The least cost route is not being used about brouter HOT 3 CLOSED

This is a problem with the height buffer. If you take a longer route and force the Route by no-go areas (don't use intermediate points, because they reset the buffer) you see in the data that this segment is evaluated with 6000/km.
https://brouter.de/brouter-web/#map=16/50.0058/8.2233/osm-mapnik-german_style,route-quality&lonlats=8.23367,50.007737;8.20204,50.002272&nogos=8.224322,50.006674,32;8.219283,50.001746,205;8.223221,50.008357,185

With the detour you get a lower overall cost:

This is your uphillcostfactor for this segment. If you lower mixed_traffic_uphill_penalty from 4.3 to 3.5 or rise the uphillcutoff from 1.1 to 3 you won't have the detour.

from brouter.

At first glance this seems to be some kind of aliasing issue in the elevation buffer logic. You can fix it by either raising the downhillcutoff and uphillcutoff values back to the default of 1.5 m or by raising the elevationpenaltybuffer to 10 m.

Edit: On an aside the problem does not occur when using Sonny's LiDAR elevation data.

from brouter.

Ok, wow! Thank you @vodie and @quaelnix for the detailed and very helpful explanation!

I raised the elevationpenaltybuffer to 10m as suggested which resolved this problem for me 👍

I will try to further dig into the elevation data topic when I find some time, looks promising.

from brouter.