OpenTripPlanner is a popular open-source multi-modal trip planner. It can be used to calculate routes that involve multiple transportation modes like walking, biking, buses, trains, and more.
- GitHub Repository: [OpenTripPlanner](https://github.com/opentripplanner/OpenTripPlanner)

- GraphHopper is an open-source routing engine that can be used for car, bike, and pedestrian routing. It's highly customizable and can be used as a backend for route planning.
- GitHub Repository: [GraphHopper](https://github.com/graphhopper/graphhopper)

Mapbox provides a Directions API that can be used for route optimization and navigation. While it's not open source, it's a popular choice for building travel-related applications.
- Website: [Mapbox Directions API](https://www.mapbox.com/directions)

- OSRM is an open-source routing engine for calculating shortest paths. It's designed for use with OpenStreetMap data and supports various travel modes.
- GitHub Repository: [OSRM](https://github.com/Project-OSRM/osrm-backend)

Leaflet is an open-source JavaScript library for interactive maps. You can combine it with other routing libraries to create a front-end for your travel planning application. - GitHub Repository: [Leaflet](https://github.com/Leaflet/Leaflet)

GTFS is not a software but a data format used by many public transportation agencies to provide their transit data. You can use GTFS feeds in your application to integrate public transit information.
- More Information: [GTFS on GitHub](https://github.com/google/transitfeed)