Path Planning of Ant Colony Algorithm Based on Decision Tree in the Context of COVID-19

Reasonable planning of travel routes can keep people away from crowded areas and reduce the probability of contracting the COVID-19. In view of the characteristics related to virus infection and human ﬂ ow density, it can overcome the shortcomings of using the same pheromone initial value and slow initial convergence in route planning of ant colony optimization (ACO) algorithm. In this paper, the decision tree algorithm is used to divide the human ﬂ ow density into three levels: high risk, medium risk, and low risk; and different pheromone volatility coef ﬁ cients are set to change the distribution of pheromone concentration. The experimental results show that the improved ACO algorithm could help to reduce the likehood of passing through the medium-risk areas and the high-risk areas, which is reduced to less than 1 % . This scheme provides an ef ﬁ cient route planning method for epidemic prevention and control that can be applied in the daily prevention of COVID-19 in universities.


Introduction
In recent years, public health emergencies such as epidemics have been threatening people's lives. The sudden outbreak of COVID-19 in early 2020 has not only brought serious damage to the world, but also directly threatened human lives [1]. The COVID-19 is mainly contracted by "person-to-person" through respiratory droplets and close contact [2]. When people gather together, it is very likely to cause the infection of COVID-19, owing to the close distance between people, poor air circulation, and other problems. Therefore, in order to effectively prevent and control the epidemic, residents should reasonably plan travel routes in daily life and try to avoid crowded areas, which would help reduce the possibility of being infected by the COVID-19 [3].
With the development of robotics, Internet of Things (IoT) and automation technology [4][5][6], path planning has attracted wider attention of scholars at home and abroad. Common path planning methods are mainly divided into three categories: traditional path planning algorithm, sampling-based path planning algorithm, and intelligent bionic path planning algorithm. Traditional path planning algorithms mainly include A * algorithm [7], Dijkstra algorithm [8], and artificial potential field (APF) method [9]. Sampling-based path planning algorithms include probabilistic road map (PRM) algorithm [10] and rapidly-exploring random tree (RRT) algorithm [11]. Intelligent bionic path planning algorithms include neural network (NN) algorithm [12], ant colony optimization (ACO) algorithm [13], genetic algorithm (GA) [14] and so on.
ACO is a famous and popular probabilistic algorithm used to find optimal paths, which was proposed by Italian scholar Dorigo [15,16] in 1992. It has the advantages of good environmental adaptability, robustness, and easiness to be combined with other algorithms, and has a good effect in solving path planning problems [13]. In recent years, ACO algorithm is still widely used in the field of path planning. For example, Xue et al. [17] proposed an improved ACO algorithm for route planning of logistics robots, which adopted a multistep search strategy and redesigned the pheromone updating mechanism. It solved the problem that ACO algorithm easily concentrated on the local optimum in the iterative process, and improved the efficiency of warehousing, sorting, and distribution work in the logistics industry. An improved ACO algorithm based on the strategy of time taboo by Xiong et al. [18] is proposed, which is to solve the problem of path planning for mobile robot in dynamic environment. Adaptive initial pheromone distribution, rollback strategy, and pheromone priority limited updating are used to improve the convergence speed and global search ability of the algorithm. Hou et al. [19] proposed an enhanced ACO algorithm on communication mechanism that could effectively integrate historical paths, which improved the global search ability and stability of the algorithm and realized the global optimal path for mobile robots. In order to calculate the optimal path of obstacle avoidance for unmanned surface vehicles in complex dynamic environments, an improved fuzzy logic ACO algorithm was proposed by Lyridis et al. [20]. A dynamic ACO algorithm based on fuzzy gain for dynamic path planning was proposed by Sangeetha et al. [21], which can effectively plan safe and smooth collisionfree paths to minimize the path length and time. By combining ACO algorithm and chaos optimization algorithm (COA), and introducing pheromone differential updating strategy and search optimization strategy, Xie et al. [22] proposed an effective ACO algorithm for multiobjective detection path planning in radiation environment.
Although the above literature has improved the method and performance of path planning problem based on ACO algorithm, still there are shortcomings in it when we are confronted with the actual situation. This paper focuses on the path planning problem and expect to use this study to provide people with an effective method to avoid crowded areas and find safe travel routes in low-density areas under the background of COVID-19.
The main contributions of this paper are as follows: (1) A path planning method combining machine learning and ACO algorithm is proposed to optimize pheromone volatility coefficient matrix dynamically based on the human flow density. (2) The decision tree algorithm is used to automatically predict and divide the crowd density of outdoor places with mobility, according to the idea of hierarchical management of epidemic prevention and control. (3) A realistic and feasible path planning scheme to avoid virus infection is provided and efficiently accomplished by combining grid method, machine learning algorithm, and dynamic path planning algorithm.
The improved ACO algorithm is applied to route selection in public places based on the principle of avoiding clustering, and provides theoretical guidance for safe travel plans for people under the influence of COVID-19.

