Research article 研究文章

Research on optimization method for traffic signal control at intersections in smart cities based on adaptive artificial fish swarm algorithm
基于自适应人工鱼群算法的智慧城市交叉口交通信号控制优化方法研究

Smart cities emphasize the rapid development of cities in informatization, digitalization and intelligence. With the progress and innovation of science and technology, smart cities have become an important direction of urban development, aiming at improving the sustainability, quality of life and economic benefits of cities [[1], [2], [3]]. Under the background of smart city, intelligent transportation, as an important part of it, has received more and more attention and application. Intelligent transportation intelligently manages and optimizes the urban transportation system by comprehensively applying information technology, communication technology, big data, artificial intelligence and other means. Intelligent urban transportation system uses big data, sensor networks and other technologies to collect, analyze and utilize traffic data. By monitoring and analyzing real-time traffic conditions, urban managers can make more accurate and effective decisions and respond to traffic problems in time [4]. Intelligent traffic lights, intelligent parking guidance system, intelligent public transportation and other technical means are adopted to optimize traffic flow, reduce traffic congestion and improve traffic efficiency [5,6]. Encourage and support sustainable modes of transportation, such as public transportation, cycling and walking. By providing convenient public transport services, building cycling streets and pedestrian streets, we can reduce the use of private cars, reduce environmental pollution and improve the travel experience of urban residents. In this context, the optimization of signal light control at traffic intersections in smart cities has become a hot issue.
智慧城市强调城市在信息化、数字化和智能化方面的快速发展。随着科学技术的进步和创新，智慧城市已成为城市发展的重要方向，旨在提高城市的可持续性、生活质量和经济效益[[1], [2], [3]]。在智慧城市背景下，智能交通作为其重要组成部分，得到了越来越多的关注和应用。智能交通通过综合运用信息技术、通信技术、大数据、人工智能等手段，对城市交通系统进行智能化管理和优化。城市智能交通系统利用大数据、传感网等技术对交通数据进行采集、分析和利用。通过对实时交通状况的监测和分析，城市管理者可以做出更加准确有效的决策，及时应对交通问题[4]。采用智能交通信号灯、智能停车诱导系统、智能公共交通等技术手段，优化交通流量，减少交通拥堵，提高交通效率[5,6]。鼓励和支持公共交通、自行车和步行等可持续交通方式。通过提供便捷的公共交通服务、建设自行车道和步行街，可以减少私家车的使用，减少环境污染，改善城市居民的出行体验。在此背景下，智慧城市中交通路口信号灯控制的优化已成为一个热点问题。

