Practice makes proficient: pigeons (Columba livia) learn efficient routes on full-circuit navigational traveling salesperson problems
Visiting multiple locations and returning to the start via the shortest route, referred to as the traveling salesman (or salesperson) problem (TSP), is a valuable skill for both humans and non-humans. In the current study, pigeons were trained with increasing set sizes of up to six goals, with each set size presented in three distinct configurations, until consistency in route selection emerged. After training at each set size, the pigeons were tested with two novel configurations. All pigeons acquired routes that were significantly more efficient (i.e., shorter in length) than expected by chance selection of the goals. On average, the pigeons also selected routes that were more efficient than expected based on a local nearest-neighbor strategy and were as efficient as the average route generated by a crossing-avoidance strategy. Analysis of the routes taken indicated that they conformed to both a nearest-neighbor and a crossing-avoidance strategy significantly more often than expected by chance. Both the time taken to visit all goals and the actual distance traveled decreased from the first to the last trials of training in each set size. On the first trial with novel configurations, average efficiency was higher than chance, but was not higher than expected from a nearest-neighbor or crossing-avoidance strategy. These results indicate that pigeons can learn to select efficient routes on a TSP problem.
KeywordsTraveling salesman problem Pigeon Route learning Problem solving Nearest-neighbor strategy Crossing avoidance Planning Foraging
We thank Nicole Savignac for assistance with subject running and data scoring and Isaac Lank for assistance with constructing the apparatus. This study was funded by a Natural Sciences and Engineering Research Council of Canada Discovery grant awarded to MLS. Some of these data were presented at the 19th Annual International Conference on Comparative Cognition in March, 2012. All research was conducted in accordance with Canadian Council on Animal Care guidelines and with approval from the University of Alberta Animal Care and Use Committee. The experiments comply with the current laws of Canada.
Conflict of interest
The authors declare that they have no conflict of interest.
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