Are there some real-world optimization problems with very cheap objective functions?
If you don't consider the Traveling Salesman Problem to be "real-world" enough, maybe take a look at its close cousin the Vehicle Routing Problem (VRP). In particular, consider all the variations of VRP, many of which clearly have their origins in real-world situations (e.g.: time windows, backhauls, etc...). This survey (pdf) by Eksioglu et al. details many of these variations. And, as far as I can tell, VRP objective functions are not much more difficult to evaluate than those of TSPs.