Related Work
In order to avoid person-to-person transmission and ensure people's safe travel, it is particularly important to study path planning [23]. In recent years, scholars have done a lot of research on path planning on the prevention and control of COVID-19.
According to different research contents, it can be divided into two categories: mobile robot path planning and path planning navigation to avoid virus infection. According to different functions, mobile robot path planning is further divided into two categories: performing autonomous indoor disinfection work and delivering COVID-19 test kits. In the study of performing automatic indoor disinfection work, Banjanovic-Mehmedovic et al. [24] integrated particle swarm optimization (PSO) algorithm and dynamic window approach (DWA) for reactive collision avoidance, which was used for optimal path planning and obstacle avoidance of autonomous mobile disinfection robot. A novel trajectory planner dedicated to disinfection tasks based on adjustable APF optimized by GA has been developed by Tiseni et al. [25], which can self-adapt to the environment to generate a suitable path planning scheme to ensure the completion of disinfection tasks. Xu et al. [26] proposed an intelligent robotic system with effective zero-contact disinfection service, which used a coverage path planning (CPP) algorithm to generate a reasonable coverage path in a three-dimensional environment. In order to solve the deadlock problem caused by the complete coverage path planning (CCPP) algorithm, a preventive deadlock processing algorithm (PDPA), and an escape route generator algorithm (ERGA) were proposed to improve the disinfection path planning of mobile robots by Rodrigo et al. [27]. Wang et al. [28] improved the A * algorithm based on the NN, which would help optimize the path solution with reasonable computing power, and constructed a surface disinfection robot with a shorter total distance and collision-free path.
In a study on the delivery of COVID-19 test kits, Munawar et al. [29] optimized the routing of unmanned aerial vehicles (UAVs) based on artificial intelligence (AI) by greedy, intraroute, interroute, and tabu algorithms. The COVID-19 self-test kit was delivered to potential patients without contact and samples were brought back for testing. A low-complexity hybrid reinforcement learning algorithm consisting of a heuristic algorithm and a Q-Learning algorithm was proposed by Xing et al. [30] to determine the optimal route for UAV delivery of the COVID-19 detection kit in the shortest time.
The path planning navigation based on avoiding virus infection is mainly studied for people's safe travel. Wang et al. [31] designed a search mechanism to avoid areas related to the risk of new epidemics, and proposed a restricted reinforcement learning-artificial potential field (RRL-APF) algorithm to solve the problem of residents' travel path planning under new epidemics.
In general, research on path planning under the COVID-19 pandemic is mainly divided into two aspects: automatic disinfection and zero-contact distribution, and few studies have been conducted on path planning considering people's safe travel, as shown in Table 1.

Basic ACO Algorithm
The ACO algorithm is an intelligent optimization algorithm that simulates the path behavior of ants searching for food in nature. Ants secrete pheromones while searching for a path, the amount of which is inversely proportional to the length of their path. When choosing a path, the ant will most likely to choose the path with the highest pheromone, according to the state transition rule [32]; and as many ants continue to secrete pheromones, more and more pheromones are found along the optimal path, and eventually the entire colony could find the optimal path.
3.1. Status Transfer Rules. The basic ACO algorithm selects the path according to pheromone and heuristic information; and a certain amount of pheromone τ i; ð jÞ is released by ants on the path i; ð jÞ in the process of moving or after completing a cycle. In general, during a cycle, the ant will not select the path that has already been selected in order to satisfy the constraints of the problem.
In the initial state, without the influence of pheromone and heuristic information, the ant's path selection is random. After that, the ant's selection probability is related to the distance between nodes and the pheromone allowance contained in the path. Assuming that the ant with serial number k is currently located at point i, the probability of moving from this position to point j is: In Equation (1), η i; ð jÞ is the heuristic information from position i to position j. In general, the value of η i; ð jÞ is the inverse of the distance; N i k indicates the set of all the next optional points in the path search; and α and β represent the relative weight parameters of pheromone and heuristic information, respectively, representing the proportion of τ i; ð jÞ and η i; ð jÞ in the selection decision. It can be clearly seen from Equation (1) that path with more pheromones and shorter distances are easier to be selected.

