## 1 Introduction
### Literature Review  
Based on literature research, it is evident that the academic community has conducted extensive studies on optimizing the design of gas pipeline networks. These studies primarily focus on modeling and solving optimization challenges related to network layout. Depending on the topology of the pipeline network--such as star, tree, and cyclic topologies--different optimization problems arise. [PERSON] and [PERSON] [5] developed an optimization model for tree topology gas pipeline networks, which considers parameters like network layout, pipe diameter, and node pressures. [PERSON] et al. [6] investigated the design of multi-level star networks, addressing optimal configurations and facility placements. [PERSON] [7] explored the multi-objective optimization design of ring-type oil-gathering pipeline networks. [PERSON] et al. [8] formulated a multi-period MILP (Mixed Integer Linear Programming) model for optimizing tree topology networks, accounting for terrain and obstacles. [PERSON] et al. [9] established an MINLP (Mixed Integer Nonlin  
Figure 3: Star–tree pipeline network.  
ear Programming) model for optimizing two-level star topology pipeline networks for underground natural gas storage.  
Regarding the optimization solving methods, early research predominantly utilized operation research techniques, particularly heuristic algorithms, to address the gas-gathering pipeline network optimization models. From a mathematical optimization and operation research perspective, designing optimal gas-gathering pipeline networks is classified as an NP-hard combinatorial optimization problem, which poses significant challenges and finds application across various industrial domains [10; 11]. [PERSON] [12] formulated an optimization model for site placement in discrete spaces with unlimited site capacities, which was primarily solved using heuristic algorithms. Common exact algorithms include the branch and bound method, cutting plane algorithm, and column generation algorithm [13; 14]. However, traditional optimization theories often struggle to efficiently solve problems with natural gas pipeline network models due to lengthy computational times and occasional mismatches between theoretical outcomes and practical applications.  
In recent years, commercial solvers and heuristic algorithms have gradually become the most common way to deal with pipeline network layout optimization. A commercial solver can eliminate the tedious algorithm programming work, but the solution method is limited, and it is difficult to modify the built-in parameters of the algorithm. The heuristic algorithm has a large programming workload, but the algorithm has good scalability and can even combine the advantages of several algorithms to obtain the optimization results. [PERSON] and [PERSON] [15] solved a gas pipeline network design and expansion optimization problem using the online Bonmin solver. [PERSON] et al. [16] developed a comprehensive MILP layout optimization model that incorporates terrain and obstacle considerations. There are also scholars who use graph theory methods and machine learning methods to solve optimization problems [17; 18]. They utilized the Gurobi solver to globally solve the model. [PERSON] et al. [19] introduced a practical and efficient optimization approach for subsea production networks using the GAMS solver. [PERSON] et al. [20] put forward an enhanced particle swarm optimization algorithm with enhanced global search capabilities to tackle the MINLP model for optimizing pipeline network layouts. [PERSON] et al. [21] proposed a pipeline network layout optimization model that accounts for hydraulic characteristics and employed an ant colony algorithm for its solution.  
Figure 4: Hierarchical optimization diagram.