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.

建筑物和土木工程混凝土结构的规划和设计构成了一个受约束的复杂问题，例如，受设计代码限制的状态约束，并通过昂贵的计算（例如有限元（FE）模拟）进行评估。传统上，重点一直放在最小化成本上，而当前的趋势要求在多个标准（例如可持续性，可构建性和性能）之间做出良好的权衡，而这些标准通常可以从设计参数中便宜地计算出来。多目标方法可以提供更多相关的设计策略来找到这种折衷方案。然而，由于结构设计问题的昂贵性严重限制了适用算法的范围，因此在结构混凝土设计实践中仍未开发出多目标优化方法的潜力。贝叶斯优化已成为一种优化昂贵功能的有效方法，但据我们所知，它尚未应用于结构混凝土设计问题的约束多目标优化。在这项工作中，我们开发了一个贝叶斯优化框架，该框架明确利用结构设计问题固有的功能，即昂贵的约束条件和廉价的目标。该框架在钢筋混凝土（RC）梁结构设计的一般情况下进行了评估，同时考虑了可持续性，可建造性和性能目标，并以著名的非支配排序遗传算法II（NSGA-II）为基准）和随机搜索过程。结果表明，贝叶斯算法在改善率方面的表现要好得多，