  The optimization of high dimensional functions is a key issue in engineering
problems but it frequently comes at a cost that is not acceptable since it
usually involves a complex and expensive computer code. Engineers often
overcome this limitation by first identifying which parameters drive the most
the function variations: non-influential variables are set to a fixed value and
the optimization procedure is carried out with the remaining influential
variables. Such variable selection is performed through influence measures that
are meaningful for regression problems. However it does not account for the
specific structure of optimization problems where we would like to identify
which variables most lead to constraints satisfaction and low values of the
objective function. In this paper, we propose a new sensitivity analysis that
accounts for the specific aspects of optimization problems. In particular, we
introduce an influence measure based on the Hilbert-Schmidt Independence
Criterion to characterize whether a design variable matters to reach low values
of the objective function and to satisfy the constraints. This sensitivity
measure makes it possible to sort the inputs and reduce the problem dimension.
We compare a random and a greedy strategies to set the values of the
non-influential variables before conducting a local optimization. Applications
to several test-cases show that this variable selection and the greedy strategy
significantly reduce the number of function evaluations at a limited cost in
terms of solution performance.
