Convergence and Running Time of Time-Dependent Ant Colony Algorithms

Bodo Manthey; Jesse van Rhijn; Ashkan Safari; Tjark Vredeveld

doi:10.1007/978-3-032-26123-6_7

Convergence and Running Time of Time-Dependent Ant Colony Algorithms

Bodo Manthey
, Jesse van Rhijn^*
, Ashkan Safari^*
, Tjark Vredeveld

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

We consider two time-dependent adaptations of the n-ANT algorithm: Attiratanusanthron and Fakcharoenphol’s (2008) n-ANT algorithm with time-dependent evaporation rate (n-ANT/tdev) and n-ANT with time-dependent lower pheromone bound (n-ANT/tdlb). We analyze the running time of both variants on the single destination shortest path problem (SDSP). We show that n-ANT/tdev has a super-polynomial running time on the SDSP. In contrast, we show that n-ANT/tdlb achieves a polynomial running time on this problem. This demonstrates rigorously how these time-dependent adaptions affect the performance of ACO variants, both positively and negatively. Moreover, we show that Gutjahr’s Graph-based Ant System with time-dependent evaporation rate (GBAS/tdev) converges to the optimal solution under a slightly stronger evaporation rate function than was previously known.

Original language	English
Title of host publication	Swarm Intelligence - 15th International Conference, ANTS 2026, Proceedings
Editors	Roderich Groß, Aaron T. Becker, Gianni A. Di Caro, Bahar Haghighat, M. Ani Hsieh, Razanne Abu-Aisheh, Mohamed S. Talamali, Marco Dorigo
Publisher	Springer Verlag
Pages	82-94
Number of pages	13
ISBN (Electronic)	978-3-032-26123-6
ISBN (Print)	9783032261229
DOIs	https://doi.org/10.1007/978-3-032-26123-6_7
Publication status	Published - 1 Jan 2026
Event	15th International Conference on Swarm Intelligence, ANTS 2026 - Darmstadt, Germany Duration: 8 Jun 2026 → 10 Jun 2026 https://iussi.cyberbee.net/ants-2026-15th-international-conference-on-swarm-intelligence/

Publication series

Series	Lecture Notes in Computer Science
Volume	16515 LNCS
ISSN	0302-9743

Conference

Conference	15th International Conference on Swarm Intelligence, ANTS 2026
Abbreviated title	ANTS 2026
Country/Territory	Germany
City	Darmstadt
Period	8/06/26 → 10/06/26
Internet address	https://iussi.cyberbee.net/ants-2026-15th-international-conference-on-swarm-intelligence/

Access to Document

10.1007/978-3-032-26123-6_7

Cite this

Manthey, B., van Rhijn, J., Safari, A., & Vredeveld, T. (2026). Convergence and Running Time of Time-Dependent Ant Colony Algorithms. In R. Groß, A. T. Becker, G. A. Di Caro, B. Haghighat, M. A. Hsieh, R. Abu-Aisheh, M. S. Talamali, & M. Dorigo (Eds.), Swarm Intelligence - 15th International Conference, ANTS 2026, Proceedings (pp. 82-94). Springer Verlag. https://doi.org/10.1007/978-3-032-26123-6_7

Manthey, Bodo ; van Rhijn, Jesse ; Safari, Ashkan et al. / Convergence and Running Time of Time-Dependent Ant Colony Algorithms. Swarm Intelligence - 15th International Conference, ANTS 2026, Proceedings. editor / Roderich Groß ; Aaron T. Becker ; Gianni A. Di Caro ; Bahar Haghighat ; M. Ani Hsieh ; Razanne Abu-Aisheh ; Mohamed S. Talamali ; Marco Dorigo. Springer Verlag, 2026. pp. 82-94 (Lecture Notes in Computer Science, Vol. 16515 LNCS).

@inproceedings{90dbb1163c094f109089518766238b3f,

title = "Convergence and Running Time of Time-Dependent Ant Colony Algorithms",

abstract = "We consider two time-dependent adaptations of the n-ANT algorithm: Attiratanusanthron and Fakcharoenphol{\textquoteright}s (2008) n-ANT algorithm with time-dependent evaporation rate (n-ANT/tdev) and n-ANT with time-dependent lower pheromone bound (n-ANT/tdlb). We analyze the running time of both variants on the single destination shortest path problem (SDSP). We show that n-ANT/tdev has a super-polynomial running time on the SDSP. In contrast, we show that n-ANT/tdlb achieves a polynomial running time on this problem. This demonstrates rigorously how these time-dependent adaptions affect the performance of ACO variants, both positively and negatively. Moreover, we show that Gutjahr{\textquoteright}s Graph-based Ant System with time-dependent evaporation rate (GBAS/tdev) converges to the optimal solution under a slightly stronger evaporation rate function than was previously known.",

author = "Bodo Manthey and \{van Rhijn\}, Jesse and Ashkan Safari and Tjark Vredeveld",

note = "Funding Information: This research is supported by NWO grant OCENW.KLEIN.176. Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.; 15th International Conference on Swarm Intelligence, ANTS 2026, ANTS 2026 ; Conference date: 08-06-2026 Through 10-06-2026",

