## 4 Results and Discussion  
For a natural gas field gathering and transmission pipeline network system, the layout design is an NP problem, which is not conducive to calculation. In order to improve the efficiency of the solution, the following four assumptions are made: (1) For the external  
Figure 11: Schematic diagram of Kruskal algorithm solving process. conditions of the calculation in the layout design, the standard conditions become the default for calculation (pressure of 0.1 MPa, temperature of 20 \({}^{\circ}\)C). (2) The flow rate in the gas pipeline is unstable. In order to solve the problem of convenience, the gas flow in the pipeline is simplified as a stable flow. (3) In the pipeline flow, the temperature of the buried pipeline usually changes with the length of the pipeline, and when the pipeline is too long, the gas will eventually become close to the ambient temperature. In order to facilitate the calculations, and since the gathering pipeline network is usually located in the same area, the temperature of the pipeline is assumed to be constant in this paper. (4) For the direction of the flow of the gas in the network, it is stipulated that each node can only transport the gas from one direction to another. An actual natural gas pipeline network in China was selected for analysis and search for a solution [28]. The original layout of the pipeline network in the gas field is depicted in Figure 12. This gas field comprises 93 wells, with each producing between 2000 and 5000 m\({}^{3}\)/d of gas, with wellhead pressures ranging from 0.2 to 1.0 MPa and an average production temperature of 20 \({}^{\circ}\)C. The specification of the primary production pipelines between wells and stations was De160 \(\times\) 9.5 mm, while the specification of the secondary gathering pipelines between stations (and the plant) was De225 \(\times\) 12.8 mm. Detailed costs are provided in Table 3.  
The maximum radius constraint was 1.5 km, and the processing capacity of a single station was 20,000 m\({}^{3}\)/day. Since the data came from a low-pressure gas field, pressure constraints were not considered in this case. In the original algorithm (GA), the calculation took more than 2 h at a time. After optimizing the algorithm structure (IGA), the calculation time was shortened to 15-30 min, increasing the calculation efficiency by over 400%. The IGA was used to solve the layout of pipeline network. Utilizing the established hierarchical optimization framework, we derived an optimized layout scheme. The initial star topology layout in the first stage is illustrated in \begin{table}
\begin{tabular}{c c} \hline
**Project** & **Cost** \\ \hline Station & CNV 52.17 \(\times\) 10\({}^{4}\) \\ \hline Plant & CNV 1725.93 \(\times\) 10\({}^{4}\) \\ \hline Pipeline cost (De160 \(\times\) 9.5 mm) & CNV/km 15.636 \(\times\) 10\({}^{4}\) \\ \hline Pipeline cost (De225 \(\times\) 12.8 mm) & CNV/km 25.406 \(\times\) 10\({}^{4}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Projected costs of the pipeline network. Figure 12: Sketch of the original pipeline network layout. Figure 13. Figure 14 displays the results of well grouping and station location determination. The final optimized layout is depicted in Figure 15. This network consists of fourteen gas-collecting stations and one treatment plant, which is one station fewer than the original gas field design. Figure 14. Results for well allocation, station location, and plant location. Figure 13. Connection relationship between wells and stations. Figure 15. Design result for star–tree pipeline network layout. Using the simulation software to verify the feasibility of the pipeline network layout structure, and considering that the number of wells in the pipeline network was too large, the number of wells was determined as the sum of the gas volume and the node of the valve manifold for the connection verification.