Pheromone Update
Rules. Ants release pheromones as they move. The pheromone updating rule is: assume that L k represents the length of the path. Obviously, the value of L k is smaller, the better the quality of the solution is, and the larger the value of pheromone Δτ k i j are left on the road.
Equation (2) represents the total change of pheromone on any path i; ð jÞ. The ant leaves pheromones along its path. Δτ k i j represents the pheromone released by ant with serial number k on path i; ð jÞ; and m is the number of ants. The specific expression of Δτ k i j in Equation (2) is: The ant with number k passes through the path i; j ð Þin this iteration 0; Other In Equation (3), Q is a constant, representing pheromone intensity; and L k represents the length of the path taken by the ant with serial number k in this iteration.
The pheromone volatility mechanism is introduced in the basic ACO algorithm to update the pheromone.
In Equation (4), ρ represents pheromone retention coefficient; and 1−ρ represents pheromone volatility coefficient. The pheromones are updated according to Equation (4) and enter the next iteration process.
The main flow of basic ACO algorithm is shown in Algorithm 1.

Path Planning under Epidemic Prevention and Control
According to the latest COVID-19 prevention and control circular, people need to voluntarily adhere to the prevention strategy of not gathering. It is important to selectively avoid crowded areas when traveling. At present, the number of people entering public places, including universities, is monitored in real time by scanning codes and faces based on machine learning technology. In this paper, people are identified by scanning their faces and swiping their cards as they enter the teaching building, library, and other campus buildings. Collect statistics of the density of people in each building. Based on the decision tree algorithm, according to the known density of people in the building, the people density in the area around the building that cannot be detected can be reasonably speculated. According to the density of people in each area of the campus, the risk degree of infection can be analyzed. Based on the high, medium, and low risk levels in the region, the volatile intensity of the pheromone is changed, and then the distribution of pheromone is affected. According to the volatile strength of the pheromone on different road sections, the effect of risk aversion can be achieved, and the reasonable choice of travel path can be realized.

Decision Tree.
Decision tree is used to predict new data output variables by finding the logical correspondence or rules between the values of input variables and output variables in the data. The decision tree consists of three parts: decision point, state node, and result node. It obtains an inverted tree by grouping the sample data continuously, which is used to show the analysis results. The decision tree model is often used to solve the classification and regression problems. It has the characteristics of good data analysis ability and intuitive result presentation. In machine learning, the decision tree represents a mapping relationship between object attributes and object values, which is a prediction model. Every node in the tree represents an object, and each fork path represents a possible attribute value. Every leaf node represents the value of the object represented by the path formed from the root node to the leaf node. The decision tree is used to mark the division of human flow density in the map. The original map is divided into two parts: buildings and roads, which are marked with 1 and 0, respectively. The area where the building is located is divided into high, medium, and low risk levels according to the density of people, which are marked with 3, 2, and 1, respectively. The surrounding roads are affected by the population density of the built-up areas and will also carry the risk of infection. The decision tree rule is used to assess the risk of infection in the unmarked area. The decision tree rules can be divided into three cases: middle position, boundary position, and corner position. The neighbors around the location to be identified are shown in Figure 1, where the black square represents the location to be identified and the white square represents its neighbors.
Rule 1: When the position to be marked is in the middle position, there are eight neighbors around it, as shown in Figure 1(a). The rules for determining the risk level of the location to be marked are shown in Algorithm 2.
Rule 2: When the location to be marked is on the border, there are five neighbors around it. As shown in Figure 1(b)-1(e), they respectively represent the neighbor situation when the location to be marked is on the upper boundary, lower boundary, left boundary, and right boundary. 1: for k←1 to K do %Iterations 2: for m←1 to M do %Ant number 3: Set parameters and initialize pheromones; 4: while The stop condition is not met do 5: Constructing the solution of the problem according to the path selection rules; 6: τ i; ð jÞ←ρ: * τ i; ð jÞ þ Δτ i; ð jÞ; %Update pheromone according to pheromone update rules ALGORITHM 1: Basic ACO algorithm. 4 Wireless Communications and Mobile Computing Rule 3: When the location to be marked is in a corner, there are three neighbors around it. As shown in Figure 1 (f )-(i), they respectively represent the neighbors situation when the location to be marked is in the upper left corner, upper right corner, lower left corner, and lower right corner.
The rules for determining the risk level of the location to be marked described in Rules 2 and 3 are shown in Algorithm 3.

