# Virtual Reality Collision Detection Based on Improved Ant Colony Algorithm
## 3 An Improved Ant Colony Algorithm Based on Random Collision Detection
### Optimization of the Ant Colony Algorithm  
The traditional ant colony algorithm has two defects. As a large space search algorithm, the ant colony algorithm will perform a blind search in the early stages to generate a large number of invalid paths, and the convergence speed is slow; after all the ants have completed a pheromone update, the concentration of pheromones left on the shorter paths is higher than that on the longer paths. Under the action of positive feedback, ants will be attracted to pass through the path with more pheromones. However, if the algorithm has not found the optimal solution but rather the suboptimal solution at the beginning, the suboptimal solution will soon hold the absolute advantage and fall into the local optimal solution. In order to solve these problems, this study improved the ant colony algorithm [26; 27] as follows. 1. When selecting the next node, the ant is required to compute the transition probability of all the adjacent nodes linked to the current node and then select the route with the highest probability. The main factors affecting the probability of a transition are the factor of the pheromone's influence \(\alpha\) and the expectation heuristic factor \(\beta\). The pheromone's concentration and volatilization status in the ant colony algorithm are different in different stages: a low pheromone concentration and easy volatilization in the early stage; in the later stages, the concentration of pheromones is high and difficult to volatilize, but the traditional ant colony algorithm does not distinguish the ant colony's state. The values of the parameters \(\alpha\), \(\beta\) are fixed, and the ant colony algorithm is more likely to fall into the local optimal solution in this case [28]. Therefore, the algorithm needs to dynamically modify the value of \(\alpha\), \(\beta\) during iteration, and these take different values at different stages. In the initial stage, most ants do not find a reasonable path. At this time, the random search ability of ants should be enhanced to reduce the value of \(\alpha\), \(\beta\); in the mature stage, most ants will find a better solution. In order to improve the convergence speed of the algorithm, the value of \(\alpha\), \(\beta\) should be increased:  
\[\alpha^{\prime}=\alpha\frac{N_{c}}{n} \tag{9}\]  
\[\beta^{\prime}=\beta\frac{N_{c}}{n} \tag{10}\]  
\(\alpha^{\prime}\), \(\beta^{\prime}\) are the values of the optimized factor of the pheromone's influence and the expected heuristic factor, \(n\) is a constant value, and \(N_{c}\) is the value of the current iteration. 2. The volatilization factor \(\rho\) represents the degree of volatilization or the reduction in the concentration of pheromones. When the factor is too large, the degree of pheromone volatilization will be accelerated, and the convergence speed of the algorithm will be reduced. If the factor is too small, this will reduce the speed of pheromone volatilization, resulting in too many pheromones and the algorithm falling into the local optimal solution. The value of the factor of volatility in the traditional ant colony algorithm is fixed, so it needs to be improved to make it change dynamically. The algorithm should make the volatile factor larger in the early stage, so that the algorithm has a strong global search ability; in the mature stage, the volatilization factor should be gradually reduced to accelerate the convergence speed of the algorithm: \[\rho=\frac{N}{N_{c}+N}\] (11)  
The volatilization coefficient decreases linearly with an increase in the number of iterations. \(N\) is the total number of iterations, and \(N_{c}\) is the value of the current iteration. 3. The reciprocal of the distance between the two nodes is the heuristic factor \(\eta\). The shorter the distance between the two nodes, the larger the heuristic factor, and the higher the probability that the ants will choose the path. However, this relationship can easily make the ants fall into the local optimal solution.