Reference [7] proposes dynamic traffic light control methods with different priorities. The dynamic state constructor is used to control the signal combination conversion of traffic lights. By designing duration particles and enhancement particles, the quantum particle swarm optimization algorithm is rebuilt to allocate intersections with different optimization priorities. However, this method has a long travel time. Reference [8] proposes an optimization method for traffic signal control based on deep reinforcement learning. By extending the centralized traffic signal learning and decentralized execution mode of Actor-Critic strategy gradient algorithm, critics use additional information to simplify the traffic signal control process and complete the traffic signal control optimization. However, the average delay time of this method needs to be verified. Reference [9] puts forward an artificial fish swarm algorithm to optimize dynamic fuzzy neural network. Taking the reciprocal of the average delay of vehicles as the food concentration of AFSA, and taking the weights and thresholds of dynamic fuzzy neural network that need to be corrected as the individual state of artificial fish, a set of optimal parameters of dynamic fuzzy neural network are obtained through iterative updating, so as to realize the multi-phase phase phase-change sequence intelligent control of five forks. However, this method has a high average number of stops. Reference [10] puts forward the urban green wave traffic control system. The adaptive mechanism and crossover and mutation operators are introduced into the artificial fish swarm algorithm to adjust the evolutionary population. By setting up bulletin board measures and retaining strategies, the individual state of the optimal artificial fish is recorded, and the green wave traffic control at continuous intersections is completed. However, this method has the problem of poor control effect. Reference [11] proposes artificial fish swarm algorithm, chaotic search and feedback strategy based on signal timing optimization theory. Taking the average of vehicle delay and parking number as the goal, the optimization algorithm is used to improve the intersection timing scheme of the target road. However, this method has the problem of low efficiency. Reference [12] proposes a dynamic traffic signal system based on density. In the intelligent traffic signal, the target detection is processed and transformed, and various features are extracted. According to the calculated threshold, the contour is drawn, the vehicle density and quantity are known, and the signal distribution is completed. However, this method has high computational complexity. Reference [13] proposes an adaptive real-time traffic light control algorithm based on traffic flow. Using neural network and YOLOv3 framework, single image processing is carried out, traffic permission is established at the signal, and traffic flow distribution at traffic intersections is completed. However, the control efficiency of this method for traffic intersection signal lights needs to be verified. Reference [14] puts forward an intelligent traffic monitoring system based on pc, which captures the images of vehicles and pedestrians, helps cities optimize traffic flow and reduce congestion. According to the emergency vehicles in each lane, intelligently decide when to change signals, thus increasing road capacity and traffic flow. However, this method is easy to cause data redundancy.
参考文献[7]提出了具有不同优先级的动态交通灯控制方法。动态状态构造器用于控制交通信号灯的信号组合转换。通过设计持续时间粒子和增强粒子，重建量子粒子群优化算法，分配不同优化优先级的交叉口。然而，这种方法的行程时间较长。参考文献[8]提出了一种基于深度强化学习的交通信号控制优化方法。通过扩展行为批判策略梯度算法的集中交通信号学习和分散执行模式，批判者利用附加信息简化交通信号控制过程，完成交通信号控制优化。但该方法的平均延迟时间有待验证。参考文献[9]提出了一种人工鱼群算法来优化动态模糊神经网络。以车辆平均延误时间的倒数作为人工鱼群的食物浓度，以需要修正的动态模糊神经网络的权值和阈值作为人工鱼群的个体状态，通过迭代更新得到一组动态模糊神经网络的最优参数，从而实现五岔路口的多相位相变序列智能控制。但这种方法的平均停车次数较多。参考文献[10]提出了城市绿波交通控制系统。在人工鱼群算法中引入自适应机制和交叉、变异算子，对进化种群进行调整。 通过设置公告板措施和保留策略，记录最优人工鱼儿的个体状态，完成连续交叉口的绿波交通控制。但该方法存在控制效果不佳的问题。参考文献[11]基于信号配时优化理论，提出了人工鱼群算法、混沌搜索和反馈策略。以车辆延误和停车数量的平均值为目标，采用优化算法改进目标道路的交叉口配时方案。但这种方法存在效率低的问题。参考文献[12]提出了一种基于密度的动态交通信号系统。在智能交通信号中，对目标检测进行处理和变换，提取各种特征。根据计算出的阈值，绘制轮廓线，已知车辆密度和数量，完成信号分布。然而，这种方法的计算复杂度较高。参考文献[13]提出了一种基于交通流量的自适应实时交通灯控制算法。利用神经网络和 YOLOv3 框架，进行单幅图像处理，建立信号灯的交通许可，完成交通路口的交通流分布。然而，该方法对交通路口信号灯的控制效率还有待验证。参考文献[14]提出了一种基于pc的智能交通监控系统，该系统捕捉车辆和行人的图像，帮助城市优化交通流量，减少拥堵。根据各车道上的应急车辆情况，智能决定何时变换信号灯，从而提高道路通行能力和交通流量。 不过，这种方法容易造成数据冗余。

The traffic network structure has an important influence on the traffic efficiency of smart cities. In the actual urban traffic system, the traffic network is usually composed of complex road networks, including main roads, secondary roads, branch roads and other roads of different grades. There may be differences in traffic flow, speed and road width of these roads. Therefore, this paper establishes the traffic flow state equation of SCTI, and understands the actual traffic flow of SCTI through this equation.
交通网络结构对智慧城市的交通效率有着重要影响。在实际的城市交通系统中，交通网络通常由复杂的道路网络组成，包括主干道、次干道、支路和其他不同等级的道路。这些道路在交通流量、车速、路面宽度等方面可能存在差异。因此，本文建立了 SCTI 的交通流状态方程，并通过该方程了解 SCTI 的实际交通流。

