Efficient Multi-Objective Constrained Bayesian Optimization of Bridge Girder

The buildings and construction sector is a significant source of greenhouse gas emissions, with cement production alone contributing 7~\% of global emissions and the industry as a whole accounting for approximately 37~\%. Reducing emissions by optimizing structural design can achieve significant global benefits. This article introduces an efficient multi-objective constrained Bayesian optimization approach to address this challenge. Rather than attempting to determine the full set of non-dominated solutions with arbitrary trade-offs, the approach searches for a solution matching a specified trade-off. Structural design is typically conducted using computationally expensive finite element simulations, whereas Bayesian optimization offers an efficient approach for optimizing problems that involve such high-cost simulations. The proposed method integrates proper orthogonal decomposition for dimensionality reduction of simulation results with Kriging partial least squares to enhance efficiency. Constrained expected improvement is used as an acquisition function for Bayesian optimization. The approach is demonstrated through a case study of a two-lane, three-span post-tensioned concrete bridge girder, incorporating fifteen design variables and nine constraints. A comparison with conventional design methods demonstrates the potential of this optimization approach to achieve substantial cost reductions, with savings of approximately 10\% to 15\% in financial costs and about 20\% in environmental costs for the case study, while ensuring structural integrity.