# Customized Bus Stop Location Model Based on Dual Population Adaptive Immune Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description

#### 2.1. Description of Customized Bus Stop Location Problem

#### 2.2. Assumptions of the Customized Bus Stop Location Model

- (1)
- Each passenger can only go to one customized bus stop.
- (2)
- After choosing a bus stop, passengers will not select another customized bus stop.
- (3)
- The number of passengers accommodated at a customized bus stop cannot exceed its capacity.
- (4)
- The cost of establishing a customized bus stop cannot exceed the maximum budget.
- (5)
- The walking distance from passengers to the bus stop cannot exceed the maximum distance covered by the stop.

#### 2.3. Processing of Customized Bus Passenger Travel Data

#### 2.3.1. Acquisition of Customized Bus Passenger Travel Data

#### 2.3.2. Processing of Customized Bus Passenger Travel Data

## 3. Model Construction

#### 3.1. Objective Function of the Customized Bus Stop Location Model

#### 3.2. Constraints of the Customized Bus Stop Location Model

**Constraint 1.**A passenger cannot simultaneously go to multiple bus stops. Therefore, each passenger can only go to one customized bus stop, defined as follows in Equation (4):

**Constraint 2.**For passengers, once they select a bus stop and travel to it, they wait for the arrival of the customized bus and do not choose to go to other stops on the same route to wait for the bus. This is defined as shown in Equations (5) and (6):

**Constraint 3.**The cost of establishing customized bus stops must not exceed the maximum budget. A reasonable maximum cost is set, defined as shown in Equation (7):

**Constraint 4.**The walking distance from passengers to the bus stop must not exceed the maximum distance covered by the stop. A reasonable maximum walking distance is set, defined as shown in Equation (8):

## 4. Algorithm Design

#### 4.1. Principle of Dual Population Adaptive Immunity Algorithm (DPAIA)

#### 4.1.1. Setting Adaptive Crossover Rate and Mutation Rate

#### 4.1.2. Introduction of Intrusive Population

#### 4.2. Dual Population Adaptive Immunity Algorithm (DPAIA) Procedure

Algorithm 1. Dual Population Adaptive Immunity Algorithm |

Input: iter: Maximum number of iterations, C: Capacity of memory, Pd: Diversity assessment, Pc: Crossover probability, Pm: Mutation probabilityOutput: $\stackrel{\wedge}{X}$: Optimized antibody population1: while (i < iter)2: if $C=\varnothing $:3: then Randomly initialize antibody population4: else Initialize antibody population in C5: Encode initial antibodies using real numbers 6: Calculate antibody affinity using Formulas (12) and (13) 7: if Current population affinity == Output affinity8: then return $\stackrel{\wedge}{X}$9: else Randomly set up external invasion population10: Calculate antibody affinity 11: Merge populations using roulette wheel selection 12: Calculate antibody concentration 13: Perform selection operation using roulette wheel selection 14: Perform immune operations on new populations based on Formulas (9) and (10) 15: i = i + 1 16: end while17: return $\stackrel{\wedge}{X}$ |

## 5. Case Study

#### 5.1. Processing Custom Bus Passenger Travel Data

#### 5.2. Solution and Analysis of the Customized Bus Stop Location Model

#### 5.2.1. Parameter Calibration

#### 5.2.2. Evaluation Indicator Settings

#### 5.2.3. Solving the Customized Bus Stop Location Problem

- (1)
- Utilizing Enhanced DBSCAN for Bus Stop Clustering

- (2)
- Using Improved AP Clustering Algorithm for Platforms

- (3)
- Using IA algorithm and DPAIA algorithm to solve the model

#### 5.3. Comparison and Analysis of Experimental Results

#### 5.4. Customized Bus Stop Location Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Abnormal Type | Data Anomaly | Preprocessing Measures |
---|---|---|

Location Missing | Ride-hailing vehicle’s geographic location missing | Supplement based on the previous time point and interval |

Location Anomaly | Ride-hailing vehicle not within the considered interval at a certain time | Supplement based on the previous time point and interval |

Data Anomaly | Origin and destination points not within the considered interval | Delete this data entry |

Time Missing | Ride-hailing vehicle time missing at a certain time | Delete this data entry |

Data Deduplication | Duplicate road data | Merge consecutive road segments if the cosine of the angle θ between them is greater than 0.9848 |