In a SCTI signal light cycle [[15], [16], [17]], the set of time interval $m$ corresponding to the signal light of SCTI $J_2$ is ${\mathrm{\Omega }}_m$, and the time of green light in time interval $m\in {\mathrm{\Omega }}_m$ in SCTI $J_2$ is $u_{m,n}$. The cycle constraint of traffic signal lights at smart city intersections is:(1)$T=\sum _{m\in {\mathrm{\Omega }}_m}^{N_j}\sum _{n\in J_2}^{S_n}{u}_{m,n}+T_1$Where, $N_j$ is the number of cycles, $S_n$ is the saturated traffic flow in $n$, and $T_1$ is the loss time of traffic intersections in smart cities.
在一个 SCTI 信号灯周期中[[15]、[16]、[17]]，SCTI 信号灯 $J_2$ 对应的时间间隔 $m$ 的集合为 ${\mathrm{\Omega }}_m$ ，SCTI 信号灯 $J_2$ 中时间间隔 $m\in {\mathrm{\Omega }}_m$ 的绿灯时间为 $u_{m,n}$ 。智慧城市交叉口交通信号灯的周期约束为 (1)$T=\sum _{m\in {\mathrm{\Omega }}_m}^{N_j}\sum _{n\in J_2}^{S_n}{u}_{m,n}+T_1$ 其中， $N_j$ 为周期数， $S_n$ 为 $n$ 中的饱和交通流量， $T_1$ 为智慧城市中交通路口的损失时间。

Constraints limit the time of green light at SCTI as follows:(2)$u_{n,m}^{\min }\le u_{n,m}\le u_{n,m}^{\max }$Where, $u_{n,m}^{\min }$ is the minimum time allowed for the green light at the intersection of smart cities, and $u_{n,m}^{\max }$ is the maximum time allowed for the green light at the intersection of smart cities.
约束条件对 SCTI 绿灯时间的限制如下： (2)$u_{n,m}^{\min }\le u_{n,m}\le u_{n,m}^{\max }$ 其中， $u_{n,m}^{\min }$ 为智慧城市交叉口绿灯亮起的最短时间， $u_{n,m}^{\max }$ 为智慧城市交叉口绿灯亮起的最长时间。

The traffic flow of vehicles at the intersection of smart cities is:(3)$q_n\left(k\right)=\sum _{n\in J_2}\sum _{n+1\in J_2}v{p}_n\left(k\right)$Where, $v$ is the vehicle speed and $p_n\left(k\right)$ is the vehicle flow from the connecting section $n$.
智慧城市交叉口的车辆流量为 (3)$q_n\left(k\right)=\sum _{n\in J_2}\sum _{n+1\in J_2}v{p}_n\left(k\right)$ 其中， $v$ 为车辆速度， $p_n\left(k\right)$ 为来自连接路段 $n$ 的车辆流量。

Set the road width as $\chi$, the interval between any time periods in the period $T$ as $\Delta T$ [18,19], and the state equation of traffic flow at the intersection of smart cities is:(4)$\{\begin{array}{c}{x}_n\left(k+1\right)=q_n\left(k\right)+\Delta T{S}_n\left(k\right)\\ S_n\left(k\right)=\sum _{n\in J_2}\sum _{n+1\in J_2}v\frac{S_n}{T_2}\sum _{m\in {\mathrm{\Omega }}_m}\sum _{n\in J_2}{u}_{m,n}+\chi \end{array}$Where, $S_n\left(k\right)$ is the allowed flow of vehicles in the continuous section $n$, and $T_2$ is the time when the green light flashes in the signal period of SCTI. Establishing the state equation of traffic flow at traffic intersections in smart cities can provide real-time traffic flow information, predict congestion and provide accurate and timely data support for traffic managers.
设道路宽度为 $\chi$ ，周期 $T$ 中任意时间段的间隔为 $\Delta T$ [18,19]，则智慧城市交叉口交通流状态方程为 (4)$\{\begin{array}{c}{x}_n\left(k+1\right)=q_n\left(k\right)+\Delta T{S}_n\left(k\right)\\ S_n\left(k\right)=\sum _{n\in J_2}\sum _{n+1\in J_2}v\frac{S_n}{T_2}\sum _{m\in {\mathrm{\Omega }}_m}\sum _{n\in J_2}{u}_{m,n}+\chi \end{array}$ 其中， $S_n\left(k\right)$ 为连续段 $n$ 中允许的车辆流量， $T_2$ 为SCTI信号周期中绿灯闪烁的时间。建立智慧城市交通路口的交通流状态方程，可以提供实时交通流信息，预测拥堵情况，为交通管理者提供准确及时的数据支持。

