Efficient Multi-Objective Constrained Bayesian Optimization of Bridge Girder

TL;DR

This work tackles the detection of cost- and environment-friendly bridge designs under multiple constraints by proposing an efficient constrained Bayesian optimization framework that targets a predefined trade-off. It fuses Proper Orthogonal Decomposition (POD) and Kriging Partial Least Squares (KPLS) with constrained acquisition (EI_c) to quickly converge to a preferred solution, rather than exhaustively mapping the Pareto front. The method is demonstrated on a 3-span post-tensioned concrete bridge girder with 15 design variables and 9 high-dimensional constraints, achieving about 20% reductions in environmental cost and 10–15% reductions in monetary cost compared to a traditional benchmark, while maintaining structural feasibility. The study also benchmarks against constrained EHVI and gradient-based Bayesian optimization, showing faster convergence and more targeted trade-offs, with insights into when KPLS or POD are most advantageous for surrogate modeling in high-dimensional, data-scarce engineering problems.

Abstract

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.

Figures (14)

• Figure 1: Illustration of the proposed efficient multi-objective Bayesian optimization process
• Figure 2: Illustration of two-variable latin hypercube sampling with distribution projected to axes
• Figure 3: Illustration of best observed design for process with 2 objective functions
• Figure 4: Pareto front constructed using two acquisition functions and the PTMOO candidate solution on the Pareto front using Eq. \ref{['Eq.OptimumParetoPoint']}
• Figure 5: Illustration of a 3 span post-tensioned concrete road bridge with 2 lanes