Animal Cognition

, Volume 18, Issue 1, pp 53–64 | Cite as

Practice makes proficient: pigeons (Columba livia) learn efficient routes on full-circuit navigational traveling salesperson problems

  • Danielle M. Baron
  • Alejandro J. Ramirez
  • Vadim Bulitko
  • Christopher R. Madan
  • Ariel Greiner
  • Peter L. Hurd
  • Marcia L. Spetch
Original Paper

Abstract

Visiting multiple locations and returning to the start via the shortest route, referred to as the traveling salesman (or salesperson) problem (TSP), is a valuable skill for both humans and non-humans. In the current study, pigeons were trained with increasing set sizes of up to six goals, with each set size presented in three distinct configurations, until consistency in route selection emerged. After training at each set size, the pigeons were tested with two novel configurations. All pigeons acquired routes that were significantly more efficient (i.e., shorter in length) than expected by chance selection of the goals. On average, the pigeons also selected routes that were more efficient than expected based on a local nearest-neighbor strategy and were as efficient as the average route generated by a crossing-avoidance strategy. Analysis of the routes taken indicated that they conformed to both a nearest-neighbor and a crossing-avoidance strategy significantly more often than expected by chance. Both the time taken to visit all goals and the actual distance traveled decreased from the first to the last trials of training in each set size. On the first trial with novel configurations, average efficiency was higher than chance, but was not higher than expected from a nearest-neighbor or crossing-avoidance strategy. These results indicate that pigeons can learn to select efficient routes on a TSP problem.

Keywords

Traveling salesman problem Pigeon Route learning Problem solving Nearest-neighbor strategy Crossing avoidance Planning Foraging 

Notes

Acknowledgments

We thank Nicole Savignac for assistance with subject running and data scoring and Isaac Lank for assistance with constructing the apparatus. This study was funded by a Natural Sciences and Engineering Research Council of Canada Discovery grant awarded to MLS. Some of these data were presented at the 19th Annual International Conference on Comparative Cognition in March, 2012. All research was conducted in accordance with Canadian Council on Animal Care guidelines and with approval from the University of Alberta Animal Care and Use Committee. The experiments comply with the current laws of Canada.

