternationalConferenceonAgentsandArtificialIntelligence
484