On the finite-time dynamics of ant colony optimization

Methodology and Computing in Applied Probability

Volumn 8, Issue 1, 2006, Pages 105-133

  Gutjahr, Walter J ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Ant colony optimization; Convergence speed; Probabilistic algorithms; Stochastic approximation; Stochastic optimization

Indexed keywords

EID: 33747593718     PISSN: 13875841     EISSN: 15737713     Source Type: Journal    
DOI: 10.1007/s11009-006-7291-4     Document Type: Article

References (36)

1. S. Baluja and R., Caruana, "Removing the genetics from the standard genetic algorithm." In A. Prieditis and S. Russell (eds.), Proc. 12th Int. Conf. on Machine Learning, pp. 38-46, Morgan Kaufmann: San Francisco, 1995.
2. A. Bauer, B. Bullnheimer, R. F. Hartl, and C. Strauss, "An ant colony optimization approach for the single machine total tardiness problem." Proc. Congress on Evolutionary Computation CEC '99, vol. 2 pp. 1445-1450, Piscataway, NJ, 1999.
3. L. Bianchi, L. M. Gambardella, and M. Dorigo, "Solving the homogeneous probabilistic travelling salesman problem by the ACO metaheuristic." Proc. ANTS '02, 3rd International Workshop on Ant Algorithms, pp. 177-187, 2002.
4. M. Birattari, P. Balaprakash, and M. Dorigo, "ACO/F-Race: Ant colony optimization and racing techniques for combinatorial optimization under uncertainty." Proceedings of MIC 2005' 6th Metaheuristics International Conference, pp. 107-112, 2005.
5. C. Blum and M., Blesa, "New metaheuristic approaches for the edge-weighted k-cardinality tree problem," Computers & Operations Research vol. 32 pp. 1355-1377, 2005.
6. C. Blum and M. Dorigo, "Search bias in ant colony optimization: On the role of competition-balanced systems," IEEE Transactions on Evolutionary Computation vol. 9 pp. 159-174, 2005.
7. B. Bullnheimer, R. F. Hartl, and C. Strauss, "A new rank-based version of the Ant System: A computational study," Central European Journal for Operations Research and Economics vol. 7(1) pp. 25-38, 1999.
8. K. Doerner, W. J. Gutjahr, R. F. Hartl, C. Strauss, and C. Stummer, "Ant colony optimization in multiobjective portfolio selection," Proc. 4th Metaheuristics International Conference, pp. 243-248, 2001.
9. K. Doerner, W. J. Gutjahr, R. F. Hartl, C. Strauss, and C. Stummer, "Pareto Ant Colony Optimization: A metaheuristic approach to multiobjective portfolio selection," Annals of Operations Research vol. 131 pp. 79-99, 2004.
10. M. Dorigo and G. Di Caro, "The Ant Colony Optimization metaheuristic." In D. Corne, M. Dorigo, and F. Glover (eds.), New Ideas in Optimization, pp. 11-32, McGraw Hill: London, UK, 1999.
11. M. Dorigo and T. Stützle, Ant Colony Optimization, MIT Press: Cambridge, MA, 2004.
12. M. Dorigo, G. Di Caro, and L. M. Gambardella, "Ant algorithms for discrete optimization," Artificial Life vol. 5(2) pp. 137-172, 1999.
13. M. Dorigo, V. Maniezzo, and A. Colorni, "The Ant System: An autocatalytic optimization process." Technical Report 91-016, Dept. of Electronics, Politecnico di Milano: Italy, 1991.
14. M. Dorigo, V. Maniezzo, and A. Colorni, "Ant System: Optimization by a colony of cooperating agents," IEEE Transactions on Systems, Man, and Cybernetics, Part B vol. 26(1) pp. 29-41, 1996.
15. S. Fenet and C. Solnon, "Searching for maximum cliques with ant colony optimization." Applications of Evolutionary Computing, Proceedings of EvoWorkshops 2003, Lecture Notes in Computer Science 2611, Springer: Berlin, Germany, pp. 236-245, 2003.
16. W. J. Gutjahr, "A graph-based Ant System and its convergence," Future Generation Computer Systems vol. 16 pp. 873-888, 2000.
17. W. J. Gutjahr, "ACO algorithms with guaranteed convergence to the optimal solution," Information Processing Letters vol. 82 pp. 145-153, 2002.
18. W. J. Gutjahr, "A generalized convergence result for the Graph-based Ant System," Probability in the Engineering and Informational Sciences vol. 17 pp. 545-569, 2003a.
