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.
Highlights
The construction, operation, and maintenance of civil engineering and building structures account for Gothenburg, Sweden very large costs, and major negative environmental and social impacts in terms of the tremendous material consumption, as well as health and safety issues often associated with construction activities.Today, it becomes increasingly important to take various objectives into account to improve buildability and performance of structures and reduce their economic, environmental, and social impacts in a life cycle perspective
A state-of-the-art constrained Bayesian optimization algorithm has been adapted to a reinforced concrete (RC) beam optimization problem incorporating multiple objectives
Contrasting previous approaches, the Bayesian algorithm proposed in this work explicitly utilizes that objective functions are cheap to evaluate while constraint functions have expensive evaluations, as constraint function evaluations include expensive numerical computations, which are common characteristics in structural engineering design problems
Summary
The construction, operation, and maintenance of civil engineering and building structures account for . Multi-objective optimization concerns the problem of simultaneously maximizing the utility values of multiple, typically conflicting, objective functions (Tamaki et al 1996) For engineering applications, this setting is generally more common than the single-objective setting as usually many objectives have to be balanced (Nakayama 2005), e.g., the cost and performance of a construction. The benchmark problem considered consists of structurally optimizing a doubly reinforced concrete beam over a number of design parameters (i.e., dimensions, reinforcement layout, material type) with respect to objective functions covering economic, environmental, and social factors, buildability, and performance aspects of the design options, while fulfilling structural design constraints according to design codes.
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