4.2.
Improved ACO Algorithm. COVID-19 is spread from person to person mainly through respiratory droplets and close contact. Areas with high human flow density are prone to result in outbreaks. Considering the influence of the COVID-19 epidemic, people should choose to travel through low-density population areas in order to avoid crowded areas.
According to the idea of hierarchical management of epidemic prevention and control, the density of people in public places is divided into high-density population area, medium-density population area, and low-density population area. According to the different human flow density, the infection risk level marked by the decision tree is used to adjust the pheromone volatility coefficient of the corresponding region. The volatility coefficient of pheromone is set to A1 when moving from high-density flow area to lowdensity flow area or moving in low-density flow area. The volatility coefficient of pheromone is set to A2 in the case of moving in high-density or medium-density area. The volatility coefficient of the pheromone is set to A3 when moving from a low-density flow area to high-density flow area, where the value of A1 is less than the value of A2, and the value of A2 is less than the value of A3.
ACO algorithms are often used for path optimization because ants always find the best path based on the pheromones they release. In the basic ACO algorithm, the volatility rate of the pheromone is the same on each path segment. However, in real life, the volatility rate of pheromone will be affected by the environment and change dynamically.
The principle of risk aversion is introduced into the path selection of ACO algorithm. By adjusting the volatility coefficient of pheromone, the concentration of pheromone can be redistributed. When the density of human traffic becomes higher, the probability of human-to-human transmission of COVID-19 is higher, and the risk of people becoming infected is higher. When the density of people is low, the probability of human-to-human transmission of COVID-19 is lower, and the risk of people becoming infected is lower. In order to prevent people from moving to high-density areas, the pheromone volatility coefficient is set to a higher value when moving from medium-density and low-density population areas to high-density population areas, which would help reduce the residual pheromone concentration on this path and reduce the probability of this path being selected. At the same time, people are encouraged to flow to the lowdensity population areas, and the pheromone volatility coefficient when moving from medium-density and high-density population areas to low-density population areas is set to a small value, which would help increase the concentration of pheromones left on this path and increase the probability of this path being selected. For the inevitable movement behavior between medium-density or high-density flow areas, the pheromone volatility coefficient of the path is set as an intermediate value according to the principle of neither encouraging nor discouraging.
Based on the epidemic prevention and control idea of avoiding crowded gathering, the pheromones between areas with different densities in public places are updated by changing the volatility speed of pheromones. The main process of the improved ACO algorithm is shown in Algorithm 4.
By adjusting the volatility coefficient of the pheromone in the ACO algorithm, we can apply it to the path selection of public places based on the principle of avoiding aggregation under the influence of COVID-19. It can also be used to provide advice with risk avoidance for various types of navigation software, as well as to provide point selection advice for companies that need to travel frequently and so on. It provides theoretical guidance for people's demand for safe travel under the COVID-19 epidemic.

