# Global sensitivity analysis for optimization with variable selection

arXiv: https://arxiv.org/abs/1811.04646 · HTML: https://mlsanity.com/paper/1811.04646/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2018.

## Built on by (most cited first, 9 of 9)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Making Sense of Dependence: Efficient Black-box Explanations Using Dependence Measure](https://mlsanity.com/paper/2206.06219/) (2022)
- [Revisiting Bayesian Optimization in the light of the COCO benchmark](https://mlsanity.com/paper/2103.16649/) (2021)
- [High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft](https://mlsanity.com/paper/2311.06130/) (2023)
- [Global Optimization of Gaussian Process Acquisition Functions Using a Piecewise-Linear Kernel Approximation](https://mlsanity.com/paper/2410.16893/) (2024)
- [Active Learning for Derivative-Based Global Sensitivity Analysis with Gaussian Processes](https://mlsanity.com/paper/2407.09739/) (2024)
- [A Tutorial on the Design, Experimentation and Application of Metaheuristic Algorithms to Real-World Optimization Problems](https://mlsanity.com/paper/2410.03205/) (2024)
- [Goal-Oriented Sensitivity Analysis of Hyperparameters in Deep Learning](https://mlsanity.com/paper/2207.06216/) (2022)
- [Shared active subspace for multivariate vector-valued functions](https://mlsanity.com/paper/2401.02735/) (2024)

## Abstract (arXiv)

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.