# Convex hull and tour crossings in the Euclidean traveling salesperson problem: Implications for human performance studies

@article{Rooij2003ConvexHA, title={Convex hull and tour crossings in the Euclidean traveling salesperson problem: Implications for human performance studies}, author={Iris van Rooij and Ulrike Stege and Alissa Schactman}, journal={Memory \& Cognition}, year={2003}, volume={31}, pages={215-220} }

Recently there has been growing interest among psychologists in human performance on the Euclidean traveling salesperson problem (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent hypothesis is the convex-hull hypothesis, originally proposed by MacGregor and Ormerod (1996). We argue that, in the literature so far, there is no evidence for this hypothesis. Alternatively we propose and motivate the hypothesis that…

## 66 Citations

Convex hull or crossing avoidance? Solution heuristics in the traveling salesperson problem

- Psychology, MedicineMemory & cognition
- 2004

The crossing avoidance hypothesis was examined from the perspectives of its capacity to explain existing data, its theoretical adequacy, and its ability to explain the results of three new experiments, which were more consistent with the convex hull than with the crossing avoidance hypotheses.

The Perception of Minimal Structures: Performance on Open and Closed Versions of Visually Presented Euclidean Travelling Salesperson Problems

- Psychology, MedicinePerception
- 2003

An experiment examines the relationships between three objective measures and performance measures of optimality and response uncertainty in tasks requiring participants to construct a closed tour or an open path and finds results are generally consistent with a locally focused process based initially on the detection of nearest-neighbour clusters.

Introducing convex layers to the Traveling Salesman Problem

- Computer ScienceArXiv
- 2012

This paper proposes convex layers to the Traveling Salesman Problem based on the argument that, by the analogy to the social insect behavior, untrained humans' cognition should be able to help in the TSP.

A Comparison of Heuristic and Human Performance on Open Versions of the Traveling Salesperson Problem

- Mathematics, Computer ScienceJ. Probl. Solving
- 2006

Of the three heuristics compared with that of subjects on variants of a well-known combinatorial optimization task, the Traveling Salesperson Problem, the convex hull appeared to result in the best overall fit with human solutions.

Acknowledging crossing-avoidance heuristic violations when solving the Euclidean travelling salesperson problem

- Computer Science, MedicinePsychological research
- 2018

This study systematically investigates whether the occurrence of crossings is impacted by geometric properties by modelling their relationship using binomial logistic regression as well as random forests, and shows that properties, such as the number of nodes making up the convex hull, are significant predictors of whether crossings are likely to occur.

People Efficiently Explore the Solution Space of the Computationally Intractable Traveling Salesman Problem to Find Near-Optimal Tours

- Medicine, PsychologyPloS one
- 2010

The first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics are provided.

The roles of the convex hull and the number of potential intersections in performance on visually presented traveling salesperson problems

- Psychology, MedicineMemory & cognition
- 2003

Evidence for and against the idea that people solve such problems by using a global-to-local perceptual organizing process based on the convex hull of the array are reviewed, before considering an alternative, local- to-global perceptual process,based on the rapid automatic identification of nearest neighbors.

Human Performance on Visually Presented Traveling Salesperson Problems with Varying Numbers of Nodes

- Mathematics, Computer ScienceJ. Probl. Solving
- 2006

The most likely polynomial model for describing the relationship between mean solution time and the size of a TSP is linear or near-linear over the range of problem sizes tested, supporting the earlier finding of Graham et al. (2000).

Some Tours are More Equal than Others: The Convex-Hull Model Revisited with Lessons for Testing Models of the Traveling Salesperson Problem

- Mathematics, Computer ScienceJ. Probl. Solving
- 2008

It is argued that the empirical tests performed by MacGregor et al. do not constitute support for the model, because they instantiate what Meehl (1997) coined "weak tests" (i.e., tests with a high probability of yielding confi rmation even if the model is false).

Traveling Salesman Problem: The Human Case

- Computer ScienceKünstliche Intell.
- 2008

This paper systematically disentangle the cognitive processes and the range of external factors that influence problem solving in tasks that resemble the classical TSP, covering the area so as to include everyday human navigation tasks.

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