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78 András Erik Csallner, Tibor Csendes, and András Balázs KocsisA simple example for a civil engineering problem consisting only of the nonlinear partis the simplified footing design problem [2]. The problem was to find the minimal volumedimensions of a concrete footing in such a way that given constraints hold. In detail:subject tomin hµB 2 (1)σ Sd ≤ σ Eff ,1 ≤ µ ≤ 5,0.5µB ≤ h ≤ −a s − 0.5,B > 0,− 5 6 B ≤ a x ≤ 5 6 B,− 5 6 µB ≤ a y ≤ 5 6 µB.where a x , a y , h, µ and B are the variables to be optimized. The functional dependencies arethe following:R = P z + µhB 2 ρ rc ,σ Sd =R() (),B − 2| Pzax+Pxh−MyR| µB − 2| Pzay+Pyh+MxR|(N t = e π tan φ tan 2 45 o + φ ),2σ 2 =σ 1 =f = P xP z,i t = (1 − 0.7f) 3(1 − 1 )γ 1 B(N t + 1) tan φ(1 − f) 3 j B ,3µ(1 + 1 ) ((γ 2 (|a s | − 0.1)N t i t j t + c(N t − 1) cot φ i t − 1 − i ) )tj c ,2µN t − 1σ Eff = α 1 α 2 α 3 (σ 1 + σ 2 ).The variable h contains the height of the footing, B is its width, and the respective lengthis µB. The building’s support point is shifted by the vector (a x , a y ) from the center of thefooting’s projection to the x-y plane.An interval method could supply a good inclusion for a suboptimal feasible set, while thetraditional engineers’ approach could only point out a single solution of this set near to theborder of it. Note that we were not able to find the global minimum even in this simple case.