The ability to keep track of one’s location in space is a critical behavior for animals navigating to and from a salient location, and its computational basis is now beginning to be unraveled. Here, we tracked flies in a ring-shaped channel as they executed bouts of search triggered by optogenetic activation of sugar receptors. Unlike experiments in open field arenas, which produce highly tortuous search trajectories, our geometrically constrained paradigm enabled us to monitor flies’ decisions to move toward or away from the fictive food. Our results suggest that flies use path integration to remember the location of a food site even after it has disappeared, and flies can remember the location of a former food site even after walking around the arena one or more times. To determine the behavioral algorithms underlying Drosophila search, we developed multiple state transition models and found that flies likely accomplish path integration by combining odometry and compass navigation to keep track of their position relative to the fictive food. Our results indicate that whereas flies re-zero their path integrator at food when only one feeding site is present, they adjust their path integrator to a central location between sites when experiencing food at two or more locations. Together, this work provides a simple experimental paradigm and theoretical framework to advance investigations of the neural basis of path integration.