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Global sensitivity analysis for optimization with variable selection

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Global sensitivity analysis for optimization with variable selection

Adrien Spagnol

1,3

Rodolphe Le Riche

2,1

Sebastien Da Veiga

3

Olivier Roustant

1

1

Ecole Nationale Superieure des Mines de Saint-Etienne, F-42023 Saint-Etienne, France,

[email protected], [email protected]

2

CNRS LIMOS UMR 6158, France

3

Safran Tech, Safran SA, Magny-Les-Hameaux, France,

[email protected], [email protected] Keywords: Variable selection, sensitivity analysis, HSIC, optimization.

The optimization of high dimensional functions is a key issue in engineering problems but it often comes at a cost that is not acceptable since it usually involves a complex and expensive computer code. In practice, engineers usually overcome this limitation by rst identifying which parameters drive the most the function variations: non-inuential variables are set to a xed value and the optimization procedure is then carried out with the remaining inuential variables only [1]. However, such variable selection is performed through inuence measures typically designed for regression problems, and does not account for the specic structure of an optimiza- tion problem. Ideally, we would like to identify which variables have an impact on constraints satisfaction and lead to low values of the objective function.

In this paper, we propose a new sensitivity analysis that incorporates the specic aspects of optimization problems. In particular, we introduce an inuence measure based on the Hilbert- Schmidt Independence Criterion to characterize [2] whether a design variable matters to reach low values of the objective function and to satisfy the constraints. This measure makes it possible to sort the inputs and reduce the problem dimension. We estimate the sensitivity for optimization measure from a design of experiments and propose a random and a greedy strategies to set the values of the non-inuential variables before conducting a local optimization. We apply our methods to several test-cases from common optimization benchmarks. Our results show how variable selection for optimization and the greedy strategy can signicantly reduce the number of function evaluations while still attaining satisfying minima.

References

[1] Zabalza-Mezghani, I., Manceau, E., Feraille, M., Jourdan, A. (2004). Uncertainty manage- ment: From geological scenarios to production scheme optimization. Journal of Petroleum Science and Engineering, 44(1), 11-25.

[2] Gretton, A., Bousquet, O., Smola, A., Scholkopf, B. (2005, October). Measuring statistical

dependence with Hilbert-Schmidt norms. In ALT (Vol. 16, pp. 63-78).

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