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Applegate DL, Bixby RE, Chvatal V, Cook WJ (2007). The traveling salesman problem: a computational study. Princeton series in applied mathematics, Princeton University Press, PrincetonGoogle Scholar
  2. Blaser RE, Ginchansky RR (2012) Route selection by rats and humans in a navigational traveling salesman problem. Anim Cogn 15:239–250. doi:10.1007/s10071-011-0449-7 PubMedCrossRefGoogle Scholar
  3. Blaser RE, Wilber J (2013) A comparison of human performance in figural and navigational versions of the traveling salesman problem. Psychol Res 77:761–772. doi:10.1007/s00426-012-0470-8 PubMedCrossRefGoogle Scholar
  4. Bures J, Buresova O, Nerad L (1992) Can rats solve a simple version of the traveling salesman problem? Behav Brain Res 52:133–142. doi:10.1016/S0166-4328(05)80223-2 PubMedCrossRefGoogle Scholar
  5. Cramer AE, Gallistel CR (1997) Vervet monkeys as travelling salesmen. Nature 38:464. doi:10.1038/387464a0 CrossRefGoogle Scholar
  6. de Jong LW, Gereke B, Martin GM, Fellous JM (2011) The traveling salesrat: insights into the dynamics of efficient spatial navigation in the rodent. J Neural Eng 8: 65010–65020. doi:10.1088/1741-2560/8/6/065010
  7. Dorigo M, Gambardella LM (1997) Ant colonies for the travelling salesman problem. BioSystems 43:73–81. doi:10.1016/S0303-2647(97)01708-5 PubMedCrossRefGoogle Scholar
  8. Foti F, Petrosini L, Cutuli D, Menghini D, Chiarotti F, Vicari S, Mandolesi L (2011) Explorative function in Williams syndrome analyzed through a large-scale task with multiple rewards. Res Dev Disabil 32:972–985. doi:10.1016/j.ridd.2011.02.001 PubMedCrossRefGoogle Scholar
  9. Gallistel CR (1990) The organization of learning. MIT Press, CambridgeGoogle Scholar
  10. Gibson B, Wasserman EA, Kamil AC (2007) Pigeons and people select efficient routes when solving a one-way travelling salesperson task. J Exp Psychol Anim B 33:244–261. doi:10.1037/0097-7403.33.3.244 CrossRefGoogle Scholar
  11. Gibson B, Wilkinson M, Kelly D (2012) Let the pigeon drive the bus: pigeons can plan future routes in a room. Anim Cogn 15:379–391. doi:10.1007/s10071-011-0463-9 PubMedCrossRefGoogle Scholar
  12. Golden B, Bodin L, Doyle T, Stewart W (1980) Approximate travelling salesman algorithms. Oper Res 28:694–711CrossRefGoogle Scholar
  13. Graham SM, Joshi A, Pizlo Z (2000) The traveling salesman problem: a hierarchical model. Mem Cogn 28:1191–1204. doi:10.3758/BF03211820 CrossRefGoogle Scholar
  14. Janson CH (2007) Experimental evidence for route integration and strategic planning in wild capuchin monkeys. Anim Cogn 10:341–356. doi:10.1007/s10071-007-0079-2 PubMedCrossRefGoogle Scholar
  15. Janson C (2014) Death of the (traveling) salesman: primates do not show clear evidence of multi-step route planning. Am J Primatol 76(5):410–420. doi:10.1002/ajp.22186 PubMedCrossRefGoogle Scholar
  16. Kacelnik A (1984) Central place foraging in starlings (Sturnus vulgaris). I. Patch residence time. J Anim Ecol 53:283–299. doi:10.2307/4357 CrossRefGoogle Scholar
  17. Lihoreau M, Chittka L, Raine N (2010) Travel optimization by foraging bumblebees through readjustments of traplines after discovery of new feeding locations. Am Nat 176:744–757. doi:10.1086/657042 PubMedCrossRefGoogle Scholar
  18. Lihoreau M, Chittka L, Le Comber SC, Raine NE (2012a) Bees do not use nearest-neighbour rules for optimization of multi-location routes. Biol Lett 8:13–16. doi:10.1098/rsbl.2011.0661 PubMedCentralPubMedCrossRefGoogle Scholar
  19. Lihoreau M, Raine NE, Reynolds AM, Stelzer RJ, Lim KS, Smith AD, Osborne JL, Chittka L (2012b) Radar tracking and motion sensitive cameras on flowers reveal the development of pollinator multi-destination routes over large spatial scales. PLoS Biol. doi:10.1371/journal.pbio.1001392
  20. Lührs M, Dammhahn M, Kappeler PM, Fichtel C (2009) Spatial memory in the grey mouse lemur (Microcebus murinus). Anim Cogn 12:599–609. doi:10.1007/s10071-009-0219-y PubMedCentralPubMedCrossRefGoogle Scholar
  21. MacDonald SE, Wilkie DM (1990) Yellow-nosed monkeys’(Cercopithecus ascanius whitesidei) spatial memory in a simulated foraging environment. J Comp Psychol 104(4):382–387. doi:10.1037/0735-7036.104.4.382 CrossRefGoogle Scholar
