The exploration of novel architectures requires physics-based simulation due to a lack of prior experience to start from, which introduces two specific challenges for optimization algorithms: evaluations become more expensive (in time) and evaluations might fail. The former challenge is addressed by Surrogate-Based Optimization (SBO) algorithms, in particular Bayesian Optimization (BO) using Gaussian Process (GP) models. An overview is provided of how BO can deal with challenges specific to architecture optimization, such as design variable hierarchy and multiple objectives: specific measures include ensemble infills and a hierarchical sampling algorithm. Evaluations might fail due to non-convergence of underlying solvers or infeasible geometry in certain areas of the design space. Such failed evaluations, also known as hidden constraints, pose a particular challenge to SBO/BO, as the surrogate model cannot be trained on empty results. This work investigates various strategies for satisfying hidden constraints in BO algorithms. Three high-level strategies are identified: rejection of failed points from the training set, replacing failed points based on viable (non-failed) points, and predicting the failure region. Through investigations on a set of test problems including a jet engine architecture optimization problem, it is shown that best performance is achieved with a mixed-discrete GP to predict the Probability of Viability (PoV), and by ensuring selected infill points satisfy some minimum PoV threshold. This strategy is demonstrated by solving a jet engine architecture problem that features at 50% failure rate and could not previously be solved by a BO algorithm. The developed BO algorithm and used test problems are available in the open-source Python library SBArchOpt.

Ship design is a years-long process that requires balancing complex design trade-offs to create a ship that is efficient and effective. Finding new ways to improve the ship design process can lead to significant cost savings for ship building and operation. One promising technology is generative artificial intelligence, which has been shown to reduce design cycle time and create novel, high-performing designs. In literature review, generative artificial intelligence has been shown to generate ship hulls; however, ship design is particularly difficult as the hull of a ship requires the consideration of many objectives. This paper presents a study on the generation of parametric ship hull designs using a parametric diffusion model that considers multiple objectives and constraints for the hulls. This denoising diffusion probabilistic model (DDPM) generates the tabular parametric design vectors of a ship hull for evaluation. In addition to a tabular DDPM, this paper details adding guidance to improve the quality of generated ship hull designs. By leveraging classifier guidance, the DDPM produced feasible parametric ship hulls that maintain the coverage of the initial training dataset of ship hulls with a 99.5% rate, a 149x improvement over random sampling of the design vector parameters across the design space. Parametric ship hulls produced with performance guidance saw an average of 91.4% reduction in wave drag coefficients and an average of a 47.9x relative increase in the total displaced volume of the hulls compared to the mean performance of the hulls in the training dataset. The use of a DDPM to generate parametric ship hulls can reduce design time by generating high-performing hull designs for future analysis. These generated hulls have low drag and high volume, which can reduce the cost of operating a ship and increase its potential to generate revenue.

Many real-world optimisation problems such as hyperparameter tuning in machine learning or simulation-based optimisation can be formulated as expensive-to-evaluate black-box functions. A popular approach to tackle such problems is Bayesian optimisation (BO), which builds a response surface model based on the data collected so far, and uses the mean and uncertainty predicted by the model to decide what information to collect next. In this paper, we propose a novel variant of the well-known Knowledge Gradient acquisition function that allows it to handle constraints. We empirically compare the new algorithm with four other state-of-the-art constrained Bayesian optimisation algorithms and demonstrate its superior performance. We also prove theoretical convergence in the infinite budget limit.