# Path Planning of Mobile Robots with an Improved Grey Wolf Optimizer and Dynamic Window Approach
## 1 Introduction
Gray Wolf Optimization (GWO) algorithm [21] is a swarm intelligence algorithm proposed in 2014, widely used in various fields due to its strong global search capability. It primarily finds the global optimal solution through the natural predatory behavior of wolves. Compared with other intelligent algorithms, GWO offers advantages such as fewer parameters, faster convergence speed, and improved stability. However, in complex environments, GWO may exhibit reduced convergence accuracy and is prone to falling into local optima. Therefore, improving GWO has become an active area of research in recent years. To address the issue of GWO falling into local optima in complex multi-modal problems, [PERSON] et al. [22] proposed HGWODE, which introduces a ranking-based mutation strategy and enhances the exploratory capability using the Differential Evolution algorithm, thereby enabling the algorithm to escape local optima. [PERSON] et al. [23] introduced a probabilistic jump mechanism into GWO to help it escape local optima and improve its the convergence speed by replacing the linear convergence factor with an exponentially decaying one. [PERSON] et al. [24] enhanced GWO by using a Gaussian map to improve the quality of the initial gray wolf population, incorporating the Levy flight strategy to increase the population's diversity, and integrating the Golden Sine function to improve the convergence accuracy. [PERSON] et al. [25] introduced the \(\varepsilon\)-_level_ comparison method in GWO to enhance the algorithm's exploratory capability by dynamically adjusting the \(\varepsilon\)-value. Additionally, they incorporated a communication mechanism that randomly selects individuals to exchange information with the optimal individual, thereby improving the population's diversity. [PERSON] et al. [26] introduced the centrifugal distance rate of change to calculate the population distribution and dynamically assigned weights based on the centrifugal distance rate of change between individuals and leaders, thereby enhancing the algorithm's optimization performance and convergence speed. [PERSON] et al. [27] simplified the position update formula of GWO, accelerating convergence while retaining global search capability, and modified the symbiotic phase of the Symbiotic Organisms Search (SOS) algorithm, enhancing information exchange among individuals and avoiding local optima. They combined the improved SOS algorithm with the simplified GWO algorithm, proposing a new algorithm, HSGWO-MSOS, which balances global exploration and local exploitation, thereby improving the effectiveness of path planning. [PERSON] et al. [28] significantly enhanced the search efficiency and stability of GWO path planning through the introduction of a discrete search mechanism, adaptive parameter adjustment, and local optimization strategies, demonstrating superior performance in path planning for porous materials. [PERSON] et al. [29] integrated the Gaussian mutation strategy and spiral function perturbation to enhance the algorithm's ability to escape local optima by randomly perturbing the position of the optimal individual. Additionally, they enhanced the global search ability of the algorithm by dynamically adjusting the weights, thereby increasing the influence of a wolf via Gaussian distribution. They applied the proposed NAS-GWO to trajectory planning in agricultural drone applications. [PERSON] et al. [30] developed a poor solution repair strategy, thereby improving the population quality, and incorporated a multi-constraint path cost function to optimize the efficiency and safety of UAV path planning. Although the existing improvement methods have improved the performance of GWO, the algorithm remains constrained in complex environments. For example, the algorithm tends to fall into local optima and exhibits suboptimal path smoothness. Moreover, in dynamic environments, traditional GWO cannot handle dynamic obstacle avoidance in dynamic settings.