Fast and efficient discrimination of traveling salesperson problem stimulus difficulty

Abstract

The Travelling Salesperson Problem (TSP) is a computationally difficult combinatorial optimization problem. In spite of its relative difficulty human solvers are able to generate close-to-optimal solutions in a close-to-linear time frame, and it has been suggested that this is due to the visual system’s inherent sensitivity to certain geometric properties of TSP stimuli. In the current study we employed a novel experimental paradigm in which we presented participants with sets of four TSP stimuli that varied in terms of their relative solution difficulty and asked them to indicate which of the four stimuli they would prefer to solve. The results indicated that the participants’ choice frequencies followed the same ordering as the stimuli’s empirical solution difficulty; i.e., easy-to-solve stimuli were chosen with a higher frequency than hard-to-solve stimuli. It is suggested that these results provide further evidence of the speed and efficiency of human processing of TSPs, and provide further evidence implicating the role of rapid visuo-perceptual organization in generating TSP solutions. An analysis of the geometric properties of the stimuli uncovered a number of factors that may have influenced the choice preferences of participants in the current experiment, and the performance quality of participants in previous experiments.