Cognitive Processing

, Volume 10, Issue 2, pp 143–161 | Cite as

The verbalization of multiple strategies in a variant of the traveling salesperson problem

  • Thora TenbrinkEmail author
  • Jan Wiener
Research Report


What kinds of strategies do humans employ when confronted with a complex spatial task, and how do they verbalize these strategies? Previous research concerned with the well-known traveling salesperson problem (TSP) typically aimed at the identification of a generally applicable heuristics that adequately represents human behavior in relation to the abstract task of combining points. This paper adopts a novel perspective in two respects. On the one hand, it addresses the strategies people employ when confronted with a more complex task, involving distractors and feature information rather than identical points. On the other hand, retrospective linguistic representations of the strategies used are analyzed in relation to the behavioral data, using discourse analytic methods. Results show that both the behavioral results and the verbalizations point to a range of strategies related to those proposed for solving abstract TSPs. However, in contrast to earlier accounts in the literature, the participants employ a repertory of multi-faceted strategies and planning processes, simplifying and structuring the problem space across subtasks and processes in flexible ways. These findings provide further insight into the nature of human strategies in spatial problem solving tasks and their retrospective verbalization, highlighting how procedures generally known in the literature may be adapted to more complex tasks, and how they may be verbalized spontaneously.


Traveling salesperson problem Discourse analysis Wayfinding strategies Spatial cognition Retrospective reports 



Funding by the Volkswagen Foundation is gratefully acknowledged. We thank Elena Andonova, Lucie Salwiczek, and Inessa Seifert for helpful comments on an earlier version of this paper, our student assistants and the participants for their valuable contributions to this project, and the anonymous reviewers for providing excellent advice. The experiments comply with the current laws in Germany. All participants gave their informed consent prior to the participation in the study, and all procedures administered complied with the ethical guidelines of the German Psychological society (DGPs).


