Route selection by rats and humans in a navigational traveling salesman problem

Abstract

Spatial cognition is typically examined in non-human animals from the perspective of learning and memory. For this reason, spatial tasks are often constrained by the time necessary for training or the capacity of the animal’s short-term memory. A spatial task with limited learning and memory demands could allow for more efficient study of some aspects of spatial cognition. The traveling salesman problem (TSP), used to study human visuospatial problem solving, is a simple task with modifiable learning and memory requirements. In the current study, humans and rats were characterized in a navigational version of the TSP. Subjects visited each of 10 baited targets in any sequence from a set starting location. Unlike similar experiments, the roles of learning and memory were purposely minimized; all targets were perceptually available, no distracters were used, and each configuration was tested only once. The task yielded a variety of behavioral measures, including target revisits and omissions, route length, and frequency of transitions between each pair of targets. Both humans and rats consistently chose routes that were more efficient than chance, but less efficient than optimal, and generally less efficient than routes produced by the nearest-neighbor strategy. We conclude that the TSP is a useful and flexible task for the study of spatial cognition in human and non-human animals.

Appendix

A simplified, 4-node TSP example is presented here to illustrate the scoring procedure that was used. All four configurations were designed on a 10 × 10 grid, with 1 unit mapping to approximately 10 cm in the rat arena, and 60 cm in the human arena. Transition distances between each pair of targets are indicated on the grid in units.

In this example, assuming the “Start” node is 1, the optimal route (left) is 1–2–3–4, which can be completed in 3 total transitions (1–2; 2–3; 3–4). A hypothetical rat might produce the example route to the right: Visit target 1, transition to 2, then to 3, return to the previously visited 2, then proceed directly from 2 to 4. This route would include 4 transitions (1–2; 2–3; 3–2; 2–4), producing the example matrix below. Three of those transitions (1–2; 2–3; 3–2) are along the optimal route (the diagonal), while one (2–4) is not; therefore 75% of transitions are along the optimal route. Similarly, the total path distance is 5.6 units, with 3.4 units along the optimal route; therefore, 61% of the travel distance is along the optimal route. According to chance (equal probability of each transition), 50% of transitions are on the optimal route, and 40% of the total path distance is along the optimal route.