Parameter Type | Symbol | Meaning | Value |
---|---|---|---|

Model Parameter | g | Walking Distance Cost per Passenger (CNY/m) | 0.002 |

R | Maximum Walking Distance to the Stop (m) | 1000 | |

l | Construction Cost per Stop (CNY 10,000) | 3 | |

Nmax | Maximum Number of Stops | 100 | |

Nmin | Minimum Number of Stops | 20 |

Parameter Type | Symbol | Meaning | Value |
---|---|---|---|

DPAIA Algorithm | Popsize | Initial Population Size | 50 |

C | Memory Pool Capacity | 33 | |

iter | Number of Iterations | 100 | |

PC | Crossover Probability | 0.5 | |

Pm | Mutation Probability | 0.76 | |

pd | Diversity Evaluation Parameter | 0.78 | |

Improved DBSCAN Clustering | EPs | Neighborhood Radius in Dense Regions | 300 |

minPts | Threshold for Core Points | 3 | |

Improved AP Clustering | p | Reference Degree Value | −51,465 |

dm | Weight of Central Node | 7 | |

d | Weight of Other Nodes | 1 |

ID | Algorithm | r (m) | n (Unit) | A (CNY 10,000) |
---|---|---|---|---|

1 | Improved DBSCAN Clustering Algorithm | 731 | 41 | 29.94 |

2 | Improved AP Clustering Algorithm | 737 | 39 | 29.30 |

3 | IA Algorithm | 689 | 50 | 32.47 |

4 | DPAIA Algorithm | 512 | 50 | 28.95 |

ID | Longitude | Latitude | CAP | ID | Longitude | Latitude | CAP |
---|---|---|---|---|---|---|---|

1 | 104.085266 | 30.64744 | 2 | 26 | 104.02248 | 30.665162 | 8 |

2 | 104.074639 | 30.67136 | 8 | 27 | 104.078657 | 30.655443 | 8 |

3 | 104.038649 | 30.64032 | 6 | 28 | 104.085738 | 30.67301 | 3 |

4 | 104.043943 | 30.67384 | 5 | 29 | 104.070935 | 30.643456 | 8 |

5 | 104.06004 | 30.6694 | 6 | 30 | 104.093768 | 30.645855 | 7 |

6 | 104.075266 | 30.66889 | 7 | 31 | 104.027078 | 30.653181 | 3 |

7 | 104.074907 | 30.62563 | 7 | 32 | 104.050291 | 30.66709 | 4 |

8 | 104.067628 | 30.65542 | 5 | 33 | 104.070654 | 30.645089 | 5 |

9 | 104.083968 | 30.64107 | 5 | 34 | 104.045577 | 30.652966 | 8 |

10 | 104.061432 | 30.66351 | 5 | 35 | 104.066496 | 30.64604 | 4 |

11 | 104.021416 | 30.63958 | 7 | 36 | 104.060397 | 30.638691 | 8 |

12 | 104.074224 | 30.67425 | 4 | 37 | 104.062469 | 30.676571 | 6 |

13 | 104.071578 | 30.69363 | 6 | 38 | 104.089822 | 30.631629 | 6 |

14 | 104.032089 | 30.66554 | 6 | 39 | 104.051657 | 30.69175 | 9 |

15 | 104.106389 | 30.67425 | 8 | 40 | 104.031138 | 30.656536 | 4 |

16 | 104.092949 | 30.64713 | 3 | 41 | 104.078599 | 30.66527 | 4 |

17 | 104.063943 | 30.62159 | 2 | 42 | 104.092285 | 30.655384 | 3 |

18 | 104.078334 | 30.6629 | 9 | 43 | 104.095183 | 30.680443 | 13 |

19 | 104.047736 | 30.66235 | 8 | 44 | 104.052423 | 30.65304 | 4 |

20 | 104.079633 | 30.63328 | 8 | 45 | 104.090646 | 30.657583 | 7 |

21 | 104.08753 | 30.66646 | 4 | 46 | 104.041551 | 30.639371 | 7 |

22 | 104.096185 | 30.65867 | 4 | 47 | 104.080865 | 30.656261 | 5 |

23 | 104.0878 | 30.68394 | 7 | 48 | 104.097522 | 30.678579 | 9 |

24 | 104.062463 | 30.68097 | 8 | 49 | 104.050807 | 30.635731 | 5 |

25 | 104.081143 | 30.66281 | 6 | 50 | 104.083984 | 30.648692 | 6 |

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## Share and Cite

**MDPI and ACS Style**

Yuan, T.; Liu, H.; Wang, Y.; Yang, F.; Gu, Q.; Wang, Y.
Customized Bus Stop Location Model Based on Dual Population Adaptive Immune Algorithm. *Mathematics* **2024**, *12*, 2382.
https://doi.org/10.3390/math12152382

**AMA Style**

Yuan T, Liu H, Wang Y, Yang F, Gu Q, Wang Y.
Customized Bus Stop Location Model Based on Dual Population Adaptive Immune Algorithm. *Mathematics*. 2024; 12(15):2382.
https://doi.org/10.3390/math12152382

**Chicago/Turabian Style**

Yuan, Tengfei, Hongjie Liu, Yawen Wang, Fengrui Yang, Qinyue Gu, and Yizeng Wang.
2024. "Customized Bus Stop Location Model Based on Dual Population Adaptive Immune Algorithm" *Mathematics* 12, no. 15: 2382.
https://doi.org/10.3390/math12152382