  Toward a multi-objective optimization robust problem, the variations in
design variables and design environment pa-rameters include the small
variations and the large varia-tions. The former have small effect on the
performance func-tions and/or the constraints, and the latter refer to the ones
that have large effect on the performance functions and/or the constraints. The
robustness of performance functions is discussed in this paper. A
post-optimality sensitivity analysis technique for multi-objective robust
optimization problems is discussed and two robustness indices are introduced.
The first one considers the robustness of the performance func-tions to small
variations in the design variables and the de-sign environment parameters. The
second robustness index characterizes the robustness of the performance
functions to large variations in the design environment parameters. It is based
on the ability of a solution to maintain a good Pareto ranking for different
design environment parameters due to large variations. The robustness of the
solutions is treated as vectors in the robustness function space, which is
defined by the two proposed robustness indices. As a result, the designer can
compare the robustness of all Pareto optimal solutions and make a decision.
Finally, two illustrative examples are given to highlight the contributions of
this paper. The first example is about a numerical problem, whereas the second
problem deals with the multi-objective robust optimization design of a floating
wind turbine.