19. W. J. Gutjahr, "A converging ACO algorithm for stochastic combinatorial optimization." Proc. SAGA 2003 (Stochastic Algorithms: Foundations and Applications), In A. Albrecht and K. Steinhoefl (eds.), Lecture Notes in Computer Science 2827, pp. 10-25, Springer: Berlin, Germany, 2003b.
20. W. J. Gutjahr, "S-ACO: An ant-based approach to combinatorial optimization under uncertainty," Ant Colony Optimization and Swarm Intelligence: Proceedings of ANTS 2004 - Fourth International Workshop, Lecture Notes in Computer Science 3172, pp. 238-249, Springer: Berlin, Germany, 2004.
21. W. J. Gutjahr, "First steps to the runtime complexity analysis of ant colony optimization." Technical Report TR 2006-01, Department of Statistics and Decision Support Systems, University of Vienna, Vienna, Austria, 2006.
22. W. J. Gutjahr and M. Rauner, "An ACO algorithm for a dynamic regional nurse-scheduling problem in Austria," Computer & Operations Research (in press).
23. R. Hadji, M. Rahoual, E. Talbi, and V. Bachelet, "Ant colonies for the set covering problem." In: M. Dorigo, M. Middendorf, and T. Stuetzle (eds.), Abstract Proceedings of ANTS 2000 - From Ant Colonies to Artificial Ants: Second International Workshop on Ant Algorithms, pp. 63-66, Université Libre de Bruxelles: Brussels, 2000.
24. H. J. Kushner and G. G., Yin, Stochastic Approximation and Recursive Algorithms and Applications, Springer: Berlin, Germany, 2003.
25. D. Merkle and M. Middendorf, "Modeling the dynamics of ant colony optimization," Evolutionary Computation vol. 10 pp. 235-262, 2002.
26. D. Merkle and M. Middendorf, "Competition controlled pheromone update for ant colony optimization," Ant Colony Optimization and Swarm Intelligence: Proc. ANTS 2004, Lecture Notes in Computer Science 3172, pp. 95-105, Springer: Berlin, Germany, 2004.
27. M. Mitchell, J. H. Holland, and S. Forrest, "When will a genetic algorithm outperform hill climbing?" Advances in Neural Information Processing Systems vol. 6 pp. 51-58, 1994.
28. J. Montgomery and M. Randall, "Alternative pheromone applications for ant colony optimization," Technical Report TR02-07, Bond University: Australia, 2002.
29. H. Mühlenbein and T. Mahnig, "Evolutionary algorithms: From recombination to search distributions." In L. Kallel, B. Naudts, and A. Rogers (eds.), Theoretical Aspects of Evolutionary Computing, Natural Computing Series, Springer: Berlin, Germany, pp. 134-173, 2001.
30. A. Prügel-Bennett and A. Rogers, "Modelling genetic algorithm dynamics." In L. Kallel, B. Naudts, and A. Rogers (eds.), Theoretical Aspects of Evolutionary Computing, Natural Computing Series, Springer: Berlin, Germany, pp. 59-85, 2001.
31. A. Prügel-Bennett and J. L. Shapiro, "The dynamics of a genetic algorithm for simple Ising systems," Physica D vol. 104 pp. 75-114, 1997.
32. M. Rattray and J. L. Shapiro, "Noisy fitness evaluations in genetic algorithms and the dynamics of learning." In R. K. Belew and M. D. Vose (eds.), Foundations of Genetic Algorithms 4, Morgan Kaufmann, pp. 117-139, 1997.
33. M. Rauner, S. C. Brailsford, W. J. Gutjahr, and W. Zeppelzauer, "Optimal screening policies for diabetic retinopathy using a combined discrete-event simulation and ant colony optimization approach." In J. G. Anderson and M. Katzper (eds.), Proc. Int. Conference on Health Sciences Simulation, Western MultiConference '05, pp. 147-152, 2005.
34. R. Sedgewick and P. Flajolet, An Introduction to the Analysis of Algorithms, AddisonWesley: Reading, Massachusetts, 1996.
35. T. Stüzle and M. Dorigo, "A short convergence proof for a class of ACO algorithms," IEEE Transactions on Evolutionary Computation vol. 6 pp. 358-365, 2002.
36. T. Stützle and H. H. Hoos, "MAX-MIN Ant System," Future Generation Computer Systems vol. 16 pp. 889-914, 2000.