Making stops not in certain sequence in order to find shortest route with ArcGIS Network Analyst?

Is it possible to make stops not in a certain sequence in order to find the shortest route with the network analyst?

I now use the small green points as an input stops because I want the lines with a pink dot beside it in the route. Then I reorder them and don't preserve the end and startpoint. I thought this meant that the network analyst doesn't make a real sequence of the input stops and doesn't choose a real start and end point, and just finds the shortest route in between the points.

However if I look at the output of the tool (light green), it seems like the network analyst tool still uses a kind of sequence and begin and endpoint. Because in the picture it looks like the point where the blue arrow points to is a start or end point. The red line is the route I want. So the route makes a round now (at the left where the black arrow is) going past the south segment instead of going to the north and connect via the small grey link near the blue arrow (like the red route I want). The green output I now receive is not the shortest route.

I thought that one problem could be that the point near the blue arrow is assigned by the tool as start or end point and the other problem that the network analyst takes segment near the black arrow because the point in the south west (black circle) comes later in the sequence than the point in the middle (black circle). So, it gives each point 1,2,3 and so on, instead of tread them like all 0,0,0. So, I thought that this could be solved by having the stops as equal points (all zeros or something) and calculating the shortest route in between those instead of having the stops as a sequence and going from 1 to 2 and 3 and so on. But I don't know if this is right, see also last comment of @ChrisW, Using line feature as stops input in network analyst?.