Global Sensitivity Analysis for Optimization with Variable Selection

Abstract

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