# Ship Type Selection and Cost Optimization of Marine Container Ships Based on Genetic Algorithm
## 3 Case Study Analysis  
This paper uses the example of an international shipping logistics company selecting from seven candidate ship types and allocating a monthly cargo volume of 4000 tons for logistics transportation to validate the model and algorithm. The population size and number of iterations used by the genetic algorithm are 50 and 8, respectively. The unit transportation costs, unit value-added service prices, and fixed outsourcing costs for the candidate ship models are shown in Figure 2 below:The EEDI is a key technical indicator for measuring the energy efficiency level of ship design and construction, used to control carbon emissions. It was adopted as an amendment to Annex VI of the International Convention for the Prevention of Pollution from Ships at the 62 nd meeting of the IMO Marine Environment Protection Committee (MEPC) on 15 July 2011, and has been in effect since 1 January 2013. The EEDI parameters for the transport ships purchased by the shipping company are shown in Table 2.  
By combining genetic algorithms with linear planning, the optimal ship type selection scheme and the optimal allocation scheme for each ship type's cargo capacity, under the upper-level planning goal of minimizing the company's operational costs and the lower-level planning goal of minimizing carbon emissions, are determined as shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Ship Type** & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline EEDI/(g(CO2)t\(\cdot\)nm) & 22.8 & 103.4 & 5.38 & 6.26 & 80.77 & 49.27 & 19.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Energy efficiency design index for ships. Figure 2: Unit transportation cost for each ship type. From Table 3, it can be observed that the selected ship types are four in total: Ship Type 1, Ship Type 2, Ship Type 6, and Ship Type 7. In the allocation scheme, Ship Types 1, 2, and 7 have been assigned the maximum cargo weight within their capacity range. It can be concluded that for this transport task, Ship Types 1, 2, and 7 are the optimal choices for minimizing both carbon emissions and costs, with Ship Type 6 being the next best option. Table 3 presents the operational cost and carbon emissions per unit weight for each ship type. In the bi-level programming model designed in this paper, the upper-level planning objective is to minimize operational costs, leading to the selection of ship types. Through the upper-level model centered on genetic algorithms, the chosen ship types are those with lower cargo unit operational costs. The lower-level planning aims to minimize carbon emissions, resulting in an optimal allocation scheme for cargo volume based on the ship types determined in the upper-level programming. The results from Table 3 demonstrate the rationality of the model design. Specifically, Ship Types 1, 2, and 7 not only have lower unit cargo operational costs but also lower unit cargo carbon emissions, which is why their cargo volumes are maximized. The trends in operational costs through iterations is shown in Figure 3.  
During the solving process of the bi-level programming model, observing how the total operational costs of the shipping company approach the optimal solution through multiple iterations further verifies the advantages of genetic algorithms in handling multi-objective optimization problems. The mutation operations in the genetic algorithm effectively avoid the risk of falling into local optima and accelerate the con  
Figure 3: Iterative trend in operating costs.