There's OSRM and a very good commercial routing engine from Graphopper. I believe they also offer the core features as an opensource Java routing server. For cy

There's OSRM and a very good commercial routing engine from Graphopper. I believe they also offer the core features as an opensource Java routing server. For cycling it has three separate profiles favouring one route over the other and two profiles for walking and hiking. The commercial version allows multi routing and route optimisation. You give it a fleet of vehicles and a number of POIs for them to visit and it splits the work between vehicles and optimally routes them.