Ship piping arrangement is a nondeterministic polynomial problem. Based on the advantages of the grey wolf optimization (GWO) algorithm, which is simple, easy to implement, and has few adjustment parameters and fast convergence speed, the study adopts the grey wolf optimization (GWO) algorithm to solve the ship piping arrangement problem. First, a spatial model of ship piping arrangement is established. The grid cell model and the simplified piping arrangement environment model are established using the raster method. Considering the piping arrangement constraint rules, the mathematical optimization model of piping arrangement is constructed. Secondly, the grey wolf optimization algorithm was optimized and designed. A nonlinear convergence factor adjustment strategy is adopted for its convergence factor. Powell’s algorithm is introduced to improve its local search capability, which solves the problem that the grey wolf algorithm easily falls into the local optimum during the solving process. Simulation experiments show that compared with the standard grey wolf algorithm, the improved algorithm can improve the path layout effect by 38.03% and the convergence speed by 36.78%. The improved algorithm has better global search ability, higher solution stability, and faster convergence speed than the standard grey wolf optimization algorithm. At the same time, the algorithm is applied to the actual ship design, and the results meet the design expectations. The improved algorithm can be used for other path-planning problems.

As an emerging approach in computational fluid dynamics, surrogate models often face challenges of long-term stability and high physical fidelity when dealing with unsteady complex flow fields. In this work, we propose a multi-scale enhanced transformer (MUSE-T) that integrates a multi-scale physical feedback gating mechanism. This mechanism operates on two levels: a physically enhanced encoder ensures instantaneous snapshots conform to the Navier–Stokes equations, while a transformer model captures temporal evolution guided by a gated feedback loop that injects spatiotemporal physical residuals into its attention layers. This dual-level integration ensures spatial accuracy and long-term stability. We demonstrate our model's superiority on the standard problem of cylinder wake. Results show that MUSE-T not only achieves reduced prediction errors compared to baseline models but also more accurately captures key flow phenomena such as vortex shedding and energy spectra. Our work establishes a new paradigm for developing physically consistent and highly accurate data-driven models for complex dynamic systems.