Topology optimization. minimizing compliance for specified volume fraction

In topology optimization when minimizing compliance for specified volume fraction, the maximum deflection of optimized structure is less than the maximum deflection of original structure?

based on this formula 

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For constant F when compliance is minimized U( deflection) should be minimized and vice versa. but in this formula volume fraction is not considered. 

I don't understand the concept of minimum compliance. The compliance of the optimized structure which is lighter than the original structure (since some material is removed from it) is even less than the original structure??!!