Why does an additional waypoint produce less overall kilometers?

[Bernd Welter]

Ive just been asked why inserting a single stop somewhere on a tour might cause the overall length of the tour to get reduced instead of increased.

Here's a simple example...

• ZThe blue route i just the route from Karsruhe to Heilbronn with a standard VAN profile. As the focus on distTimeWeight is 80% (prio towards traveltime) the ROUTING decides to go via the highway though this is a detour.
• The green route is created with an additional enforded stop in th countryside. This pushes a shorter overall distance but at the same time the travel time increases from 54:52 to 1:18:05.

In the mathematical perspective one would doubt in the "triangle inequality"... but in fact this has to be applied on the underlying cost metric:

• Cost(KARLSRUHE : HEILBRONN) <= Cost(KARLSRUHE : VIA) + Cost(VIA : HEILBRONN)