A Manifold Alignment and Hierarchical Surrogate-Assisted Transfer Optimization Algorithm for Multi-UUV Shape Design

Abstract

In engineering practice, different requirements often give rise to distinct product designs. For the specific case of multi-UUVs, small-scale vehicles are typically designed with a rotational body shape to ensure superior hydrodynamic performance, whereas large-scale vehicles are often configured with a near-rectangular body shape to satisfy the demands of substantial payload capacity. These two tasks share a portion of common variables, while each also maintains its own task-specific variables. When each task is optimized independently, redundant computational efforts are incurred and inherent similarities among tasks remain unexploited, which frequently leads to suboptimal solutions. Typical multitask optimization algorithms assume completely heterogeneous tasks and therefore become inefficient when applied to this kind of partially heterogeneous problem. To address this, a manifold alignment and hierarchical surrogate-assisted transfer optimization algorithm (MAHSTO) is proposed in this work. In MAHSTO, an implicit knowledge transfer strategy is developed via manifold alignment. The design variables of both tasks are mapped onto a common low-dimensional latent space via manifold alignment, which enables implicit knowledge transfer across tasks. In addition, a hierarchical multisurrogate model with adaptive sampling is established. It comprises one shared global surrogate model that captures common trends across tasks and two task-specific surrogate models that focus on accurately fitting their respective tasks. Furthermore, an adaptive sampling criterion is adopted for different surrogate models to balance exploration and exploitation. Experiments on benchmark cases demonstrate that the proposed MAHSTO outperforms four state-of-the-art optimization algorithms, achieving the best performance in 58.3% of cases. Finally, MAHSTO is applied to the shape optimization of multi-UUVs. The results further verify its competitiveness in handling computationally expensive engineering problems.

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