Route choice is often modelled as a two-step procedure in which travellers choose their routes from small sets of promising candidates. Many methods developed to identify such choice sets rely on assumptions about the mechanisms behind the route choice and require corresponding data sets. Furthermore, existing approaches often involve considerable complexity or perform many repeated shortest path queries. This makes it difficult to apply these methods in comprehensive models with numerous origin-destination pairs. In this paper, we address these issues by developing an algorithm that efficiently identifies locally optimal routes. Such paths arise from travellers acting rationally on local scales, whereas unknown factors may affect the routes on larger scales. Though methods identifying locally optimal routes are available already, these algorithms rely on approximations and return only few, heuristically chosen paths for specific origin-destination pairs. This conflicts with the demands of route choice models, where an exhaustive search for many origins and destinations would be necessary. We therefore extend existing algorithms to return (almost) all admissible paths between a large number of origin-destination pairs. We test our algorithm on a road network modelling the Canadian province British Columbia and analyze the distribution of locally optimal paths in the province.