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Routing multiple addresses is quite a puzzle. With 20 First, you'll need a distance matrix for all destinations the from-to . Or better: travel times matrix has roughly 20 x 20 = 400 elements. Each element represents one route between two points. To sort 20 destinations , as the algorithm first needs to calculate 400 individual routesminimizes total travel time. No wonder route optimization is much more time consuming than simple A-to-B routing!

The number of possible routes to visit With 20 destinations is even larger than that. The first pick can be any of the travel times matrix has roughly 20 destinations, so there are x 20 possible choices for the first stop= 400 elements. For the second there are 19 choices leftEach element represents one route between two points. That means there are To sort 20 x 19 = 380 combinations for destinations the algorithm first two stops. There are 18 choices for the third stop after that, making 20 x 19 x 18 combinationsneeds to calculate 400 individual routes. And so on. For the full No wonder route there are approximately 20 x 19 x 18 x ... x 3 x 2 x 1 = 2,432,902,008,176,640,000 combination.optimization is much more time consuming than simple A-to-B routing!

Secondly, 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 solution to this routing problem.

However, Operations Research researchers however have found some very good approximation 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.