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doi = "10.1007/978-3-032-26123-6\_7",

language = "English",

isbn = "9783032261229",

series = "Lecture Notes in Computer Science",

publisher = "Springer Verlag",

pages = "82--94",

editor = "Roderich Gro{\ss} and Becker, \{Aaron T.\} and \{Di Caro\}, \{Gianni A.\} and Bahar Haghighat and Hsieh, \{M. Ani\} and Razanne Abu-Aisheh and Talamali, \{Mohamed S.\} and Marco Dorigo",

booktitle = "Swarm Intelligence - 15th International Conference, ANTS 2026, Proceedings",

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Manthey, B, van Rhijn, J, Safari, A & Vredeveld, T 2026, Convergence and Running Time of Time-Dependent Ant Colony Algorithms. in R Groß, AT Becker, GA Di Caro, B Haghighat, MA Hsieh, R Abu-Aisheh, MS Talamali & M Dorigo (eds), Swarm Intelligence - 15th International Conference, ANTS 2026, Proceedings. Springer Verlag, Lecture Notes in Computer Science, vol. 16515 LNCS, pp. 82-94, 15th International Conference on Swarm Intelligence, ANTS 2026, Darmstadt, Hesse, Germany, 8/06/26. https://doi.org/10.1007/978-3-032-26123-6_7

Convergence and Running Time of Time-Dependent Ant Colony Algorithms. / Manthey, Bodo; van Rhijn, Jesse; Safari, Ashkan et al.
Swarm Intelligence - 15th International Conference, ANTS 2026, Proceedings. ed. / Roderich Groß; Aaron T. Becker; Gianni A. Di Caro; Bahar Haghighat; M. Ani Hsieh; Razanne Abu-Aisheh; Mohamed S. Talamali; Marco Dorigo. Springer Verlag, 2026. p. 82-94 (Lecture Notes in Computer Science, Vol. 16515 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

TY - GEN

T1 - Convergence and Running Time of Time-Dependent Ant Colony Algorithms

AU - Manthey, Bodo

AU - van Rhijn, Jesse

AU - Safari, Ashkan

AU - Vredeveld, Tjark

N1 - Funding Information: This research is supported by NWO grant OCENW.KLEIN.176. Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

PY - 2026/1/1

Y1 - 2026/1/1

N2 - We consider two time-dependent adaptations of the n-ANT algorithm: Attiratanusanthron and Fakcharoenphol’s (2008) n-ANT algorithm with time-dependent evaporation rate (n-ANT/tdev) and n-ANT with time-dependent lower pheromone bound (n-ANT/tdlb). We analyze the running time of both variants on the single destination shortest path problem (SDSP). We show that n-ANT/tdev has a super-polynomial running time on the SDSP. In contrast, we show that n-ANT/tdlb achieves a polynomial running time on this problem. This demonstrates rigorously how these time-dependent adaptions affect the performance of ACO variants, both positively and negatively. Moreover, we show that Gutjahr’s Graph-based Ant System with time-dependent evaporation rate (GBAS/tdev) converges to the optimal solution under a slightly stronger evaporation rate function than was previously known.

AB - We consider two time-dependent adaptations of the n-ANT algorithm: Attiratanusanthron and Fakcharoenphol’s (2008) n-ANT algorithm with time-dependent evaporation rate (n-ANT/tdev) and n-ANT with time-dependent lower pheromone bound (n-ANT/tdlb). We analyze the running time of both variants on the single destination shortest path problem (SDSP). We show that n-ANT/tdev has a super-polynomial running time on the SDSP. In contrast, we show that n-ANT/tdlb achieves a polynomial running time on this problem. This demonstrates rigorously how these time-dependent adaptions affect the performance of ACO variants, both positively and negatively. Moreover, we show that Gutjahr’s Graph-based Ant System with time-dependent evaporation rate (GBAS/tdev) converges to the optimal solution under a slightly stronger evaporation rate function than was previously known.

U2 - 10.1007/978-3-032-26123-6_7

DO - 10.1007/978-3-032-26123-6_7

M3 - Conference article in proceeding

SN - 9783032261229

T3 - Lecture Notes in Computer Science

SP - 82

EP - 94

BT - Swarm Intelligence - 15th International Conference, ANTS 2026, Proceedings

A2 - Groß, Roderich

A2 - Becker, Aaron T.

A2 - Di Caro, Gianni A.

A2 - Haghighat, Bahar

A2 - Hsieh, M. Ani

A2 - Abu-Aisheh, Razanne

A2 - Talamali, Mohamed S.

A2 - Dorigo, Marco

PB - Springer Verlag

T2 - 15th International Conference on Swarm Intelligence, ANTS 2026

Y2 - 8 June 2026 through 10 June 2026

ER -

Manthey B, van Rhijn J, Safari A , Vredeveld T. Convergence and Running Time of Time-Dependent Ant Colony Algorithms. In Groß R, Becker AT, Di Caro GA, Haghighat B, Hsieh MA, Abu-Aisheh R, Talamali MS, Dorigo M, editors, Swarm Intelligence - 15th International Conference, ANTS 2026, Proceedings. Springer Verlag. 2026. p. 82-94. (Lecture Notes in Computer Science, Vol. 16515 LNCS). doi: 10.1007/978-3-032-26123-6_7

Convergence and Running Time of Time-Dependent Ant Colony Algorithms

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