## 1 Introduction  
Cruise tourism has emerged as one of the rapidly expanding industries in recent years [1]. However, the global COVID-19 pandemic outbreak in 2020 has significantly impacted the cruise industry [2, 3], leading to a period of poor performance until 2021, followed by a gradual recovery in 2022. Projections by the Cruise Lines International Association indicate that the global number of cruise tourists is expected to reach 39.5 million by 2027, highlighting the promising development prospects and substantial market potential of the global cruise market [4]. The focus has shifted towards the manufacturing upgrading of the cruise industry, particularly in the construction of large cruise ships, which is recognized as a significant challenge in the shipbuilding sector [5]. Large cruise ships, unlike conventional vessels, present a major complexity in their construction due to the dense distribution of thousands of cabins across multiple decks. The intricate and time-consuming nature of constructing such a vast number of cabins significantly impacts the overall manufacturing efficiency. Therefore, optimizing the process for on-deck cabin construction holds significant importance. The process for constructing cruise ship on-deck cabins is outlined as follows. The cabins are categorized into prefabricated cabins and bulk cabins. Prefabricated cabins are pre-assembled and then moved onto the deck as a whole unit, while bulk cabins are gradually built on-site on the decks. The construction of bulk cabins is notably more intricate, as their materials and components must first be transported to a temporary storage location onboard, then distributed to their designated locations, navigating through limited on-deck spaces obstructed by prefabricated cabins and existing materials before assembly. The improper selection of the temporary on-deck storage location and subsequent distribution path can easily lead to extensive blockages due to the complex and narrow on-deck spaces, significantly impacting overall construction efficiency and smooth progress. Therefore, optimizing the temporary on-deck storage location and subsequent distribution paths of materials and components for bulk cabins is crucial for enhancing the construction efficiency and resource management of large cruise ships. The above issue can be interpreted as a location-routing problem (LRP). The selection of the on-deck temporary storage location is the \"location problem\", while the subsequent distribution path selection is the \"routing problem\". Facility location and vehicle routing are two of the key issues in logistics network design. In the past, these two combinatorial optimization problems were solved, respectively, by determining the location of facilities and then planning the route. These traditional methods usually lead to suboptimal results because they are closely related [6]. However, the continuous development of optimization research shows that these problems can be solved at the same time. At present, this comprehensive method is called the location-routing problem (LRP). There exist numerous variations of the location-routing problem (LRP), each tailored to specific constraints related to customers, vehicle warehouses, and other pertinent factors. These constraints encompass distribution distance, distribution cycle, time window, and capacity constraints. Furthermore, based on the number of targets, LRP variants can be categorized into single-target and multi-target types. Metaheuristic algorithms remain the predominant approach for addressing the LRP, while a minority of scholars have endeavored to devise precise solutions for the various LRP iterations [7; 8]. The location-routing problem with capacity constraints has always been the focus of research, which is reflected in the actual capacity constraints of vehicles and warehouses. Its optimization goal is to determine the optimal warehouse set and the optimal vehicle routing assignment. For many years, scholars have been studying the capacitated location-routing problem (CLPR).