Multi-objective constrained Bayesian optimization for structural design
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RESEARCH PAPER
Multi-objective constrained Bayesian optimization for structural design 3,4 · Magnus Onnheim 3,4 · Kristine Ek2 · ¨ ¨ Alexandre Mathern1,2 · Olof Skogby Steinholtz3,4 · Anders Sjoberg 1 3,4 3,4 Rasmus Rempling · Emil Gustavsson · Mats Jirstrand
Received: 21 February 2020 / Revised: 9 July 2020 / Accepted: 10 August 2020 © The Author(s) 2020
Abstract 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. Keywords Structural design · Multi-objective optimization · Bayesian optimization · Reinforced concrete beam · Sustainability · Buildability
1 Introduction The construction, operation, and maintenance of civil engineering and building structures account for not only
Responsible Editor: Ji-Hong Zhu Alexandre Mathern
[email protected] 1
Department of Architecture and Civil Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
2
NCC AB, SE-405 14 Gothenburg, Sweden
3
Fraunhofer-Chalmers Centre, SE-412 88 Gothenburg, Sweden
4
Fraunhofer Center for Machine Learning, SE-412 88 Gothenburg, Sweden
very large costs, but also major negative environmental and social impacts in terms of the tremendous material consumption, as well as health and safety issues often associated with construction activiti
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