Theoretical analysis of two ACO approaches for the traveling salesman problem
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Bioinspired algorithms, such as evolutionary algorithms and ant colony optimization, are widely used for different combinatorial optimization problems. These algorithms rely heavily on the use of randomness and are hard to understand from a theoretical point of view. This paper contributes to the theoretical analysis of ant colony optimization and studies this type of algorithm on one of the most prominent combinatorial optimization problems, namely the traveling salesperson problem (TSP). We present a new construction graph and show that it has a stronger local property than one commonly used for constructing solutions of the TSP. The rigorous runtime analysis for two ant colony optimization algorithms, based on these two construction procedures, shows that they lead to good approximation in expected polynomial time on random instances. Furthermore, we point out in which situations our algorithms get trapped in local optima and show where the use of the right amount of heuristic information is provably beneficial.
KeywordsAnt colony optimization Traveling salesperson problem Run time analysis Approximation
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- Eiben, A., & Smith, J. (2007). Introduction to evolutionary computing (2nd ed.). Berlin: Springer. Google Scholar
- Englert, M., Röglin, H., & Vöcking, B. (2007). Worst case and probabilistic analysis of the 2-opt algorithm for the TSP: extended abstract. In N. Bansal, K. Pruhs, & C. Stein (Eds.), SODA’07: Proceedings of the eighteenth annual ACM–SIAM symposium on discrete algorithms (pp. 1295–1304). Philadelphia: Society for Industrial and Applied Mathematics. Google Scholar
- Horoba, C., & Sudholt, D. (2009). Running time analysis of ACO systems for shortest path problems. In T. Stützle, M. Birattari, & H. H. Hoos (Eds.), Lecture notes in computer science: Vol. 5752. Engineering stochastic local search algorithms. Designing, implementing and analyzing effective heuristics, second international workshop, SLS, 2009 (pp. 76–91). Berlin: Springer. CrossRefGoogle Scholar
- Johnson, D. S., & McGeoch, L. A. (1997). The traveling salesman problem: a case study in local optimization. In E. H. L. Aarts & J. K. Lenstra (Eds.), Local search in combinatorial optimization. Somerset: Wiley. Google Scholar
- Kötzing, T., Neumann, F., Röglin, H., & Witt, C. (2010). Theoretical properties of two ACO approaches for the traveling salesman problem. In M. Dorigo, M. Birattari, G. A. D. Caro, R. Doursat, A. P. Engelbrecht, D. Floreano, L. M. Gambardella, R. Groß, E. Sahin, H. Sayama, & T. Stützle (Eds.), Lecture notes in computer science: Vol. 6234. Swarm intelligence, 7th international conference, ANTS, 2010 (pp. 324–335). Berlin: Springer. Google Scholar
- Neumann, F., Sudholt, D., & Witt, C. (2008). Rigorous analyses for the combination of ant colony optimization and local search. In M. Dorigo, M. Birattari, C. Blum, M. Clerc, T. Stützle, & A. F. T. Winfield (Eds.), Lecture notes in computer science: Vol. 5217. Ant colony optimization and swarm intelligence, 6th international conference, ANTS, 2008 (pp. 132–143). Berlin: Springer. CrossRefGoogle Scholar