The Euclidean Traveling Salesperson Problem (E-TSP) is a useful task to study how humans optimize when faced with computational intractability. It has been found that humans are capable of finding high-quality solutions for E-TSP in a relatively short time and with seemingly little cognitive effort. This observation has led to two general proposals: The high quality of performance on E-TSP reflects (a) the output of automatic and innate perceptual processes or (b) a fundamentally intelligent approach to the task by humans. An experiment was performed to compare performance of three age groups (7- year-olds, 12-year-olds, and adults). Our findings provide corroborating evidence that high-level performance on E-TSP is attainable with perceptual processing alone. At the same time, the exceptionally high performance of adult participants suggests that they additionally exploit their cognitive-analytic skills to improve upon what their visual systems provide.