# Airport Field Path Optimization Method Based on Conflict Hotspot Avoidance Mechanism
## 3 Algorithm Design
### Operator Design  
(1) Coding  
The conventional binary coding method may produce more non-feasible solutions, which makes the search time increase greatly and makes it easy to fall into the local optimum. Therefore, based on the field hotspot area path optimization model established above, this section adopts the real number coding method to encode the aircraft taxi paths, using real numbers as chromosomes to reduce the complexity of the correspondence between the solution space and the coding space. The gene segment of the chromosome consists of the numerical numbering of the nodes of the airport field network topology model, and the order of the nodes reflects the sequence of the taxi paths of the aircraft from the start point to the endpoint. The chromosome shown in Figure 3 represents the sequence of the taxi paths for Aircraft \(f_{i}\) as it rolls out of the parking position (node number 174) and taxis to the runway entrance (node number 10) using runway 33. (2) Population Initialization  
It is known that the starting node of the aircraft is \(o\) and the target node is \(d\). Use a heuristic search algorithm to obtain \(N\) initial feasible solutions (i.e., \(N\) initial glide paths) to form the first generation of the population, The specific process is shown in Figure 4 and the specific steps are as follows:  
Step 1: Initialize the sequence of the starting nodes, and set the initial \(N=1\). When running to the \(N\) th time, determine whether \(N\) satisfies the cyclic condition; if not go to Step 2, if so, go to Step 6. Step 2: Search the neighboring node \(n_{1},n_{2},n_{3}\cdots\) of the starting node \(o\), sort the distance cost of the neighboring node sequence, and calculate the sum. Step 3: Calculate the cumulative probability \(p\) of the costs of all neighboring nodes and generate \((0,1)\) random number \(random\). Step 4: Compare \(random\) and \(p\), select the node \(p\) corresponding to the probability interval, add the node \(n_{1}\) to the path sequence, and store the \(N\) th cycle path sequence. Step 5: Determine whether the selected node a is the target node of the aircraft; if not, take the node as the current node and go to Step 2, if it is the target node then go to Step 1. Step 6: Output the initial pre-gliding path set of all aircraft. (3) Selection  
In this section, the combination of the elite preservation method and sorting selection method is used to carry out the selection operation. Firstly, the fitness values of individuals are calculated and sorted to eliminate the individuals with poor fitness values in the population; then, the individuals with superior fitness values are selected according to a certain proportion to evolve to the next generation. (4) Crossovers and Variations  
To ensure that the encoding does not affect the global optimal solution in the crossover and mutation process, an adaptive genetic algorithm is used so that the crossover operator and mutation operator can carry out the corresponding genetic operation according to the change of the fitness, which helps to improve the convergence speed and global search  
Figure 3: Example of a chromosome coding path sequence. ability of the algorithm. The crossover probability and mutation probability are calculated as follows:  
\[P_{c}=\left\{ \begin{array}{ll}\frac{k_{1}(f_{\max}-f^{\prime})}{f_{\max}-f}&,f \geq\overline{f}\\ k_{3}&,f<\overline{f}\end{array} \right. \tag{18}\]  
\[P_{v}=\left\{ \begin{array}{ll}\frac{k_{2}(f_{\max}-f^{\prime})}{f_{\max}-f}&, f\geq\overline{f}\\ k_{4}&,f<\overline{f}\end{array} \right.