SCTI is an important node in the urban traffic network, and its design also has an important impact on the traffic efficiency of smart cities. The design of traffic intersections in smart cities includes the number of lanes, the width of lanes, the timing of signal lights and other parameters, which have a direct impact on the traffic efficiency of vehicles. After establishing the Equation of state of traffic flow at the SCTI, the optimization model of traffic light control at the SCTI is constructed. The Equation of state of traffic flow at the SCTI is taken as the input parameter of the optimization model to determine the optimal optimization strategy of traffic light control.
SCTI 是城市交通网络中的重要节点，其设计对智慧城市的交通效率也有重要影响。智慧城市中交通路口的设计包括车道数量、车道宽度、信号灯配时等参数，这些参数直接影响车辆的通行效率。在建立小城镇交通枢纽的交通流状态方程后，构建了小城镇交通枢纽的交通灯控制优化模型。将小站交通流量状态方程作为优化模型的输入参数，以确定交通灯控制的最优优化策略。

According to the parameters shown in Table 1, set the signal time parameters for SCTIs to ensure that the SCTIs are in a normal and orderly traffic state in real time.
根据表 1 所示参数，设置 SCTI 的信号时间参数，确保 SCTI 实时处于正常有序的交通状态。

Improper control of traffic lights at intersections will easily lead to traffic delays and increase the overall traffic congestion. Therefore, minimizing the average delay can effectively reduce the time for vehicles to stay at intersections, improve the efficiency of vehicles passing through intersections, and relieve traffic pressure. In terms of average delay $e$, the calculation is mainly based on the sum of random delay $e_r$ and consistent delay $e_u$ [[23], [24], [25]]. The calculation process of random delay $e_r$ and consistent delay $e_u$ is shown in (5), (6):(5)$e_r=\frac{w_{ij}^2}{\left|1-w_{ij}\right|r_{ij}}$(6)$e_u=\frac{{\left(1-\lambda \right)}^2}{\left|1-p_{ij}\right|}\times C$Where, $w_{ij}$ is the saturation of the $j$ inlet in phase $i$, $r_{ij}$ is the actual traffic volume at the $j$ inlet in phase $i$, and $p_{ij}$ is the flow ratio at the $j$ inlet in phase $i$.
交叉路口红绿灯控制不当，容易造成交通延误，加剧整体交通拥堵。因此，尽量减少平均延误可以有效减少车辆在交叉口的停留时间，提高车辆通过交叉口的效率，缓解交通压力。就平均延误 $e$ 而言，其计算主要基于随机延误 $e_r$ 和一致延误 $e_u$ 之和[[23], [24], [25]]。随机延迟 $e_r$ 和一致延迟 $e_u$ 的计算过程如（5）、（6）所示： (5)$e_r=\frac{w_{ij}^2}{\left|1-w_{ij}\right|r_{ij}}$ (6)$e_u=\frac{{\left(1-\lambda \right)}^2}{\left|1-p_{ij}\right|}\times C$ 其中， $w_{ij}$ 为 $i$ 阶段 $j$ 入口的饱和度， $r_{ij}$ 为 $i$ 阶段 $j$ 入口的实际交通量， $p_{ij}$ 为 $i$ 阶段 $j$ 入口的流量比。

The calculation of the average delay $E_I$ required in this article can be obtained by weighting the average delay of different signal phases:(7)$\begin{array}{c}{e}_i=e_r+e_u\\ E_I=\frac{\sum _{i=1}{e}_i{r}_i}{\sum _{i=1}{r}_i}\end{array}$Where, $e_i$ is the average delay of the $i$ phase, and $r_i$ is the actual traffic flow of the $i$ phase.
本文所需的平均延迟 $E_I$ 的计算可通过对不同信号阶段的平均延迟进行加权来获得： (7)$\begin{array}{c}{e}_i=e_r+e_u\\ E_I=\frac{\sum _{i=1}{e}_i{r}_i}{\sum _{i=1}{r}_i}\end{array}$ 其中， $e_i$ 为 $i$ 阶段的平均延迟， $r_i$ 为 $i$ 阶段的实际交通流量。

Too long signal light period will lead to frequent parking of vehicles, increase the time of vehicle queuing and parking times, and reduce the overall operating efficiency of the transportation system. By minimizing the average number of stops, the number of stops at intersections can be reduced, the delay time of vehicles can be reduced, and the traffic efficiency can be improved. In terms of the average number of stops, in order to ensure normal traffic at smart city intersections, efforts should be made to avoid secondary parking of vehicles and strive to fully release all vehicles within a cycle [[26], [27], [28]]. The calculation process of the average number of stops $s_i$ is shown in formula (8):(8)$s_i=\frac{C-G_e}{1-p_{ij}}$
信号灯周期过长会导致车辆频繁停放，增加车辆排队时间和停车时间，降低交通系统的整体运行效率。通过尽量减少平均停车次数，可以减少交叉口的停车次数，减少车辆的延误时间，提高交通效率。就平均停车次数而言，为了保证智慧城市交叉口的正常交通，应努力避免车辆的二次停放，力争在一个周期内将所有车辆全部放行[[26], [27], [28]]。平均停车次数 $s_i$ 的计算过程如式（8）所示： (8)$s_i=\frac{C-G_e}{1-p_{ij}}$

