# An Improved Vicsek Model of Swarms Based on a New Neighbor Strategy Considering View and Distance
###### Abstract  
Collective behaviors in nature and human societies have been intensively studied in recent decades. The Vicsek model is one of the typical models that explain self-ordered particle systems well. In the original Vicsek model, the neighbor strategy takes all its neighbors' mean directions into account when updating particles' directions, which leads to a longer convergence time and higher computation cost due to the excess number of neighbors. In this paper, we introduce a new neighbor strategy to the Vicsek model. It defines that each particle will only select a certain number of particles with the farthest distance that fall into its vision sector as its neighbors. In addition, we classify the Vicsek model as the static model and the dynamic model according to whether the features of particles in the model are constant or not. Moreover, we design a new rule to apply the new neighbor strategy to dynamic Vicsek models. The simulation results indicate that our new neighbor strategy can significantly decrease the average number of particles' neighbors but still be able to further enhance the Vicsek model's convergence performance. The comparative results found that the static and dynamic model applied with the new neighbor strategy outperforms the models that only apply view restriction or remote neighbor strategy in noiseless and noisy conditions. V 2023 13 11513. 11513.  
of real creatures. Moreover, due to limited convergence performance, VM needs to be improved to be applied in practical applications. Many dynamic features of VM also need to be studied. Thus, research on VM has attracted numerous researchers' attention. Adjustments of the original VM realize the simulation of real creatures, such as bacterial colonies [16] and marching locusts [2]. More recent studies introduce response delay [17], obstacles [18], evolutionary game theory [19], and proportional-integral control strategy [20] to VM. In addition, phenomena including scale-free chaos [21] and multi-species flocking [22] were also studied. Another study proposes a neighbor selection strategy based on FNN [23]. Methods to accomplish improvements in the convergence performance of the original VM are another popular research branch, and this paper divides them into two categories. The first category realizes improvement by providing particles in VM with more information when updating their directions [24; 25; 26; 27; 28], and the second category is ultimately the opposite, providing less information [19; 29; 30; 31]. Examples of the first category include the adaptive velocity model proposed by [PERSON] et al., where particles adjust their speed constantly according to additional consensus information provided [28]. [PERSON] et al. introduced hierarchical society into VM [24], where each particle has additional social status information. Both these two improved VM above improve convergence performance with more environmental information provided for particles in the VM. On the contrary, research on the second category found that too much environmental information obtained by particles in the system may obstruct synchronization [29; 30], which is counter-intuitive. The decrease in environmental information provided for particles is mainly realized by reducing the average number of neighbors. In particular, [PERSON] et al. proposed an improved VM with a restricted vision field (RVFVM) [29]. Similar to the limited vision field of real creatures [32; 33], RVFVM limits the vision field of particles in the model, leading to fewer neighbors. Similarly, the improved VM with remote neighbor strategy (RNSVM) also reduces the average number of neighbors by selecting the farthest proportion of particles that fall into the visual field as neighbors [31]. In RVFVM and RNSVM, less environmental information is provided for particles by reducing their neighbors in different ways, and the convergence performance is improved. Table 1 sums up the research progress related to the improvement of VM.