## 1 Introduction  
The process of ship design involves intricate phases, including concept, preliminary, and detailed design for production. This multifaceted endeavor, depicted as a spiral in Figure 1[1], unfolds through concept design, preliminary design, contract design, and production design stages. Concept design, also known as feasibility verification, stands out as the cornerstone of ship design, given its role in translating the requirements of the mission or ship owner into precise naval architecture and engineering specifications. This phase involves conducting preliminary estimates for critical elements of the proposed vessel, including dimensions, power requirements, and alternative feature sets such as speed range, bollard pull and cargo capacity. Moreover, in the preliminary design stage, it necessitates the creation of essential technical documentation, including the ship's line plan, while further refining fundamental ship features to align with the owner's needs and economic considerations. Following concept design, the process advances to contract design, which involves the meticulous preparation of technical specifications for shipbuilding, along with the completion of necessary calculations and naval architecture drawings. Subsequently, detail design, or production design, represents the concluding phase of ship design, where detailed workshop plans for ship construction are developed. This iterative process, likened to a spiral, ensures that adjustments made to any parameter affecting ship characteristics prompt corresponding modifications throughout the design stages, ultimately leading to the realization of an optimal solution in line with economic criteria and owner requirements. Throughout these design stages, the focus is on optimizing the main particulars of the tugboat to ensure it can effectively fulfill its role in servicing ships in busy ports and harbors. By considering these factors at every stage of the design process, harbor tugs must be adapted to meet the specific demands of their operating environments while ensuring safety, efficiency, and reliability. Naval architects grapple with a plethora of ship parameters, encompassing the main dimensions, strength, hull form, displacement, resistance, powering, freeboard, machinery, endurance, capacities, trim, stability, economic considerations, efficiency, environmental impact, and cost factors [2]. Critical ship features, such as stability, power requirements, and economic efficiency, hinge significantly on the main dimensions. Thus, specifying parameters like length (L), width (B), draft (T), depth (D), freeboard (F), and block coefficient (C\({}_{\text{B}}\)) is a pivotal aspect of ship design, where these dimensions are harmonized to meet the ship's design conditions. For example, the important considerations for harbor tugboats include a high bollard pull capacity to tow large ships at a very low speed during towing and pushing duties, a service speed that enables tugboats to reach their destinations faster, and maneuverability to navigate congested harbors. The traditional approach involves using statistical regression equations based on data from a comparable ship with known features [3]. In the preliminary design phase, designers play a crucial role in defining a ship's major features based on implicit client requirements, including draft length, service speed range, and bollard pull capacity. Designers iteratively adjust dimensions by analyzing comparable ships or resort to empirical formulations and machine learning (ML) methods like neural networks (NN) to predict a ship's main particulars and to analyze dynamic systems, especially in early design stages [4; 5; 6; 7]. During the early design stage of a ship, it could benefit from using an ML approach, where a large number of configurations must be tested, which could be prohibitive to achieve  
Figure 1: A ship design process model. using Computational Fluid Dynamics (CFD) or model experiments.