# Algorithm

The RouteXL planning algorithm uses travel times and a optimization method to minimize total travel time.

## Travel times

To find the best route, the travel times between all locations are required. While most other route optimization tools use geographic distances (as the crow flies), RouteXL uses a crowdsourced road network. OpenStreetMap is the free Wiki World Map, an openly licensed map of the world being created by volunteers using local knowledge, GPS tracks and donated sources.

Learn more: https://www.openstreetmap.org/

### Traffic

The travel times do not incorporate actual or forecasted traffic. There are some ways to adjust the routes for traffic:

- You can set time windows for your stops, which can be used to visited certain places during specific hours. E.g. you could set a ready time at 10AM to visit some address after morning rush hours.

- You can change the speed parameter, which makes travel times shorter or longer. E.g. maximum speeds during rush hours may be to optimistic, setting the speed to 60% may be more realistic.

- You can drag & drop stops in order manually after the route optimization.

- When driving, you can launch third-party navigation apps which have actual traffic, e.g. Google Maps or Waze.

## Optimization

Routing multiple addresses is quite a puzzle. With 20 destinations the from-to travel times matrix has roughly 20 x 20 = 400 elements. Each element represents one route between two points. To sort 20 destinations the algorithm first needs to calculate 400 individual routes. No wonder route optimization is much more time consuming than simple A-to-B routing!

The number of possible routes to visit 20 destinations is even larger than that. The first pick can be any of the 20 destinations, so there are 20 possible choices for the first stop. For the second there are 19 choices left. That means there are 20 x 19 = 380 combinations for the first two stops. There are 18 choices for the third stop after that, making 20 x 19 x 18 combinations. And so on. For the full route there are approximately 20 x 19 x 18 x ... x 3 x 2 x 1 = 2,432,902,008,176,640,000 combination.

Mathematicians call route optimization a "hard" problem and there is no final one-size-fits-all solution available. They even have a name for it: *The Travelling Salesman Problem* (TSP). Indeed, humans can fly to the moon, but in math there is no ultimate answer to this problem.

Learn more: https://en.wikipedia.org/wiki/Travelling_salesman_problem

Operations Research researchers however have found some very good methods. Our algorithm is an effective implementation that finds the optimal route in most cases. But it is an algorithm for matter of speed that does not guarantee optimality.

### Runtime

The maximum runtime for the optimization algorithm is 15 minutes. If you have a large route, with many stops and a complex distribution (e.g. scattered in a large/urban area), the calculations may take the full 15 minutes. During this you can not optimize another route due to the Fair Use Policy.

When the algorithm is running on the website or webapp, a progress indicator is shown. The expected runtime may however not be enough for the algorithm. If the algorithm needs more time, the progress indicator will pause at approximately 80% until the algorithm finishes and the route is shown on the map.