Implementation of a genetic algorithm for the maximum clique problem in C++. A clique of a graph is a set of vertices in which each pair in the set have an edge between them i.e. it is a complete subgraph. A clique of maximum size is called the maximum clique. The algorithm uses new types of crossovers to achieve good results on several public graph datasets.
Cite this code:
@misc{shah2020gclique,
title={GCLIQUE: An Open Source Genetic Algorithm for the Maximum Clique Problem},
author={Shah, Shalin},
year={2020},
doi={10.5281/zenodo.3829645}
}
Usage:
- Compile the code using g++ - e.g. g++ gaClique.cpp - Run ./a.out filename generations - e.g. ./a.out instances/C500.9.CLQ 100 - Typical value for generations is 100
(If you are looking for a simpler algorithm in Java, please see clique2)
(The intersection crossover was borrowed from a similar idea in this algorithm)
Results on some DIMACS instances are show in the following table. The algorithm is allowed to run for a maximum duration of 30 seconds.
- The best performance is on the hamming, p_hat and c-fat instances.
- The worst performance is on the san1000 and brock instances.
- Please remove all comments and other extraneous text from the graph text instance file.
| Instance | Vertices | Edges | Best Known | Found | Duration (seconds) |
| brock200_1 | 200 | 14834 | 21 | 21 | 9 |
| brock200_2 | 200 | 9876 | 12 | 12 | 30 |
| brock200_3 | 200 | 12048 | 15 | 15 | 10 |
| brock200_4 | 200 | 13089 | 17 | 16 | 2 |
| brock400_1 | 400 | 59723 | 27 | 25 | 5 |
| brock400_2 | 400 | 59786 | 29 | 25 | 14 |
| brock400_3 | 400 | 59681 | 31 | 25 | 10 |
| brock800_1 | 800 | 207505 | 23 | 20 | 2 |
| C125.9 | 125 | 6963 | 34 | 34 | 0 |
| C250.9 | 250 | 27984 | 44 | 43 | 30 |
| C500.9 | 500 | 112332 | 57 | 55 | 5 |
| C1000.9 | 1000 | 450079 | 67 | 65 | 3 |
| C2000.5 | 2000 | 999836 | 16 | 15 | 5 |
| C2000.9 | 2000 | 1799532 | 75 | 73 | 9 |
| C4000.5 | 4000 | 4000268 | 18 | 16 | 28 |
| c-fat200-1 | 200 | 1534 | 12 | 12 | 0 |
| c-fat200-2 | 200 | 3235 | 24 | 24 | 0 |
| c-fat200-5 | 200 | 8473 | 58 | 58 | 0 |
| c-fat500-1 | 500 | 4459 | 14 | 14 | 0 |
| c-fat500-2 | 500 | 9139 | 26 | 26 | 0 |
| c-fat500-5 | 500 | 23191 | 64 | 64 | 0 |
| c-fat500-10 | 500 | 46627 | 126 | 126 | 1 |
| DSJC500.5 | 500 | 125248 | 13 | 13 | 3 |
| DSJC1000.5 | 1000 | 499652 | 15 | 14 | 5 |
| gen200_p0.9_44 | 200 | 17910 | 44 | 40 | 5 |
| gen400_p0.9_55 | 400 | 71820 | 55 | 51 | 2 |
| hamming6-2 | 64 | 1824 | 32 | 32 | 0 |
| hamming6-4 | 64 | 704 | 4 | 4 | 0 |
| hamming8-2 | 256 | 31616 | 128 | 128 | 1 |
| hamming8-4 | 256 | 20864 | 16 | 16 | 0 |
| hamming10-2 | 1024 | 518656 | 512 | 512 | 1 |
| hamming10-4 | 1024 | 434176 | 40 | 40 | 10 |
| johnson32-2-4 | 496 | 107880 | 16 | 16 | 0 |
| keller4 | 171 | 9435 | 11 | 11 | 0 |
| keller5 | 776 | 225990 | 27 | 27 | 10 |
| MANN_a27 | 378 | 70551 | 126 | 125 | 1 |
| MANN_a45 | 1035 | 533115 | 345 | 342 | 2 |
| MANN_a81 | 3321 | 5506380 | >=1100 | 1096 | 25 |
| p_hat300-1 | 300 | 10933 | 8 | 8 | 0 |
| p_hat300-2 | 300 | 21928 | 25 | 25 | 0 |
| p_hat300-3 | 300 | 33390 | 36 | 36 | 30 |
| p_hat500-1 | 500 | 31569 | 9 | 9 | 0 |
| p_hat500-2 | 500 | 62946 | 36 | 36 | 0 |
| p_hat500-3 | 500 | 93800 | >=50 | 49 | 0 |
| p_hat700-1 | 700 | 60999 | 11 | 11 | 9 |
| p_hat700-2 | 700 | 121728 | >=44 | 44 | 0 |
| p_hat700-3 | 700 | 183010 | >=62 | 62 | 3 |
| p_hat1000-1 | 1000 | 122253 | >=10 | 10 | 2 |
| p_hat1000-2 | 1000 | 244799 | >=46 | 46 | 5 |
| p_hat1000-3 | 1000 | 371746 | >=68 | 65 | 11 |
| p_hat1500-1 | 1500 | 284923 | >=12 | 11 | 2 |
| p_hat1500-2 | 1500 | 568960 | >=65 | 65 | 2 |
| p_hat1500-3 | 1500 | 847244 | >=94 | 93 | 8 |
| san200_0.7_1 | 200 | 13930 | 30 | 30 | 0 |
| san200_0.7_2 | 200 | 13930 | 18 | 18 | 2 |
| san200_0.9_1 | 200 | 17910 | 70 | 70 | 16 |
| san200_0.9_2 | 200 | 17910 | 60 | 60 | 28 |
| san200_0.9_3 | 200 | 17910 | 44 | 37 | 5 |
| san400_0.5_1 | 400 | 39900 | 13 | 13 | 1 |
| san400_0.7_1 | 400 | 55860 | 40 | 40 | 5 |
| san400_0.7_2 | 400 | 55860 | 30 | 30 | 2 |
| san400_0.7_3 | 400 | 55860 | 22 | 18 | 20 |
| san400_0.9_1 | 400 | 71820 | 100 | 100 | 1 |
| sanr200_0.7 | 200 | 13868 | 18 | 18 | 1 |
| sanr200_0.9 | 200 | 17863 | 42 | 41 | 1 |
| sanr400_0.5 | 400 | 39984 | 13 | 13 | 3 |
| sanr400_0.7 | 400 | 55869 | 21 | 21 | 5 |
| san1000 | 1000 | 250500 | 15 | 10 | 1 |