With the continuous prosperity of maritime transportation on a global scale and the resulting escalation in port trade volume, tugboats assume a pivotal role as essential auxiliary tools influencing the ingress and egress of vessels into and out of ports. As a result, the optimization of port tug scheduling becomes of paramount importance, as it contributes to the heightened efficiency of ship movements, cost savings in port operations, and the promotion of sustainable development within the realm of maritime transportation. However, a majority of current tugboat scheduling models tend to focus solely on the maximum operational time. Alternatively, the formulated objective functions often deviate from real-world scenarios. Furthermore, prevailing scheduling methods exhibit shortcomings, including inadequate solution accuracy and incompatibility with integer programming. Consequently, this paper introduces a novel multi-objective tugboat scheduling model to align more effectively with practical considerations. We propose a novel optimization algorithm, the Improved Grey Wolf Optimization (IGWO), for solving the tugboat scheduling model. The algorithm enhances convergence performance by optimizing convergence parameters and individual updates, making it particularly suited for solving integer programming problems. The experimental session designs several scale instances according to the reality of the port, carries out simulation experiments comparing several groups of intelligent algorithms, verifies the effectiveness of IGWO, and verifies it in the comprehensive port area of Huanghua Port to get the optimal scheduling scheme of this port area, and finally gives management suggestions to reduce the cost of tugboat operation through sensitivity analysis.

It is a challenging work to simulate wind and waves in virtual scenes of marine simulators. In this paper, a divergence-free position based fluid (DFPBF) framework is introduced for ocean wave modeling in marine simulators. We introduce a set of constant density constraints and divergence-free velocity constraints to enforce incompressibility. By adjusting the position distribution of fluid particles, the particle density is forced to be constant. Constraining the divergence-free velocity field can keep the density change rate at zero. When correcting the position and velocity of particles, we introduced a relaxation correction scheme to accelerate the convergence of the framework. The simulation results show that as the scene scale expands and the number of fluid particles increases, this acceleration effect will be more significant. Secondly, we propose a novel particle-based three-dimensional stochastic fluctuating wind field. The Perlin noise is introduced to disturb the constant horizontal wind field to form a stochastic wind field. On this basis, a stochastic fluctuating wind field simulation framework is proposed. By adjusting the pulse period and pulse width, users can flexibly control the fluid turnover under the action of the wind field. This wind field framework can be easily integrated into the DFPBF model. Based on this wind field model, we simulated some typical wind wave scenarios, including interaction scenarios with lighthouse and lifebuoy, and verified the effectiveness of the wind field model.

To achieve small‐scale ocean scene simulation in a marine simulator, we present an incompressible SPH algorithm by relaxing the density‐invariant condition for incompressible fluids. As there are larger density errors of the fluid particles near or on the boundary, more iteration numbers are required. Taking boundary handling to modify the density of the fluid particles, the relaxation method is used to optimize the iterative method to solve the density‐invariant condition, which can reduce the iteration numbers and average density deviation and improve the accuracy. Our proposed approach can achieve incompressible SPH and solve the problem of the particle deficiency. While ensuring the stability, the approach can allow large time steps and control the density deviation below 0.01% and improve the efficiency by reducing the iteration numbers and optimizing the calculating procedure and the initial value selection.