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

Abstract

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 of the quantiles. Finally, the methodology is adapted to account for mixed categoricalcontinuous 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.

Decision-making under uncertainty in the early phase of building façade design based on multi-objective stochastic optimization

“…As the data basis of this study, a knowledge-based database was created to integrate expert knowledge of building construction types, composition of building components and material applicability. Compared to other studies [15,26,46], the database enables a systematic integration of the most common construction types which circumvents cumbersome case-specific analysis and is thus beneficial in other arbitrary cases in the early design phase. On the basis of the knowledge-based database, categorical and continuous design parameters could be defined to calculate the objectives of LCA, LCC and thermal transmittance.…”

“…Uncertainties arise from the lack of information or knowledge about the true value of certain variables and occur during the early planning phase of a building [44,45]. In this paper, inspired by previous studies [26,46,47], two main kinds of uncertainties were defined: uncertainty in design decisions and environmental uncertainty. As aforementioned, the investigation focus within the scope of this paper is to find the optimal design solution of certain sub-component.…”

“…These uncertainties are expressed as the cumulative GWP (⇠ gwp ), costs (⇠ c ) and R-values (⇠ r ) of other sub-components that are not to be optimized. On the other hand, environmental uncertainties refer to changes in the parameters that are objectively determined only by environmental factors, such as weather and time [46]. Herein, no direct influence of design decisions is present.…”

Recommendations for robust renovation strategies of Swiss residential buildings

“…Surrogate models are useful when dealing with complex computational assessments and there are several techniques that can be used, for instance Polynomial chaos expansion or Kriging. In this work we use the methodology of coupling NSGA-II with Kriging as a Gaussian regression process for surrogate modeling proposed by Moustapha et al (Moustapha et al, 2022).…”