## 3 Model and Methodologies
### Rebalancing Phase
#### 3.2.2 Hybrid Genetic Algorithm(HGA)
The rationale behind using crowd-distance sorting is to give preference to dissimilar chromosomes (those outside crowded areas) to enhance the diversity in the population pool, thereby improving the search quality. This procedure is continued until the termination condition is satisfied. The GA generates multiple separate travel routes with one chromosome. We design and explain the chromosome with two routes, and it can be generalized to include more than two routes. Figure 2 shows this chromosome as an example. The first gene is called 'division point,' and it represents the length of the first vehicle route, including its departure point. In Figure 2, this point is indicated as 13, which implies that the first tour is composed of 13 nodes (including the departure point '0'). Because the second tour begins right after the end of the first route in the same chromosome, the departure point for the second tour is denoted as '41' in Figure 2, which corresponds to the same point as '0' in the first route. Even though the two departure points are shown differently (0 and 41), the number '41' is represented as a dummy, and this one corresponds to the same location in our model. That means that there is only one management warehouse in a district for the maintenance and storage of extra bikes. The genetic operators used to generate the next generation are as follows: Two child chromosomes are produced from the two selected parent chromosomes. Figure 3 illustrates the crossover process. Each parent chromosome has four randomly selected crossover points with two points for each path. 'Child 1' inherits the division point from 'parent A', while 'Child 2' takes the division point from 'parent B'. Since the first node in both routes of a chromosome represents a dummy node indicating the same departure point, they are fixed as '0' and '16' in the figure (excluding the departure point, there are only 15 nodes to visit in the figure). Nodes from parent A, spanning from 'crossover point 1' to  
\[\sum_{i=1}^{n}(s_{i}^{+}+s_{i}^{-})\]0 Chromosome of proposed genetic algorithm. 'crossover point 2' and from 'crossover point 3' to 'crossover point 4', are inherited by 'child 1'. The remaining nodes from 'parent A' are inherited by 'child 1' in the same order as they appear in 'parent B'. The identical procedures apply to 'child 2', with 'parent A' replaced by 'parent B.' The mutation process is illustrated in \[\sum_{i=1}^{n}(s_{i}^{+}+s_{i}^{-})\]1 First, the division point, indicated as '9', and the first nodes (departure points) for both travel routes, indicated as '0' and '16', are removed. Second, two nodes are randomly selected and swapped. Finally, a division point is randomly chosen, guaranteeing that at least one third of the nodes are visited in one path, and the two departure points '0' and '16' are appropriately located in the chromosome. In the figure, nodes '10' and '5' are swapped, and node '10' shifts to the next position because the corresponding location is for departure node '16'. During the evolutionary process, we set the crossover ratio to one-half, which implies that half of the offspring are generated through crossover operations, whereas the remaining half are produced by mutation operations.