## 1 Introduction
This article examines a novel iteration of the location path problem, referred to as the BE-LRP, which incorporates capacity constraints. The impediments in the environment on the deck are identified, and the capacity of temporary storage points for materials and delivery vehicles is restricted. Distinguished from the traditional capacitated location-routing problem (CLRP), the study on the location-routing of cruise materials on board takes into account not only the capacity limitations of warehouses and distribution vehicles but also the influence of obstacles along the actual distribution route. To the best of our knowledge, the bi-level location-routing problem (BE-LRP) has not been addressed in the existing literature. Nevertheless, prior research has addressed similar issues and can provide valuable insights for our study. Some research on the LRP in logistics and distribution management has reference significance, such as applications in newspaper distribution, food and beverage distribution, and waste collection [9]. [PERSON] proposed a heuristic algorithm based on simulated annealing to solve CLRP problem [10]; [PERSON] proposed a multi-ant colony optimization algorithm to solve the LRP with capacity constraints of vehicles and warehouses, and decomposed the CLRP into a setting location problem and multi-site vehicle routing problem [11]; [PERSON] proposed a multi-objective optimization method for food supply chain research [12]; [PERSON], [PERSON], and others applied an improved particle swarm optimization algorithm to solve the capacity location-routing problem and stochastic demand location-routing problem [13]; [PERSON] proposed a hybrid genetic algorithm to solve the CLRP. The proposed algorithm retains the GA framework and uses a local search in the mutation stage [14]; in order to deal with the strict capacity constraint, [PERSON] also proposed a hybrid genetic algorithm, which not only searched the feasible solution space, but also the infeasible solution space [15]; [PERSON] used an adaptive variable neighborhood algorithm to solve the battery switching station location-routing problem with capacity electric vehicles [16], with the goal of minimizing the sum of construction and route costs; [PERSON] considered the CLRP under random demand, and proposed a semi-heuristic algorithm, which hybridized simulation with an iterated local search metaheuristic algorithm [17]; [PERSON], [PERSON], and others applied ALNS to solve the location-routing problem of multiple distribution centers in the express service system, taking into account the capacity of distribution points and vehicles [18]; [PERSON] presented an approximation algorithm, which is an algorithm with proven worst-case guarantees both in terms of running time and solution quality, for the general capacitated version of this problem, in which both vehicles and facilities are capacitated [19]; [PERSON] considered conflict sustainability dimensions in a multi-objective formulation, focusing on the capacitated location-routing problem [20]. The current algorithm can only calculate the delivery distance based on the coordinates of the distribution center and customers, which does not align with the research problem of this paper. Therefore, algorithm optimization is needed to address obstacle hindrance distance. Since this paper deals with a bi-objective problem, the NSGAII algorithm is chosen for optimization and improvement. The classical CLRP does not consider the influence of time windows, so it is necessary to discuss the related research of the CLRP with time windows. The CLRP with time windows (CLRPTW) can be divided into customer time windows and vehicle time windows. [PERSON] used the accurate branch pricing algorithm to solve the CLRPTW [21]; [PERSON] used eight local optimization operators, two insertion operators, and one mutation operator to form a large domain algorithm to optimize the CLRPTW. Experimental comparative analysis shows that the algorithm can solve high-quality solutions in a short calculation time [22].