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

Abstract

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.

Appendices

Appendix

Example texts by one participant (Exp. 2: regionalized version)

Text 1: (Describe in as much detail as possible how you have solved the task)

“Zuerst habe ich mir die Zeichen in einer beliebigen Reihenfolge auf dem Feld angeschaut und “geistig” miteinander verbunden, dann habe ich versucht herauszufinden, an welchen Stellen ich den Weg verkürzen könnte. Dabei war es meist sinnvoller, die Zeichen der gleichen Farbe nacheinander abzuhaken, weil das eigene Farbfeld meist näher liegt als ein Anderes. Oft habe ich festgestellt, dass die Zeichen, die ich als zweiten oder dritten Schritt gewählt hatte sich viel besser am Schluss eingliederten->darin sah ich auch eine der Hauptkomplikationen. Eine Andere ist das schwarze Quadrat, da es meist als Mitte fungierte und somit die Punkte größer über das Blatt verteilt waren”.

Table 2 Strategy distribution in both experiments according to participants

Table 3 References to the path as trajectory: nouns (absolute numbers of occurrences)

Table 4 Features of the path: attributes (absolute numbers of occurrences)

Table 5 Processes associated with the path: verbs (absolute numbers of occurrences)

First I looked at the symbols in a random order in the field and “mentally” connected them with each other, then I tried to find out at which places I could shorten the path. In doing this it was mostly more sensible to tick off the symbols of the same color one after another, because the same color region was mostly closer than another. Often I realized that the symbols that I chose as second or third step were much better suitable for the end->that’s also where I saw one of the main complications. Another is the black square, since it typically served as midpoint and therefore the symbols were distributed more widely across the field.

Text 2: (Please write an instruction for a good friend of yours that allows him/her to solve the task as well as possible)

“Überlege dir, wie der kürzeste Weg über die auf der Liste aufgeführten Symbole aussehen könnte. Die Ausgangssymbol ist mit “Start” gekennzeichnet und ist gleichzeitig das Endsymbol. Achte vor allem auf das Ende der Strecke und überprüfe nochmals deine ersten Punkte. Wäre es vielleicht sinnvoller der Punkt am Ende einzugliedern? Denke nochmals nach, bevor du die Punkte legst. Wenn du einen Fehler gemacht hast, versuche ihn zu analysieren um ihn das nächste Mal zu vermeiden. Oft wird der kürzeste Weg erst offensichtlich, wenn die Punkte liegen, da du sie nicht verschieben darfst, versuche sie dir vorzustellen. Notiere anschließend die Zahlen vom zweiten Blatt (also die Positionen auf denen die Punkte liegen).”

Consider how the shortest path across the symbols shown in the list could look like. The starting symbol is marked as “start” and is simultaneously the end symbol. Pay particular attention to the end of the path and check again your first symbols. Could it be more sensible to integrate the symbol at the end? Reconsider again before you place the markers. If you have made a mistake, try to analyze it in order to avoid it next time. Often the shortest path only becomes obvious when the markers are placed, because you are not allowed to move them, try to imagine them. Note subsequently the numbers from the second sheet (that is, the positions on which the symbols lie).