An improved gray wolf optimization to solve the multi-objective tugboat scheduling problem.

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.