The calculation method for the average number of vehicle stops $S_I$ required in this article is obtained through weighted calculation:(9)$S_I=\frac{\sum _{i=1}{s}_i{r}_i}{\sum _{i=1}{r}_i}$
本文所需的平均车辆停靠次数 $S_I$ 的计算方法是通过加权计算得出的： (9)$S_I=\frac{\sum _{i=1}{s}_i{r}_i}{\sum _{i=1}{r}_i}$

By optimizing the control parameters of traffic lights, the delay time of vehicles can be reduced, and the number of vehicle stops can be reduced, thus improving the traffic capacity of intersections and the operating efficiency of the overall traffic system. By taking the average delay index and the average number of stops as the objective function, the intersection traffic can be smoother and more efficient to the greatest extent.
通过优化交通信号灯的控制参数，可以缩短车辆的延误时间，减少车辆的停车次数，从而提高交叉口的通行能力和整个交通系统的运行效率。以平均延误指数和平均停车次数为目标函数，可以最大程度地使交叉口交通更加顺畅和高效。

The weighting coefficient $\alpha$ is introduced, and $\delta$ is set to represent the signal phase of SCTI, and the signal period of SCTI satisfies $15\times \delta$ and less than or equal to 200s. The cycle time consists of green light time and lost time $L$. If the saturation $w_{ij}$ needs to be 0.6–0.9 to maintain good traffic conditions at SCTI, then:(10)$\begin{array}{c}15\times \delta \le C\le 200\\ \sum _{i=1}^{\delta }{\lambda }_{i}C=C-L\\ 0.6\le w_{ij}\le 0.9\\ g_x\le G_e\le G_{\max }\end{array}$
引入加权系数 $\alpha$ ，设置 $\delta$ 表示 SCTI 的信号相位，SCTI 的信号周期满足 $15\times \delta$ 且小于等于 200 秒。周期时间由绿灯时间和丢失时间 $L$ 组成。如果饱和度 $w_{ij}$ 需要达到 0.6-0.9 才能维持 SCTI 的良好交通状况，那么： (10)$\begin{array}{c}15\times \delta \le C\le 200\\ \sum _{i=1}^{\delta }{\lambda }_{i}C=C-L\\ 0.6\le w_{ij}\le 0.9\\ g_x\le G_e\le G_{\max }\end{array}$

Establishing the optimization model of traffic signal control at intersections in smart cities:(11)$\begin{array}{c}\min F\left(x\right)=x_n\left(k+1\right)\frac{\alpha s_i{r}_i\beta +\left(1-\alpha \right)e_i{r}_i}{\sum _{i=1}{r}_i}\\ s.t.\{\begin{array}{c}15\times \delta \le C\le 200\\ \sum _{i=1}^{\delta }{\lambda }_{i}C=C-L\\ 0.6\le w_{ij}\le 0.9\\ g_x\le G_e\le G_{\max }\end{array}\end{array}$
建立智慧城市交叉口交通信号控制优化模型： (11)$\begin{array}{c}\min F\left(x\right)=x_n\left(k+1\right)\frac{\alpha s_i{r}_i\beta +\left(1-\alpha \right)e_i{r}_i}{\sum _{i=1}{r}_i}\\ s.t.\{\begin{array}{c}15\times \delta \le C\le 200\\ \sum _{i=1}^{\delta }{\lambda }_{i}C=C-L\\ 0.6\le w_{ij}\le 0.9\\ g_x\le G_e\le G_{\max }\end{array}\end{array}$

Based on the establishment of an optimization model for traffic signal control at smart city intersections, an adaptive artificial fish swarm algorithm is used to solve the optimization model for traffic signal control at smart city intersections. The artificial fish swarm algorithm is a population intelligent optimization algorithm. The basic idea is to simulate the foraging behavior, tail chasing behavior, and herd behavior of fish [[29], [30], [31]]. This algorithm can be used to solve various continuous optimization problems and Combinatorial optimization problems.
在建立智慧城市交叉口交通信号控制优化模型的基础上，采用自适应人工鱼群算法求解智慧城市交叉口交通信号控制优化模型。人工鱼群算法是一种群体智能优化算法。其基本思想是模拟鱼类的觅食行为、追尾行为和群居行为[[29], [30], [31]]。该算法可用于解决各种连续优化问题和组合优化问题。

