# GA-PSO Algorithm for Microseismic Source Location
## 1 Introduction
Despite various location schemes proposed by scholars, challenges remain, including difficulties in solving objective functions, local range locking, and slow convergence, which can lead to location errors. Improvements to single heuristic algorithms are constrained by inherent theoretical performance ceilings, which have propelled research into hybrid algorithms, particularly the synergistic combination of complementary heuristics. Table 1 summarizes the characteristics of existing microseismic location methods: non-heuristic algorithms are theoretically simple but highly reliant on initial values and velocity models; single heuristic algorithms demonstrate enhanced robustness but face challenges in convergence and accuracy; hybrid heuristic algorithms enhance performance by leveraging collaborative mechanisms. The PSO algorithm is inspired by the predatory behavior observed in bird flocks. This approach has gained widespread popularity due to its ease of implementation and its ability to be seamlessly integrated with other algorithms to achieve high precision [16]. [PERSON] et al. [17] proposed a hybrid approach that combines Multi-Objective Particle Swarm Optimization (MOPSO) with SA. This method leverages MOPSO to obtain the optimal solution, while SA is employed to resolve the seismic source location. [PERSON] et al. [18] applied the NM-PSO algorithm to seismic source location, using PSO for global optimization to provide initial values for the Nelder-Mead (NM) algorithm. Furthermore, the integration of PSO with other optimization algorithms demonstrates significant potential in solving multimodal problems, such as Ant Colony Optimization (ACO) [19] and Differential Evolution (DE) [20]. The GA exhibits strong global search capabilities and does not rely on mathematical models, demonstrating significant robustness in solving nonlinear equations. [PERSON] et al. [21] utilized the GA to determine initial values, followed by a simplex search method for location determination. This hybrid localization approach demonstrated approximately a 10% improvement in accuracy over the traditional simplex algorithm. The Genetic Algorithm has shown tremendous potential in the field of seismic source localization. The PSO algorithm has become an ideal foundation for the design of hybrid algorithms due to its ease of implementation and strong compatibility. Its integration with the GA is particularly noteworthy. Currently, the GA-PSO algorithm has demonstrated exceptional performance across multiple engineering fields. Examples include medical equipment development and disease diagnosis [22], antenna array design [23], workflow scheduling [24; 25], power grid demand management [26], and slope stability prediction [27]. The cross-disciplinary success of the GA-PSO algorithm validates its robustness, highlighting its unique advantages in high-noise environments and multi-parameter coupled scenarios. These findings align well with the accuracy and stability requirements of microseismic localization. This research innovatively introduces the GA-PSO algorithm into the field of microseismic localization by combining GA with the PSO algorithm, enhancing PSO by introducing dynamic learning factors and adaptively adjusting inertia weights. This approach enables global search in the early stages and local search in the later stages, increasing population diversity through GA integration, which significantly enhances the search capability and avoids local optima. The results demonstrate that this algorithm exhibits improved search capability, convergence speed, and location accuracy.