# Prediction of Waterway Cargo Transportation Volume to Support Maritime Transportation Systems Based on GA-BP Neural Network Optimization

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

#### 3.1. BP Neural Network

#### 3.1.1. Process of Signal forward Propagation

#### 3.1.2. Error Backpropagation Process

_{p}:

#### 3.1.3. Disadvantages of the BP Algorithm

- The initial solution value randomly generated by the BP algorithm has a great impact on the performance of the algorithm, so the algorithm has unstable factors.
- The gradient descent method is used in the BP algorithm, and this algorithm is prone to the situation that the convergence speed is too slow, and even falls into a local minimum and cannot converge.

#### 3.1.4. Increase the Momentum Term in the BP Algorithm to Accelerate Learning Speed

#### 3.2. Genetic Algorithm (GA)

- (1)
- Genetic algorithms do not easily fall into local optima when searching in space and can easily obtain the global optimum solution.
- (2)
- The genetic algorithm is particularly suitable for dealing with complex nonlinear problems, because the conventional algorithm adopts gradient descent, the search direction is fixed, and the genetic algorithm adopts the overall search strategy.
- (3)
- The genetic algorithm adopts a parallel search mechanism, which has a small amount of calculation and more processing modes.

#### 3.3. Construction of the GA-BP Neural Network Model

- (1)
- Use floating-point numbers to encode the weight threshold of the neural network.
- (2)
- In the coding space, an initial population is randomly generated.
- (3)
- Calculate the group fitness value as a training sample according to Formula (13).

- (4)
- Genetic manipulation of populations.

- (5)
- Generate a new generation of groups.
- (6)
- Repeat steps (3) to (5), and when the evolution reaches N generations, the individuals with the best fitness will be retained. After the algorithm is over, the optimal individual in the final group can be decoded to obtain the weight threshold of the optimized BP neural network.

## 4. Experimental Section and Results

#### 4.1. Data Processing

#### 4.2. Setting of Experimental Parameters

- Group size NP

- 2.
- Crossover probability Pc

- 3.
- Mutation probability Pm

- 4.
- Evolutionary algebra G

#### 4.3. Experimental Results

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 11.**(

**a**) The predicted value of the top ten port cargo throughputs. (

**b**) Proportion of the predicted value of the top ten port cargo throughputs. (

**c**) Distribution of the top ten ports by port cargo throughput.

Number of Groups | First Three Months of Shipments (10,000 Tons) | Fourth Month as Forecast (10,000 Tons) | ||
---|---|---|---|---|

1 | 49,119 | 42,051 | 46,316 | 48,898 |

2 | 42,051 | 46,316 | 48,898 | 52,116 |

3 | 46,316 | 48,898 | 52,116 | 53,649 |

4 | 48,898 | 52,116 | 53,649 | 53,590 |

5 | 52,116 | 53,649 | 53,590 | 54,164 |

● | ● | ● | ● | ● |

● | ● | ● | ● | ● |

● | ● | ● | ● | ● |

80 | 69,633 | 69,431 | 71,266 | 76,480 |

81 | 69,431 | 71,266 | 76,480 | 75,392 |

Number of Hidden Layer Nodes | Corresponding Mean Squared Error |
---|---|

3 | 0.051892 |

4 | 0.049354 |

5 | 0.056236 |

6 | 0.084958 |

7 | 0.063768 |

8 | 0.046552 |

9 | 0.057265 |

10 | 0.042412 |

11 | 0.041436 |

**Table 3.**Prediction error of the BP neural network and the prediction error of the GA-BP neural network.

The Mean Absolute Error MAE | Mean Square Error MSE | Root Mean Square Error RMSE | Mean Absolute Percentage Error MAPE | |
---|---|---|---|---|

BP | 7358.3795 | 71,125,714.7667 | 8433.6063 | 10.4958% |

GA-BP | 2231.0894 | 6,353,182.3153 | 2520.552 | 3.2148% |

Sample No. | Measured Value | BP Predicted Value | GA-BP Value | BP Error | GA-BP Error | |
---|---|---|---|---|---|---|

1 | 7.0659 | 6.4759 | 6.9597 | −0.5900 | −0.1062 | 1 × 10^{4} * |

2 | 7.3313 | 6.4412 | 7.0472 | −0.8901 | −0.2841 | 1 × 10^{4} * |

3 | 7.1487 | 6.5285 | 7.2324 | −0.6202 | 0.0837 | 1 × 10^{4} * |

4 | 6.5414 | 6.3248 | 6.9319 | −0.2166 | 0.3905 | 1 × 10^{4} * |

5 | 5.3129 | 5.4497 | 5.1590 | 0.1368 | −0.1539 | 1 × 10^{4} * |

6 | 6.5329 | 4.6166 | 6.1679 | −1.9163 | −0.3650 | 1 × 10^{4} * |

7 | 6.8389 | 6.0750 | 6.7424 | −0.7639 | −0.0965 | 1 × 10^{4} * |

8 | 6.9858 | 6.5746 | 6.8256 | −0.4112 | −0.1602 | 1 × 10^{4} * |

9 | 7.0717 | 6.4535 | 6.9454 | −0.6182 | −0.1263 | 1 × 10^{4} * |

10 | 6.8934 | 6.4193 | 7.1275 | −0.4741 | 0.2341 | 1 × 10^{4} * |

11 | 6.9633 | 6.1698 | 6.7041 | −0.7935 | −0.2592 | 1 × 10^{4} * |

12 | 6.9431 | 6.2977 | 7.0987 | −0.6454 | 0.1556 | 1 × 10^{4} * |

13 | 7.1266 | 6.3018 | 7.0109 | −0.8248 | −0.1157 | 1 × 10^{4} * |

14 | 7.6480 | 6.4426 | 7.2671 | −1.2054 | −0.3809 | 1 × 10^{4} * |

15 | 7.5392 | 6.6081 | 7.1045 | −0.9311 | −0.4347 | 1 × 10^{4} * |

^{4}.

Month | GA-BP Forecast (10,000 Tons) |
---|---|

1 | 69,580 |

2 | 56,950 |

3 | 67,130 |

4 | 72,240 |

5 | 72,530 |

6 | 74,210 |

7 | 65,890 |

8 | 68,760 |

9 | 71,300 |

10 | 68,920 |

11 | 72,470 |

12 | 76,150 |

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**MDPI and ACS Style**

Jin, G.; Feng, W.; Meng, Q.
Prediction of Waterway Cargo Transportation Volume to Support Maritime Transportation Systems Based on GA-BP Neural Network Optimization. *Sustainability* **2022**, *14*, 13872.
https://doi.org/10.3390/su142113872

**AMA Style**

Jin G, Feng W, Meng Q.
Prediction of Waterway Cargo Transportation Volume to Support Maritime Transportation Systems Based on GA-BP Neural Network Optimization. *Sustainability*. 2022; 14(21):13872.
https://doi.org/10.3390/su142113872

**Chicago/Turabian Style**

Jin, Guangying, Wei Feng, and Qingpu Meng.
2022. "Prediction of Waterway Cargo Transportation Volume to Support Maritime Transportation Systems Based on GA-BP Neural Network Optimization" *Sustainability* 14, no. 21: 13872.
https://doi.org/10.3390/su142113872