# Swarm Robots Cooperative and Persistent Distribution Modeling and Optimization Based on the Smart Community Logistics Service Framework

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- The power and load-bearing capacity of the robot itself, not like heavy-duty tool trucks, and their speed and travel time will be affected by the weight of the load.
- (2)
- Each robot needs to be charged at intervals and cannot work continuously for a long time.
- (3)
- The charging of the robot takes a certain amount of time, and the charging time is related to the power loss. The longer the travel time, the more the power loss, the longer the charging time.
- (4)
- Each robot should be placed in a service station instead of stopping outside when it completes a task or is not performing the task in order to avoid the loss of the robot.

## 2. Related Works

## 3. Materials and Methods

#### 3.1. Problem Description

#### 3.2. Mathematical Formulation

#### 3.2.1. Model Parameters

#### 3.2.2. Load Weight Influence Function

#### 3.2.3. Service Station Charging Function

#### 3.2.4. The Model

_{gkf}is the penalty cost where the robot exceeds the customer service time in the $fth$ transportation; the weighting factor a1 is used to provide a balanced solution between two goals; and a2 represents the penalty coefficient for exceeding the service time.

_{bk}represents the initial service station. In the same manner, Equation (9) indicates that each time the robot $k$ enters a service station, it means that the $fth$ transportation is completed.

#### 3.3. Solving Algorithm

#### 3.3.1. S-PSO Algorithm

_{1}≠ nb

_{2}.

#### 3.3.2. GA Improved S-PSO Algorithm

## 4. Experimental Evaluation

#### 4.1. Example Background

#### 4.2. Performance Evaluation of CPLEX and S-GAIPSO

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Study on the influence of load weight. (

**a**) Relationship between power and load; (

**b**) Relationship between transport capacity factor and load.

Task | Delivery Point | Earliest Service Time (E_{g}) | Latest Service Time (L_{g}) | Service Time (P_{g}) | |
---|---|---|---|---|---|

X | Y | ||||

1 | 31 | 82 | 0 | 2 | 0.4 |

2 | 57 | 28 | 5 | 6 | 2 |

3 | 57 | 28 | 5 | 6 | 2 |

4 | 90 | 94 | 1 | 3 | 0.5 |

5 | 87 | 34 | 7 | 8 | 0.3 |

6 | 24 | 16 | 2 | 6 | 0.2 |

7 | 48 | 8 | 2 | 3 | 0.4 |

8 | 71 | 32 | 7 | 9 | 0.6 |

9 | 73 | 10 | 1 | 3 | 0.2 |

10 | 104 | 56 | 6 | 7 | 0.1 |

Station | Robot | Optimal Scheduling |
---|---|---|

1 | 1 | station1→2→8→5→station1 |

2 | station1→10→4→9→station1 | |

2 | 3 | Station2→3→7→6→1→station2 |

4 | station1 | |

Obj. value | 5496.2 |

Experiment | Task Size | CPLEX | S-GAIPSO | GAP | ||
---|---|---|---|---|---|---|

CPU Time (s) | Obj. Value | CPU Time (s) | Obj. Value | |||

1 | 5 | 0.63 | 2563 | 0.063 | 2563 | 0% |

2 | 0.59 | 2436.8 | 0.065 | 2436.8 | 0% | |

3 | 0.86 | 2957.7 | 0.062 | 2946.3 | 0.385% | |

4 | 1.03 | 2531.6 | 0.065 | 2531.6 | 0% | |

5 | 0.92 | 2879.4 | 0.064 | 2876.9 | 0.087% | |

1 | 10 | 50.53 | 5597.5 | 0.105 | 5496.2 | 1.842% |

2 | 123.25 | 5563.2 | 0.103 | 5426.8 | 2.416% | |

3 | 83.9 | 5296.1 | 0.105 | 5296.1 | 0% | |

4 | 125.04 | 5632.4 | 0.096 | 5563.2 | 1.225% | |

5 | 42.69 | 5432.8 | 0.098 | 5432.8 | 0% | |

1 | 20 | 3965 | 10,213.3 | 0.107 | 10,110.3 | 1.008% |

2 | 3662 | 11,356.1 | 0.118 | 11,029.6 | 2.88% | |

3 | 3869 | 10,697.6 | 0.129 | 10,002.4 | 6.497% | |

4 | - | - | - | 12,658.6 | 0.225 | |

5 | - | - | - | 11,972.4 | 0.113 | |

1 | 30 | 4352 | 12,536.9 | 0.234 | 11,965.4 | 4.559% |

2 | - | N/A | 0.306 | 12,878.9 | - | |

3 | - | N/A | 0.166 | 12,536.9 | - | |

4 | - | N/A | 0.193 | 13,142.8 | - | |

5 | - | N/A | 0.154 | 12,897.4 | - |

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Zhang, M.; Yang, B.
Swarm Robots Cooperative and Persistent Distribution Modeling and Optimization Based on the Smart Community Logistics Service Framework. *Algorithms* **2022**, *15*, 39.
https://doi.org/10.3390/a15020039

**AMA Style**

Zhang M, Yang B.
Swarm Robots Cooperative and Persistent Distribution Modeling and Optimization Based on the Smart Community Logistics Service Framework. *Algorithms*. 2022; 15(2):39.
https://doi.org/10.3390/a15020039

**Chicago/Turabian Style**

Zhang, Meng, and Bin Yang.
2022. "Swarm Robots Cooperative and Persistent Distribution Modeling and Optimization Based on the Smart Community Logistics Service Framework" *Algorithms* 15, no. 2: 39.
https://doi.org/10.3390/a15020039