  22. MacDonald SE, Pang JC, Gibeault S (1994) Marmoset (Callithrix jacchus) spatial memory in a foraging task: win-stay versus win-shift strategies. J Comp Psychol 108:328–334. doi:10.1037/0735-7036.108.4.328 PubMedCrossRefGoogle Scholar
  23. MacGregor JN (2012) Indentations and starting points in traveling sales tour problems: implications for theory. J Probl Solving 5(1):3. doi:10.7771/1932-6246.1140 Google Scholar
  24. MacGregor JN, Chu Y (2011) Human performance on the traveling salesman and related problems: a review. J Probl Solving 3(2):2. doi:10.7771/1932-6246.1090 Google Scholar
  25. MacGregor JN, Ormerod T (1996) Human performance on the traveling salesman problem. Percept Psychophys 58:527–539. doi:10.3758/BF03213088 PubMedCrossRefGoogle Scholar
  26. MacGregor JN, Ormerod TC, Chronicle EP (2000) A model of human performance on the traveling salesperson problem. Mem Cogn 28(7):1183–1190. doi:10.3758/BF03211819 CrossRefGoogle Scholar
  27. Madan CR, Spetch ML (2014) Visualizing and quantifying movement from pre-recorded videos: the spectral time-lapse (STL) algorithm. F1000Research 3:19. doi:10.12688/f1000research.3-19.v1 Google Scholar
  28. Menzel EW (1973) Chimpanzee spatial memory organization. Science 182:943–945. doi:10.1126/science.182.4115.943 PubMedCrossRefGoogle Scholar
  29. Miyata H, Fujita K (2008) Pigeons (Columba livia) plan future moves on computerized maze tasks. Anim Cogn 11:505–516. doi:10.1007/s10071-008-0141-8 PubMedCrossRefGoogle Scholar
  30. Miyata H, Fujita K (2010) Route selection by pigeons (Columba livia) in “traveling salesperson” navigation tasks presented on an LCD screen. J Comp Psychol 124:433–446. doi:10.1037/a0019931 PubMedCrossRefGoogle Scholar
  31. Ohashi K, Thomson JD, D’Souza D (2007) Trapline foraging by bumblebees. IV. Optimization of route geometry in the absence of competition. Behav Ecol 18:1–11. doi:10.1093/beheco/ar1053 CrossRefGoogle Scholar
  32. Ormerod TC, Chronicle EP (1999) Global perceptual processing in problem solving: the case of the traveling salesperson. Percept Psychophys 61(6):1227–1238. doi:10.3758/BF03207625 PubMedCrossRefGoogle Scholar
  33. Reid RA, Reid AK (2005) Route finding by rats in an open arena. Behav Proc 68:51–67. doi:10.1016/j.beproc.2004.11.004 CrossRefGoogle Scholar
  34. Rose E, Haag-Wackernagel D, Nagel P (2006) Practical use of GPS-localization of feral pigeons Columba livia in the urban environment. Ibis 148(2):231–239. doi:10.1111/j.1474-919X.2006.00499.x CrossRefGoogle Scholar
  35. Stephens DW, Brown JS, Ydenberg RC (eds) (2007) Foraging: behavior and ecology. University of Chicago Press, ChicagoGoogle Scholar
  36. Tolman EC (1948) Cognitive maps in rats and men. Psychol Rev 55:189–208. doi:10.1037/h0061626 PubMedCrossRefGoogle Scholar
  37. van Rooij I, Stege U, Schactman A (2003) Convex hull and tour crossings in the Euclidean traveling salesperson problem: implications for human performance studies. Mem Cogn 31:215–220. doi:10.3758/BF03194380 CrossRefGoogle Scholar
  38. Vickers D, Butavicius M, Lee M, Medvedev A (2001) Human performance on visually presented traveling salesman problems. Psychol Res 65:34–45. doi:10.1007/s004260000031 PubMedCrossRefGoogle Scholar
  39. Vickers D, Lee MD, Dry M, Hughes P (2003) The roles of the convex hull and the number of potential intersections in performance on visually presented traveling salesperson problems. Mem Cogn 31:1094–1104. doi:10.3758/BF03196130 CrossRefGoogle Scholar
  40. Wiener JM, Ehbauer NN, Mallot HA (2009) Planning paths to multiple targets: memory involvement and planning heuristics in spatial problem solving. Psychol Res 73(5):644–658. doi:10.1007/s00426-008-0181-3 PubMedCrossRefGoogle Scholar
  41. Wystrach A, Schwarz S, Schultheiss P, Beugnon G, Cheng K (2011) Views, landmarks, and routes: how do desert ants negotiate an obstacle course? J Comp Physiol A 197(2):167–179. doi:10.1007/s00359-010-0597-2 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Danielle M. Baron
    • 1
  • Alejandro J. Ramirez
    • 2
  • Vadim Bulitko
    • 2
  • Christopher R. Madan
    • 1
  • Ariel Greiner
    • 1
  • Peter L. Hurd
    • 1
  • Marcia L. Spetch
    • 1
  1. 1.Department of Psychology, BSP-217University of AlbertaEdmontonCanada
  2. 2.Department of Computing ScienceUniversity of AlbertaEdmontonCanada

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