Algorithm

Routing multiple addresses is quite a puzzle. With 20 destinations the from-to travel distance matrix has roughly 20 x 20 = 400 elements. The number of possible routes is even bigger, approximately 20 x 19 x 18 x ... x 3 x 2 x 1 = 2432902008176640000

Mathematicians call it 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. Indeed, humans can fly to the moon, but can't solve this problem.

Method

RouteXL optimizes routes with an iterative search algorithm. That means that itineraries may not always be optimal, but they're close enough. RouteXL uses a hybrid method to minimize total travel time:

• Initial: several insertion methods to build a good initial route
• Improvement: several of improvement methods inspired by k-opt optimization
• Checking: if the quality check fails, the improvement phase is repeated

For more information on algorithms: https://en.wikipedia.org/wiki/Travelling_salesman_problem