Abstract
In this paper, we describe new ways to apply Ant Colony Optimization (ACO) to the Probabilistic Traveling Salesperson Problem (PTSP). PTSP is a stochastic extension of the well known Traveling Salesperson Problem (TSP), where each customer will require a visit only with a certain probability. The goal is to find an a priori tour visiting all customers with minimum expected length, customers not requiring a visit simply being skipped in the tour.We show that ACO works well even when only an approximative evaluation function is used, which speeds up the algorithm, leaving more time for the actual construction. As we demonstrate, this idea can also be applied successfully to other state-of-the-art heuristics. Furthermore, we present new heuristic guidance schemes for ACO, better adapted to the PTSP than what has been used previously. We show that these modifications lead to significant improvements over the standard ACO algorithm, and that the resulting ACO is at least competitive to other state-of-the-art heuristics.
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J. Bartholdi L. Platzman (1982) ArticleTitleAn O(N log N) planar traveling salesman heuristic based on spacefilling curves Oper. Res. Lett. 1 2121–125
D. J. Berstimas P. Jaillet A. Odoni (1990) ArticleTitleA priori optimization Oper. Res. 38 1019–1033
D. Bertsimas P. Chervi M. Peterson (1995) ArticleTitleComputational approaches to stochastic vehicle routing problems Transport. Sci. 29 IssueID(4) 2342–352
D. Bertsimas L. H. Howell (1993) ArticleTitleFurther results on the probabilistic traveling salesman problem European J. Oper. Res. 65 68–95
L. Bianchi L. M. Gambardella M. Dorigo (2002) ArticleTitleAn ant colony optimization approach to the probabilistic traveling salesman problem Lecture Notes in Comput. Sci. 2439 883–892
L. Bianchi L. M. Gambardella M. Dorigo (2002) ArticleTitleSolving the homogeneous probabilistic traveling salesman problem by the ACO metaheuristic Lectures Notes in Comput. Sci. 2463 176–187
L. Bianchi J. Knowles (2002) Local search for the probabilistic traveling salesman problem: A proof of the incorretness of Bertsimas’ proposed 2-p-opt and 1-shift algorithms IDSIA Lugano, Switzerland
Bianchi, L., Knowles, J. and Bowler, N.: Local search for the probabilistic traveling salesman problem: Correction to the 2-p-opt and 1-shift algorithms, European J. Oper. Res. (2004), to appear.
Bowler, N., Fink, T. and Ball, R. C.: Characterization of the probabilistic travelling salesman problem, Phys. Rev. (2003), to appear.
Branke, J. and Guntsch, M.: New ideas for applying ant colony optimization to the probabilistic TSP, in Applications of Evolutionary Computing: Proceedings of EvoWorkshops 2003, 2003, pp. 165–175.
Dorigo, M. and Di Caro, G.: The ant colony optimization meta-heuristic, in D. Corne, M. Dorigo and F. Glover (eds), New Ideas in Optimization, 1999, pp. 11–32.
M. Dorigo L. M. Gambardella (1997) ArticleTitleAnt colony system: A cooperative learning approach to the traveling salesman problem IEEE Trans. Evolut. Comput. 1 IssueID(1) 253–66
M. Dorigo A. C. V. Maniezzo (1996) ArticleTitleThe ant system: Optimization by a colony of cooperating agents IEEE Trans. Systems Man Cybernet. B IssueID(26) 29–41
Guntsch, M. and Middendorf, M.: Pheromone modification strategies for ant algorithms applied to dynamic TSP, in E. B. et al. (eds), Applications of Evolutionary Computing: Proceedings of EvoWorkshops 2001, 2000, pp. 213–222.
Guntsch, M., Middendorf, M. and Schmeck, H.: An ant colony optimization approach to dynamic TSP, in L. S. et al. (eds), Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), 2001, pp. 860–867.
P. Jaillet (1985) Probabilistic traveling salesman problems MIT Cambridge, MA
Jaillet, P.: Analysis of probabilistic combinatorial optimization problems in Euclidean spaces, MOR: Math. Oper. Res. 18 (1993).
A. Jezequel (1985) Probabilistic vehicle routing problems Massachusetts Institute of Technology Cambridge, MA
G. Laporte F. V. Louveaux H. Mercure (1994) ArticleTitleA priori optimization of the probabilistic traveling salesman problem Oper. Res. 42 IssueID(3) 543–549
E. Lawler (Eds) (1985) The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization Wiley Chichester
F. Rossi I. Gavioli (1987) Aspects of heuristic methods in the probabilistic traveling salesman problem G. Andreatta F. Mason P. Serani (Eds) Advanced School on Stochastics in Combinatorial Optimization World Scientific Singapore 214–227
TSPLIB: http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/index.html, 2002.
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Branke, J., Guntsch, M. Solving the Probabilistic TSP with Ant Colony Optimization. J Math Model Algor 3, 403–425 (2005). https://doi.org/10.1007/s10852-005-2585-z
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DOI: https://doi.org/10.1007/s10852-005-2585-z
Key words
- Probabilistic Traveling Salesperson Problem
- PTSP
- Ant Colony Optimization
- ACO
- approximated evaluation
- heuristic guidance