  1. Allen GL (1999) Spatial abilities, cognitive maps, and wayfinding: bases for individual differences in spatial cognition and behavior. In: Golledge R (ed) Wayfinding behavior: cognitive maps and other spatial processes. Johns Hopkins University Press, Baltimore, pp 46–80Google Scholar
  2. Applegate DL, Bixby RE, Chvátal V, Cook WJ (2007) The traveling salesman problem: a computational study. Princeton University Press, NJGoogle Scholar
  3. Basso D, Bisiacchi PS, Cotelli M, Farinello C (2001) Planning times during traveling salesman’s problem: differences between closed head injury and normal subjects. Brain Cogn 46(1–2):38–42. doi: 10.1016/S0278-2626(01)80029-4 PubMedCrossRefGoogle Scholar
  4. Best BJ, Simon HA (2000) Simulating human performance on the traveling salesman problem. In: Taatgen N, Aasman J (eds) Proceedings of the third international conference on cognitive modeling. Universal Press, Groningen, pp 42–49Google Scholar
  5. Couclelis H (1996) Verbal directions for way-finding: space, cognition, and language. In: Portugali J (ed) The construction of cognitive maps. Kluwer, Dordrecht, pp 133–153CrossRefGoogle Scholar
  6. Dascal M (1983) Pragmatics and the philosophy of mind 1: thought in language. John Benjamins, AmsterdamGoogle Scholar
  7. Denis M, Pazzaglia F, Cornoldi C, Bertolo L (1999) Spatial discourse and navigation: an analysis of route directions in the city of Venice. Appl Cogn Psychol 13(2):145–174. doi :10.1002/(SICI)1099-0720(199904)13:2<145::AID-ACP550>3.0.CO;2-4CrossRefGoogle Scholar
  8. Dry M, Lee MD, Vickers D, Hughes P (2006) Human performance on visually presented traveling salesperson problems with varying numbers of nodes. J Probl Solving 1(1):20–32Google Scholar
  9. Elliot AJ, Maier MA (2007) Color and psychological functioning. Curr Dir Psychol Sci 16:250–254. doi: 10.1111/j.1467-8721.2007.00514.x CrossRefGoogle Scholar
  10. Ericsson KA, Simon HA (1984) Protocol analysis: verbal reports as data. Bradford books/MIT Press, CambridgeGoogle Scholar
  11. Gärling T (1989) The role of cognitive maps in spatial decisions. J Environ Psychol 9:269–278. doi: 10.1016/S0272-4944(89)80009-X CrossRefGoogle Scholar
  12. Gärling T, Säisä J, Böök A, Lindberg E (1986) The spatiotemporal sequencing of everyday activities in the large-scale environment. J Environ Psychol 6:261–280. doi: 10.1016/S0272-4944(86)80001-9 CrossRefGoogle Scholar
  13. Golden B, Bodin L, Doyle T, Stewart W Jr (1980) Approximate traveling salesman algorithms. Oper Res 28(3:2):694–711CrossRefGoogle Scholar
  14. Golledge RG (1997) Defining the criteria used in path selection. In: Ettema DF, Timmermans HJP (eds) Activity-based approaches to travel analysis. Elsevier, New York, pp 151–169Google Scholar
  15. Golledge RG (ed) (1999) Wayfinding behavior: cognitive mapping and other spatial processes. Johns Hopkins University Press, BaltimoreGoogle Scholar
  16. Graham SM, Joshi A, Pizlo Z (2000) The traveling salesman problem: a hierarchical model. Mem Cognit 28:1191–1204PubMedGoogle Scholar
  17. Halliday MAK (1994) An introduction to functional grammar, 2nd edn edn. Edward Arnold, LondonGoogle Scholar
  18. Hayes-Roth B, Hayes-Roth F (1979) A cognitive model of planning. Cogn Sci 3:275–310. doi: 10.1207/s15516709cog0304_1 CrossRefGoogle Scholar
  19. Helfenstein S, Saariluoma P (2007) Apperception in primed problem solving. Cogn Process 8:211–232. doi: 10.1007/s10339-007-0189-4 PubMedCrossRefGoogle Scholar
  20. Janzen G, Weststeijn CG (2007) Neural representation of object location and route direction: an event-related fMRI study. Brain Res 1165:116–125. doi: 10.1016/j.brainres.2007.05.074 PubMedCrossRefGoogle Scholar
  21. Kim MS, Cave KR (1999) Grouping effects on spatial attention in visual search. J Gen Psychol 126:326–352PubMedCrossRefGoogle Scholar
  22. Liqiang QH, Holcombe AO, Pashler H (2004) Repetition priming in visual search: episodic retrieval, not feature priming. Mem Cognit 32(1):12–20Google Scholar
  23. Loomis J, Klatzky R, Golledge R, Philbeck J (1999) Human navigation by path integration. In: Golledge R (ed) Wayfinding behavior: cognitive mapping and other spatial processes. Johns Hopkins University Press, Baltimore, pp 125–152Google Scholar
  24. MacGregor JN, Ormerod TC (1996) Human performance on the travelling salesman problem. Percept Psychophys 58:527–539PubMedGoogle Scholar
  25. MacGregor JN, Ormerod TC, Chronicle E (2000) A model of human performance on the travelling salesperson problem. Mem Cognit 7:1183–1190Google Scholar
  26. Payne JW, Bettman JR, Coupey E, Johnson EJ (1992) A constructive process view of decision making: multiple strategies in judgment and choice. Acta Psychol (Amst) 80:107–141. doi: 10.1016/0001-6918(92)90043-D CrossRefGoogle Scholar
  27. Polivanova NI (1974) On some functional and structural features of the visual-intuitive components of a problem-solving process. Vopr Psychologii 4:41–51Google Scholar
  28. Reineking T, Kohlhagen C, Zetzsche C (2008) Efficient wayfinding in hierarchically regionalized spatial environments. In: Proceedings of Spatial Cognition, Sep. 15–19, FreiburgGoogle Scholar
  29. 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 Cognit 31(2):215–220PubMedGoogle Scholar
  30. Tenbrink T (2008) The verbalization of cognitive processes: thinking-aloud data and retrospective reports. In: Ramm W, Fabricius-Hansen C (eds) Linearisation and segmentation in discourse. Multidisciplinary approaches to discourse 2008 (MAD 08) Feb 20–23, Univ. of Oslo, Lysebu, Oslo, pp 125–135Google Scholar
  31. Tenbrink T, Wiener J (2007) Wayfinding strategies in behavior and language: a symmetric and interdisciplinary approach to cognitive processes. In: Barkowsky T, Knauff M, Ligozat G, Montello D (eds) Spatial cognition V: reasoning, action, interaction. Springer, Berlin, pp 401–420Google Scholar
  32. Todd PM, Gigerenzer G (2000) Précis of simple heuristics that make us smart. Behav Brain Sci 23:727–780. doi: 10.1017/S0140525X00003447 PubMedCrossRefGoogle Scholar
  33. Vickers D, Butavicius M, Lee MD, Medvedev A (2001) Human performance on visually presented traveling salesman problems. Psychol Res 65:34–45. doi: 10.1007/s004260000031 PubMedCrossRefGoogle Scholar
  34. 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 Cognit 31(7):1094–1104PubMedGoogle Scholar
  35. Wiener JM, Tenbrink T (2008) Traveling salesman problem: The human case. Künstliche Intelligenz. KI und Kognition 1(08):18–22Google Scholar
  36. Wiener JM, Schnee A, Mallot HA (2004) Use and interaction of navigation strategies in regionalized environments. J Environ Psychol 24(4):475–493Google Scholar
  37. Wiener JM, Tenbrink T, Henschel J, Hölscher C (2008a) Situated and prospective path planning: route choice in an urban environment. In: CogSci 2008: 30th Annual Conference of the Cognitive Science Society, July 23–26, WashingtonGoogle Scholar
  38. Wiener JM, Ehbauer NN, Mallot HA (2008b) Planning paths to multiple targets: memory involvement and planning strategies (under review)Google Scholar
  39. Williams CC, Henderson JM, Zacks RT (2005) Incidental visual memory for targets and distractors in visual search. Percept Psychophys 67:816–827PubMedGoogle Scholar

Copyright information

© Marta Olivetti Belardinelli and Springer-Verlag 2008

Authors and Affiliations

  1. 1.Universität BremenBremenGermany
  2. 2.Universität FreiburgFreiburgGermany

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