Non-orthogonal ship pipe routing method based on hierarchical encoding and rollback mechanism

• A vector-based hierarchical encoding method is proposed to achieve a mathematical representation for pipes, and a pipe population tensor is constructed, which significantly improves computational precision and efficiency. • Voxelization is used to construct the routing environment and obstacles, reducing the accuracy loss caused by the bounding box method. • The rollback mechanism is introduced to enable dynamic adjustment of the routing sequence for multiple pipes, thereby avoiding the issues of failure in fixed-sequence routing and the complexity of optimizing the routing sequence. • A multi-pipe routing framework is established, which is suitable for solving non-orthogonal pipe systems. In this system, the NSGA-II algorithm is nested with a multi-subpopulation co-evolutionary mechanism to achieve optimized solutions efficiently. Ship pipe route design is a critical task in the ship detail design phase. The efficiency and quality of pipe routing have a direct influence on the overall design schedule and the orderly progression of subsequent construction design stages. Pipes are commonly categorized as orthogonal or non-orthogonal according to their bending angles. At present, research on automated ship pipe routing has mainly concentrated on orthogonal pipes. In contrast, the complexity and variability of practical engineering environments result in a considerable proportion of non-orthogonal pipes. In addition, the absence of mature automated routing approaches means that pipe routing often depends on manual operations, leading to high design complexity and extended design cycles. To resolve these issues, a multi-pipe routing method incorporating a rollback mechanism is presented. First, a vector-based hierarchical encoding strategy is adopted to numerically describe the pipe system and construct pipe population tensors, addressing the low precision of traditional grid-based pipe encoding methods and markedly improving computational accuracy and efficiency. Second, a voxelization technique is applied to model the routing environment and obstacles, thereby alleviating the accuracy degradation associated with bounding box representations. Third, a rollback mechanism is introduced to automatically regulate pipe laying sequence, while the Non-dominated Sorting Genetic Algorithm II (NSGA-II), combined with a multi-subpopulation co-evolutionary strategy, is embedded to optimize and determine the optimal pipe routing scheme. Finally, multiple case studies with different levels of complexity are optimized, demonstrating the effectiveness and stability of the proposed multi-pipe routing approach. The proposed method offers an effective preliminary reference solution for non-orthogonal pipe and multi-pipe routing.