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1. . ., . ., . .
// . . « ». –
2007. – № 2 (77). – . 18–25.
2. Dorigo M., Stützle T. Ant Colony Optimization. – London: A Bradford, 2004. – 305 p.
3. . ., . . //
. . – 2010. – № 1. – . 32–45.
4. . ., . ., . . . – .:
, 2009. – 384 .
5. . ., . . // .
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-». – 2009. – № 4 (93). – C. 16–24.
8. . . // . – 2004. – № 4 (4). – . 70–75.
9. . ., . . // .
-. – 2008-. – № 4 (81). – . 20–26.
10.Hlaing Z., Khine M. An Ant Colony Optimization Algorithm for Solving Traveling Salesman Problem //
International Proceedings of Computer Science and Information Technology. – 2011. – V. 16. – P. 54–59.
11.Hinne M., Marchiori. E. Cutting Graphs Using Competing Ant Colonies and an Edge Clustering Heuristic//
Proceedings of the 11th European conference on Evolutionary computation in combinatorial optimization. – 2011. – V. 6622. – P. 60–71.
12.Randall M., Lewis A. Modifications and additions to ant colony optimization to solve the set partitioning
problem // Proceedings of the 2010 6th IEEE International Conference on e-Science Workshops. – 2010. – P. 110–115.
13. . ., . ., . . ,
-: // . . «
-». – 2010. – № 12 (113). – C. 196–203.