Say, we have our N blocks. We make these into the nodes in a graph. Every node is connected to all other nodes.
An edge leading from A to B is a case when block A precedes block B. The weight of that edge is the AB overlap. Note that the same edge may have a different weight in the opposite direction, because it will be that of the BA overlap.
So what we are after is the heaviest path through this graph that passes through all nodes exactly once. This can be reduced to finding the heaviest cyclic path for a specific starting point (and excluding the cheapest edge from the solution and then iterating through all points). This is pretty much TSP with an inverted goal.
An edge leading from A to B is a case when block A precedes block B. The weight of that edge is the AB overlap. Note that the same edge may have a different weight in the opposite direction, because it will be that of the BA overlap.
So what we are after is the heaviest path through this graph that passes through all nodes exactly once. This can be reduced to finding the heaviest cyclic path for a specific starting point (and excluding the cheapest edge from the solution and then iterating through all points). This is pretty much TSP with an inverted goal.