Experimental Environment.
The path planning experiment considering the risk avoidance principle is conducted 1: if the number of neighbors of i marked with '3' > = 1 then %The i indicates the location to be identified 2: i←2; %The 3,2 and 1 represent high risk, medium risk and low risk areas respectively 3: elseif the number of neighbors of i marked with '2' > = 1 then 4: i←1; 5: elseif the number of neighbors of i marked with '1' > = 1 then 6: i←1; 7: else 8: i←0; %The 0 indicates the location to be identified ALGORITHM 3: Rules 2 and 3.
1: Initializing the human flow density matrix; 2: The crowd density matrix is updated based on decision tree rules; 3: Initialize the pheromone matrix; %Update the pheromone volatility matrix based on the human flow density matrix 4: if from the high-density area to the low-density area, or in the low-density area then 5: ρ←A1; %The ρ is the pheromone volatility coefficient 6: elseif in the same density area then %The A1, A2, and A3 are three different coefficient values 7: ρ←A2; %A1<A2<A3 8: elseif from the low-density area to the high-density area then 9: ρ←A3; 10: Basic ACO algorithm;  represented as high-density flow areas. Serial numbers 3,7,8,16,17,18,19,21,28,29, and 30 are marked with yellow squares and represented as medium-density flow areas. Serial numbers 2, 5, 6,9,10,11,12,13,14, and 15 are marked with blue squares and represent low-density flow areas. Table 2 lists the names of the buildings numbered 1-32.
Map initialization: Change the above raster diagram into a matrix with only 0 and 1 elements; where, 1 represents an obstacle and 0 represents an alternative open space. As shown in Figure 3, the black squares represent obstacles and white squares represent roads.
Set parameters: Initialize the pheromone matrix, set the iteration number of the algorithm, the number of ants. Set the parameters representing the importance of pheromone and the importance of heuristic factors, and establish the heuristic information matrix. Set the pheromone evaporation coefficient and pheromone increasing intensity coefficient and other algorithm initialization information.  Establish the pheromone volatility matrix. According to the human flow density of each building on the campus, it is divided into three categories: high-density human, mediumdensity area, and low-density area. The areas with highdensity, medium-density, and low-density are marked with 3, 2, and 1, respectively, and the road areas are marked with 0 to form the initial crowd density matrix. The high-density area have the highest risk of infection, the medium-density area have the moderate risk of infection, and the low-density area have the lowest risk. Because people and air are mobile, road areas around buildings will also be at risk of carrying COVID-19 virus. Based on the basic principles of epidemic prevention and control, the flow diffusion simulation of the flow density matrix is carried out according to the decision tree rule described in the "Decision Tree" section. When the human flow density matrix does not contain element 0, it indicates the end of diffusion. The flow diffusion results are shown in Figure 4. The dark blue pixels represent high-density areas, light blue pixels represent medium-density areas, and white pixels represent low-density areas. The corresponding pheromone volatility matrix is constructed according to the final human flow density matrix. Due to the high risk of infection in high-density population areas, it is necessary to avoid high-risk areas and move to low-risk areas when planning  Wireless Communications and Mobile Computing the path. When moving from the high-density flow area to the low-density flow area or within the low-density flow area, the volatilization coefficient of the corresponding pheromone is 1. The volatility coefficient of the corresponding pheromone is 2 when it moves in the area of medium-density or high-density. When moving from the low-density area to the high-density area, the corresponding pheromone volatility coefficient is 3; and 1 is less than 2 and is less than 3, respectively.
Construct the solution to the problem. The ants use an N-dimensional vector to mark whether the road is selected, and a crawling route corresponds to a solution. In each construction step, tabu table is used to judge whether the position has been passed, and the selection probability of each alternative adjacent node is calculated. In this experiment, roulette is used to decide the next step. When choosing, the ants prefer to choose the path with higher pheromone and heuristic information. After the next selection is made, the path and tabu table are updated. When each ant of each generation has finished its path-finding, the route and the length of the route are recorded. At the same time, the current known shortest path length is recorded, and an ant which completed the shortest path is also recorded.
Update the pheromone: The pheromone increment is initialized to obtain the current path length of the ants in  this iteration, and the pheromone increment is updated according to Equation (3). Pheromones are volatile. According to the established pheromone volatility matrix, Equation (4) is used to update the pheromone. In general, after pheromone renewal, the number of pheromones on the chosen path increases, and so does their preference. In this experiment, different pheromone volatility coefficients are set according to the density of people in different areas. According to the principle of risk aversion, the greater the population density is, the higher the risk of being infected by the epidemic will be, so that the pheromone is more volatile. This can guide the ants to move to low-density human traffic areas, reducing the risk of contracting COVID-19.