Assuming that the current state of an artificial fish is $Z$, set its field of view to $V$, and the viewpoint position of the artificial fish at a certain moment is $Z_v$. When the position state of the viewpoint is better than the current artificial fish state, the artificial fish can choose to move one step in that direction to reach state $Z_n$; If the state of the viewpoint is not better than the current state of the artificial fish, continue to search for other positions within the field of view. As the number of searches increases, artificial fish have a more comprehensive understanding of the surrounding environment, enabling them to have a more comprehensive understanding of the surrounding environment, which helps make corresponding judgments and decisions.
假设人造鱼的当前状态为 $Z$ ，将其视场设置为 $V$ ，人造鱼在某一时刻的视点位置为 $Z_v$ 。当视点的位置状态优于人工鱼的当前状态时，人工鱼可以选择向该方向移动一步，达到状态 $Z_n$ ；如果视点的状态不优于人工鱼的当前状态，则继续搜索视野内的其他位置。随着搜索次数的增加，人工鱼对周围环境有了更全面的了解，从而能够对周围环境有更全面的认识，有助于做出相应的判断和决策。

Reasonable adjustment of green signal ratio can directly affect the traffic flow in different directions. Priority is given to setting the green light time for straight and left-turning vehicles at peak hours to meet the demand of main traffic flow, thus reducing waiting time and improving traffic efficiency. In the low peak period, set a balanced green signal ratio according to the actual situation to avoid excessive waiting and wasting traffic resources. Among them, state $Z=\left(z_1,z_2,...,z_n\right)$ and position $Z_v=\left(z_{1v},z_{2v},...,z_{nv}\right)$, then the process can be represented as follows:(12)$\begin{array}{c}{Z}_v=Z+V\cdot Rand\left(\right)\\ Z_n=Z+\frac{Z_v-Z}{\Vert Z_v-Z\Vert }\cdot Step\cdot Rand\left(\right)\end{array}$Where, the $Rand\left(\right)$ function is used to generate a random number between 0 and 1, and $Step$ is the step size of the artificial fish movement. Because the number of companions in the environment is limited, artificial fish will perceive the state of their companions in their field of vision and adjust their own state accordingly.
绿灯比例的合理调整会直接影响不同方向的交通流量。高峰时段优先设置直行和左转车辆的绿灯时间，满足主要交通流的需求，从而减少等待时间，提高交通效率。在低峰时段，根据实际情况均衡设置绿灯信号比例，避免过度等待，浪费交通资源。其中，状态 $Z=\left(z_1,z_2,...,z_n\right)$ 和位置 $Z_v=\left(z_{1v},z_{2v},...,z_{nv}\right)$ ，则过程可表示如下： (12)$\begin{array}{c}{Z}_v=Z+V\cdot Rand\left(\right)\\ Z_n=Z+\frac{Z_v-Z}{\Vert Z_v-Z\Vert }\cdot Step\cdot Rand\left(\right)\end{array}$ 其中， $Rand\left(\right)$ 函数用于产生一个介于 0 和 1 之间的随机数， $Step$ 是人工鱼群移动的步长。由于环境中同伴的数量有限，人工鱼会感知视野中同伴的状态，并相应调整自己的状态。

The variable section includes the total number of artificial fish $N$, the state of individual artificial fish $Z=\left(z_1,z_2,...,z_n\right)$, the field of view $V$ of the artificial fish, the crowding factor $\gamma$, the maximum step length of the artificial fish movement $Step$, the number of attempts $Try$, and the distance between individual artificial fish $\xi ,\zeta$, calculated as follows:(13)$D_{\xi \zeta }=\left|X_{\xi }-X_{\zeta }\right|$
变量部分包括人造鱼总数 $N$ 、人造鱼个体状态 $Z=\left(z_1,z_2,...,z_n\right)$ 、人造鱼视野 $V$ 、拥挤系数 $\gamma$ 、人造鱼运动最大步长 $Step$ 、尝试次数 $Try$ 和人造鱼个体间距离 $\xi ,\zeta$ ，计算公式如下： (13)$D_{\xi \zeta }=\left|X_{\xi }-X_{\zeta }\right|$