  Explicitly accounting for uncertainties is paramount to the safety of
engineering structures. Optimization which is often carried out at the early
stage of the structural design offers an ideal framework for this task. When
the uncertainties are mainly affecting the objective function, robust design
optimization is traditionally considered. This work further assumes the
existence of multiple and competing objective functions that need to be dealt
with simultaneously. The optimization problem is formulated by considering
quantiles of the objective functions which allows for the combination of both
optimality and robustness in a single metric. By introducing the concept of
common random numbers, the resulting nested optimization problem may be solved
using a general-purpose solver, herein the non-dominated sorting genetic
algorithm (NSGA-II). The computational cost of such an approach is however a
serious hurdle to its application in real-world problems. We therefore propose
a surrogate-assisted approach using Kriging as an inexpensive approximation of
the associated computational model. The proposed approach consists of
sequentially carrying out NSGA-II while using an adaptively built Kriging model
to estimate the quantiles. Finally, the methodology is adapted to account for
mixed categorical-continuous parameters as the applications involve the
selection of qualitative design parameters as well. The methodology is first
applied to two analytical examples showing its efficiency. The third
application relates to the selection of optimal renovation scenarios of a
building considering both its life cycle cost and environmental impact. It
shows that when it comes to renovation, the heating system replacement should
be the priority.
