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

@article{Kyritsis2018AcknowledgingCH,
  title={Acknowledging crossing-avoidance heuristic violations when solving the Euclidean travelling salesperson problem},
  author={Markos Kyritsis and Stephen R. Gulliver and Eva Feredoes},
  journal={Psychological Research},
  year={2018},
  volume={82},
  pages={997-1009}
}
AbstractIf a salesperson aims to visit a number of cities only once before returning home, which route should they take to minimise the total distance/cost? This combinatorial optimization problem is called the travelling salesperson problem (TSP) and has a rapid growth in the number of possible solutions as the number of cities increases. Despite its complexity, when cities and routes are represented in 2D Euclidean space (ETSP), humans solve the problem with relative ease, by applying simple… 

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References

SHOWING 1-10 OF 47 REFERENCES
Convex hull or crossing avoidance? Solution heuristics in the traveling salesperson problem
TLDR
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 roles of the convex hull and the number of potential intersections in performance on visually presented traveling salesperson problems
TLDR
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.
Convex hull and tour crossings in the Euclidean traveling salesperson problem: Implications for human performance studies
TLDR
It is argued that, in the literature so far, there is no evidence for the convex-hull hypothesis, and the hypothesis that people aim at avoiding crossings is proposed and motivated.
Clustering, Randomness, and Regularity: Spatial Distributions and Human Performance on the Traveling Salesperson Problem and Minimum Spanning Tree Problem
TLDR
It is suggested that these results provide support for the ideas that human solv- ers attend to salient clusters of nodes when solving these problems, and that a similar process (or series of processes) may underlie human performance on these two tasks.
Human Performance on Visually Presented Traveling Salesperson Problems with Varying Numbers of Nodes
TLDR
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).
The Traveling Salesman Goes Shopping: The Systematic Deviations of Grocery Paths from TSP-Optimality
We examine grocery shopping paths using the traveling salesman problem (TSP) as a normative frame of reference. We define the TSP-path for each shopper as the shortest path that connects all of his
Human performance on the traveling salesman problem
TLDR
Two experiments on performance on the traveling salesman problem (TSP) are reported, testing the hypothesis that complexity of TSPs is a function of number of nonboundary points, not total number of points.
Analysis of Christofides' heuristic: Some paths are more difficult than cycles
  • H. Hoogeveen
  • Computer Science, Mathematics
    Oper. Res. Lett.
  • 1991
TLDR
This work investigates the performance of appropriate modifications of Christofides' heuristic for the problem of finding a shortest Hamiltonian path and shows that the ratio is 53 and that this bound is tight.
Research Note - The Traveling Salesman Goes Shopping: The Systematic Deviations of Grocery Paths from TSP Optimality
TLDR
The results suggest that (1) a large proportion of trip length is because of travel deviation; (2) paths that deviate substantially from the TSP solution are associated with larger shopping baskets; (3) order deviation is strongly associated with purchase behavior, while travel deviation is not; and shoppers with paths closer to the T SP solution tend to buy more from frequently purchased product categories.
Optimizing and “Pessimizing”: Human Performance with Instructional Variants of the Traveling Salesperson Problem
TLDR
Human performance was significantly worse than a simple construction algorithm (farthest-neighbor) for the task of finding long tours, consistent with the hypothesis of a specific, inherent ability to find short routes.
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