Path planning and optimization in the traveling salesman problem: Nearest neighbor vs. region-based strategies

For large numbers of targets, route planning can be a very complex and computationally expensive task. Human navigators, however, usually solve route planning tasks fastly and efficiently. Here two experiments are presented that studied human route planning performance as well as the cognitive strategies and processes involved. 25 places were arranged on a regular grid in a large room. Each place was marked by a unique symbol. Subjects were repeatedly asked to solve traveling salesman problems (TSP), i.e. to find the shortest closed loop connecting a given start place with a number of target places. For each trial, subjects were given a so-called ’shopping list’ depicting the symbols of the start place and the target places. While the exact TSP is computationally hard, approximate solutions can be found by simple strategies such as the nearest neighbor strategy. Experiment 1 testedwhether humans employed the nearest neighbor (NN) strategy when solving the TSP. Results showed that subjects outperformed the NN strategy in cases in which the NN strategy did not predict the optimal solution, demonstrating that the NN strategy is not sufficient to explain human route planning behavior. As a second possible path planning strategy a region-based approach was tested in Experiment 2. When optimal routes required more region transitions than other, sub-optimal routes, subjects preferred these sub-optimal routes. This result suggests that subjects first planned a coarse route on the region level and then refined this route plan during navigation. Such a hierarchical planning strategy allows to reduce both, computational effort and working memory load during path planning.