NP DIMACS NP An Improved Ant Colony Algorithm for the Maximum Clique Problem Abstract In this paper, an improved ant colony optimization algorithm presented for the maximum clique problem. Clique problem is one of the NP problems with various applications such as data mining, image processing, and computer networks. In the recent years, ant colony optimization algorithm attained successful results in the discrete optimization, but standard ant colony optimization algorithm for the maximum clique problem have a slow convergence. So, in the proposed algorithm for the maximum clique problem, some improvements in the pheromone update proposed in order to select proper path. The proposed algorithm not only keeps the good characteristics of standard ant colony optimization but also have low computational complexity and good convergence. It is used DIMACS dataset, in order to evaluate the proposed algorithm. The experimental results show that the proposed algorithm is better than the standard ant colony optimization in terms of convergence behavior and results. Keywords Clique problem, NP-hard, Ant colony algorithm, Pheromone update.
5
Embed
An Improved Ant Colony Algorithm for the Maximum Clique Problem
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
NP
DIMACS
NP
An Improved Ant Colony Algorithm for the Maximum
Clique Problem
Abstract
In this paper, an improved ant colony optimization algorithm presented for the maximum clique problem.
Clique problem is one of the NP problems with various applications such as data mining, image processing,
and computer networks. In the recent years, ant colony optimization algorithm attained successful results in
the discrete optimization, but standard ant colony optimization algorithm for the maximum clique problem
have a slow convergence. So, in the proposed algorithm for the maximum clique problem, some
improvements in the pheromone update proposed in order to select proper path. The proposed algorithm not
only keeps the good characteristics of standard ant colony optimization but also have low computational
complexity and good convergence. It is used DIMACS dataset, in order to evaluate the proposed algorithm.
The experimental results show that the proposed algorithm is better than the standard ant colony optimization
in terms of convergence behavior and results.
Keywords
Clique problem, NP-hard, Ant colony algorithm, Pheromone update.
-
-
NP
DIMACS
1-
TSP
-
-
ij
ijk
ij
ij
p
k
ijpij
kij
ij
-
1 . ( ) .ij ij ij ijt t r t
ij t 1
ij ij tij
ij trij
1 good solution
0 Otherwise
ij
ij
if tr t
2-
1
(1 - C )
G t
tC
|CG|
|Ct|
t
(1- )
0.95 if >0.95
old
new
old
3-
DIMACS
ρ
brock20012 10.40 0.89 12 11.00 1.00
C125.934 34.00 0.00 34 34.00 0.00
C250.944 41.80 1.64 4442.40 1.14
C500.9 53 51.40 1.14 53 52.00 0.70
DSJC500.5 12 11.60 0.54 12 12.00 0.00
gen200_p0.9 40 39.00 0.70 44 41.00 2.82
gen400_p0.9 50 48.20 1.09 50 48.80 0.83
MANN_a27 126 125.20 0.44 126 125.40 0.54
p_hat300-3 36 34.80 0.83 36 35.20 1.09
p_hat700-2 44 42.40 1.14 44 43.20 0.83
0 20 40 60 80 100 120 140 160 180 20032
33
34
35
36
37
38
39
40
41
42
Iterations
Me
an
Cliq
ue
Siz
e
Improved ACO
Standard ACO
C250.9
0 20 40 60 80 100 120 140 160 180 20038
40
42
44
46
48
50
52
Iterations
Me
an
Cliq
ue
Siz
e
Improved ACO
Standard ACO
C500.9
0 20 40 60 80 100 120 140 160 180 20022
24
26
28
30
32
34
Iterations
Me
an
Cliq
ue
Siz
e
Improved ACO
Standard ACO
p_hat300-3
0 20 40 60 80 100 120 140 160 180 20030
32
34
36
38
40
42
Iterations
Me
an
Cliq
ue
Siz
e
Improved ACO
Standard ACO
gen200_p0.9
4-
-
[1] T. Stützle, M. López-Ibáñez, and M. Dorigo, “A
concise overview of applications of ant colony
optimization,” in Wiley Encyclopedia of Operations
Research and Management Science, vol. 8, 2011.
[2] C.-J. Ting and C.-H. Chen, “A multiple ant colony
optimization algorithm for the capacitated location
routing problem,” International Journal of Production
Economics, no. doi: 10.1016/j.ijpe.2012.06.011, p.
(in–press), 2012.
[3] F. E. B. Otero, A. A. Freitas, and C. G. Johnson,