Just a WAG (wild *** guess) but I think a restriction would be the way to go. Think of it this way; if you add a cost all that does is give the solver a reason to minimize the cost. But what if it can't? Lets say a route for a vehicle is restricted due to barriers of some sort. It would then route under/over the bridge in question just because it could. The cost is what it is. But the real problem is you routed a truck over a bridge that can't support it's weight or under one that isn't tall enough for the load to pass. Ouch...A restriction like xyz,xyz lbs or xyz feet would ensure you from what I like to call a 'resume generating event'...
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