I would like to combine lines into 1 line/route based on an attribute. The LineCombiner seems not to combine lines with a different orientation. So, if two lines have the same starting point, they are not combined. I put the parameter "preserve orientation" on "no", but this doesn't seem to have any result. The result has too many lines (different line at almost each beginning or endpoint of the incoming lines, due to a different orientation). Any suggestions?
I can't reproduce your issue and I did not expect I could. I suspect the startpoints are not exactly the same. You can try to fix this with a Snapper transformer upstream the LineCombiner.
Or try the Input Feature Topology to vertex noded.
I tested both. Setting the Input Feature Topology to vertex noded results in even many more separate lines in the result. The snapper reduces it a little bit, but I still got 120 resulting features, instead of the expected 22. 
I tested both. Setting the Input Feature Topology to vertex noded results in even many more separate lines in the result. The snapper reduces it a little bit, but I still got 120 resulting features, instead of the expected 22.
I think you first need to find out what the issue is before we can help you to fix it. If you want more help I think you need to share (a sample of) your data.
I think I found a clue ... The LineJoiner keeps splitting lines where multiple lines (with different attributes) overlap. So if route F1 and F3 parlly have the same location, the resulting F1-line is split at the point where F1 and F3 get a different route.