Experimental Data Analysis.
The trajectory diagram of the basic ACO algorithm on path selection is shown in Figure 5. Figure 5(a) shows the obstacle avoidance process from the school gate to the student apartment building, by passing the campus buildings. Figure 5(b) shows the result of the planned path passing through high-density, mediumdensity, and low-density flow areas. Among them, the probability of passing through the high-density flow area is 0/46. The probability of passing through the medium-density flow area is 10/46. The probability of passing through the lowdensity flow area is 36/46. In the case of the same pheromone volatility coefficient, the shortest walking route is selected as the optimal solution. Without considering the density of people, the choice of the optimal path is only related to the length of the distance, and has nothing to do with other factors. Therefore, the selected optimal solution cannot completely avoid the crowded area.
The trajectory diagram of the improved ACO algorithm on path selection is shown in Figure 6. Figure 6(b) shows that the path planned in Figure 6(a) passes through high-density, medium-density, and low-density flow areas. Among them, the probability of passing through the high-density flow area is 0/49. The probability of passing through the mediumdensity flow area is 2/49 = 0.04. The probability of passing through the low-density flow area is 47/49. Figure 6(d) shows that the path planned in Figure 6(b) which passes through high-density, medium-density, and low-density flow areas. Among them, the probability of passing through the highdensity flow area is 0/50. The probability of passing through the medium-density flow area is 0/50. The probability of passing through the low-density flow area is 50/50. In the improved ACO algorithm, the volatility degree of the pheromone is affected by the flow density in the passing area. The more crowded the area is, the more likely it is to be infected with the COVID-19. So the faster the pheromone volatilizes, the lower the probability that the path will be chosen. Similarly, the less densely populated areas are, the less likely they are to be infected with COVID-19, and the slower the pheromone volatilizes, the higher the probability of being selected will be. Therefore, the optimal solution of the improved ACO algorithm will be affected by the flow density, and it will choose to move to the low-density flow area when considering the length of the path.
Six cases of path trajectory diagrams of the basic ACO algorithm and the improved ACO algorithm were selected, respectively, as shown in Figures 7 and 8. The probability of these paths passing through high-density, medium-density, and low-density flow areas is calculated as shown in Tables 3  and 4. According to the statistical data, the path trajectories of the basic ACO algorithm are distributed in the mediumdensity and low-density flow areas. The probability of passing through the area of medium-density flow is about 20%-30%. The path trajectory of the improved ACO algorithm basically moves in the low-density flow area, and may pass through the medium-density flow area. The probability of existing in the medium-density flow area is less than 1%, as shown in Figure 6(b). Therefore, the path trajectory of the improved ACO algorithm can well avoid the mediumdensity and high-density flow areas, and basically guide people only flow in the low-density flow area.

Conclusion Analysis.
It can be seen from the experimental results that the path trajectory diagram of the basic ACO algorithm takes the shortest path length as the only preference criterion, and does not consider the density of people on the selected path. The selected optimal solution often passes through crowded areas, which cannot effectively avoid the risk of COVID-19 infection. The path trajectory diagram of the improved ACO algorithm takes the flow density of the campus buildings into account. During the path selection process, it always moves to the low-density flow area and tries to avoid the medium-density and high-density flow areas. The optimal solution can effectively reduce the risk of COVID-19 infection.

Conclusions
Based on the decision tree algorithm, this paper divides the density of human flow in campus buildings. According to the different risks of COVID-19 infection in different density flow areas, different volatility coefficients are set, and a pheromone volatility mechanism based on the principle of risk aversion is proposed. The experimental results show that the classification of pheromone volatility coefficient affects the optimal solution of the path planning. The improved ACO algorithm can effectively avoid medium-density and highdensity flow areas, which provides theoretical guidance for path selection in public places under the influence of COVID-19.
In the future, we can consider the improvement of the algorithm from the following aspects: (1) by comparing and analyzing the newly proposed path optimization algorithms in recent years, the improved scheme based on decision tree proposed in this paper is combined with further in-depth experiments to prove the universality of the scheme; (2)   expanded in other application scenarios, such as supermarkets, shopping malls, stations, airports, and other public places, to fully verify the effectiveness of the algorithm in the case of emergency risk avoidance.

Data Availability
All data supporting this study are provided as supplementary information accompanying this paper.

Conflicts of Interest
The authors declare that they have no conflicts of interest.