# Multi-objective robust optimization using adaptive surrogate models for problems with mixed continuous-categorical parameters

arXiv: https://arxiv.org/abs/2203.01996 · HTML: https://mlsanity.com/paper/2203.01996/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 91 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 7 of 7)

- [A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors](https://mlsanity.com/paper/1806.07504/) (2018)
- [Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms](https://mlsanity.com/paper/1904.12672/) (2019)
- [Group kernels for Gaussian process metamodels with categorical inputs](https://mlsanity.com/paper/1802.02368/) (2018)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process](https://mlsanity.com/paper/2006.15273/) (2020)
- [Bayesian optimization of variable-size design space problems](https://mlsanity.com/paper/2003.03300/) (2020)
- [Targeting Solutions in Bayesian Multi-Objective Optimization: Sequential and Batch Versions](https://mlsanity.com/paper/1811.03862/) (2018)

## Abstract (arXiv)

Explicitly accounting for uncertainties is paramount to the safety of engineering structures. Optimization which is often carried out at the early stage of the structural design offers an ideal framework for this task. When the uncertainties are mainly affecting the objective function, robust design optimization is traditionally considered. This work further assumes the existence of multiple and competing objective functions that need to be dealt with simultaneously. The optimization problem is formulated by considering quantiles of the objective functions which allows for the combination of both optimality and robustness in a single metric. By introducing the concept of common random numbers, the resulting nested optimization problem may be solved using a general-purpose solver, herein the non-dominated sorting genetic algorithm (NSGA-II). The computational cost of such an approach is however a serious hurdle to its application in real-world problems. We therefore propose a surrogate-assisted approach using Kriging as an inexpensive approximation of the associated computational model. The proposed approach consists of sequentially carrying out NSGA-II while using an adaptively built Kriging model to estimate the quantiles. Finally, the methodology is adapted to account for mixed categorical-continuous parameters as the applications involve the selection of qualitative design parameters as well. The methodology is first applied to two analytical examples showing its efficiency. The third application relates to the selection of optimal renovation scenarios of a building considering both its life cycle cost and environmental impact. It shows that when it comes to renovation, the heating system replacement should be the priority.