Multi-objective constrained Bayesian optimization for structural design
Journal article, 2021

The planning and design of buildings and civil engineering concrete structures constitutes a complex problem subject to constraints, for instance, limit state constraints from design codes, evaluated by expensive computations such as finite element (FE) simulations. Traditionally, the focus has been on minimizing costs exclusively, while the current trend calls for good trade-offs of multiple criteria such as sustainability, buildability, and performance, which can typically be computed cheaply from the design parameters. Multi-objective methods can provide more relevant design strategies to find such trade-offs. However, the potential of multi-objective optimization methods remains unexploited in structural concrete design practice, as the expensiveness of structural design problems severely limits the scope of applicable algorithms. Bayesian optimization has emerged as an efficient approach to optimizing expensive functions, but it has not been, to the best of our knowledge, applied to constrained multi-objective optimization of structural concrete design problems. In this work, we develop a Bayesian optimization framework explicitly exploiting the features inherent to structural design problems, that is, expensive constraints and cheap objectives. The framework is evaluated on a generic case of structural design of a reinforced concrete (RC) beam, taking into account sustainability, buildability, and performance objectives, and is benchmarked against the well-known Non-dominated Sorting Genetic Algorithm II (NSGA-II) and a random search procedure. The results show that the Bayesian algorithm performs considerably better in terms of rate-of-improvement, final solution quality, and variance across repeated runs, which suggests it is well-suited for multi-objective constrained optimization problems in structural design.

structural design


Bayesian optimization

Reinforced concrete beam

multi-objective optimization



Alexandre Mathern


Chalmers, Architecture and Civil Engineering, Structural Engineering

Olof Skogby Steinholtz

Fraunhofer-Chalmers Centre

Anders Sjöberg

Fraunhofer-Chalmers Centre

Magnus Önnheim

Fraunhofer-Chalmers Centre

Kristine Ek


Rasmus Rempling

Chalmers, Architecture and Civil Engineering, Structural Engineering

Emil Gustavsson

Fraunhofer-Chalmers Centre

Mats Jirstrand

Fraunhofer-Chalmers Centre

Structural and Multidisciplinary Optimization

1615-147X (ISSN) 1615-1488 (eISSN)

Vol. 63 2 689-701

Sustainable design and production planning

Swedish Transport Administration, 2017-11-01 -- 2020-05-29.

VINNOVA, 2017-11-01 -- 2020-02-29.

NCC AB, 2017-11-01 -- 2020-05-29.

A pilot - Sustainability driven building design based on Artificial Intelligence

Formas, 2018-12-01 -- 2019-09-30.

Projekteringsprocess för ökad hänsyn till produktions­metoder, klimat och miljöpåverkan i byggprocessen

Swedish Transport Administration, 2018-07-01 -- 2020-06-30.

Driving Forces

Sustainable development

Subject Categories

Applied Mechanics

Civil Engineering

Computational Mathematics

Computer Science

Areas of Advance




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Latest update

3/9/2021 1