An Optimization Method for Location-Routing of Cruise Ship Cabin Materials Considering Obstacle Blocking Effects
Abstract
:1. Introduction
2. Mathematical Model of the BE-LRP
2.1. Description of the BE-LRP
2.2. Model Assumptions and Variable Definitions
2.3. Model Building
3. Blocked Distance Estimation
3.1. Gaussian Process Regression
3.2. Blocked Distance Prediction Based on Gaussian Process Regression
4. Hybrid Algorithm Design
4.1. Handling of Obstacle Blocking Effects
4.2. Encoding Method
4.3. Initial Solution Generation
4.4. Non-Dominated Sorting and Congestion Calculation
Algorithm 1: Fast Non-Dominated Sorting | |
Input: | Population P |
Output: | Pareto rank |
1: | Calculate the number of dominant individuals Ni and the combination of dominant individuals Si for each individual in population P |
2: | rank = 1 |
3: | While P is not empty DO |
4: | Form a set F of individuals with Ni = 0 and label the non-dominant |
5: | level as rank; For i ∈ F DO |
6: | For l ∈ Si DO |
7: | Nl = Nl−1 |
8: | End For |
9: | End For |
10: | New population P |
11: | rank = rank + 1 |
12: | End While |
Algorithm 2: Congestion Calculation | |
Input: | Population P |
Output: | Congestion C |
1: | Calculate each objective function f of an individual and calculate the non-dominated rank |
2: | For rank = 1: max_rank DO |
3: | Take individuals with a non-dominant rank to form a set F |
4: | For i ∈ F DO |
5: | For each f DO |
6: | Sort according to f, the maximum and minimum C are infinite |
7: | Ci = Ci + (f(i + 1) − f(i − 1))/(fmax − fmin) |
8: | End For |
9: | End For |
10: | rank = rank + 1 |
11: | End For |
4.5. Selection, Crossover, and Mutation
4.5.1. Selection Operation
4.5.2. Crossover Operation
4.5.3. Mutation Operation
5. Result and Discussion
5.1. Instance Validation Conditions
5.2. Optimization Results and Analysis
5.3. Managerial Insights Analysis
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Set | Definition |
Set of distribution centers, | |
Set of cabin positions, | |
Set of delivery vehicles, | |
Ordered set of delivery service routes, | |
Set of vehicles for cabin service | |
Set of service cabins in the nth route for the vehicle k, | |
Parameter | Definition |
Loading capacity of vehicle k | |
Speed of vehicle k | |
Storage capacity of distribution centers, | |
Material demand for cabins, | |
Number of service routes for car k, | |
The total number of cabins in the delivery area | |
Cabin serviced by car k on route n, | |
Number of vehicles serving all cabins, | |
Variable | Definition |
The distance between distribution center i or cabin c and d, | |
Obstacle blocking influence coefficient, | |
Time window for cabin j, | |
The time when the vehicle k leaves the distribution center i on the nth route, , | |
The time when the vehicle k arrives the distribution center i or cabin j on the nth route, , | |
Decision Variable | Definition |
If the vehicle k is on the nth route from the distribution center or cabin i to j, , otherwise , , | |
If the vehicle k goes from the distribution center i to the cabin j, , otherwise , , , | |
If the vehicle has a service cabin, , otherwise , | |
If distribution center i is selected as cabin service, , otherwise , | |
If distribution center i is selected as cabin j service, , otherwise , , |
Kernel Type | R2 | RMSE | MSE | MAE |
---|---|---|---|---|
Exponential | 0.99 | 2.2466 | 5.0474 | 1.3839 |
Matern5/2 | 1.00 | 0.8233 | 0.67782 | 0.58186 |
Square exponential | 1.00 | 0.81744 | 0.66821 | 0.5826 |
Number | Distribution Center | Distribution Route | Number of Vehicles | Distance (m) |
---|---|---|---|---|
Test-01A | DC1 | 8-5; 10-12-16; 9-4 | 10 | 297.166 |
DC2 | 7-11-13; 6-3-2-1 | |||
DC4 | 22-24-25; 20-19 | |||
DC5 | 23-17; 21-18; 15-14 | |||
Test-01B | DC1 | 8-5; 10-12-16; 9-4 | 11 | 268.431 |
DC2 | 7-11-13; 6-3-2-1 | |||
DC4 | 17; 22-24; 20-19 | |||
DC5 | 23-25; 21-18; 15-14 | |||
Test-01C | DC1 | 8-5; 10-12-16; 9-4 | 12 | 267.611 |
DC2 | 7; 11-13; 6-3-2-1 | |||
DC4 | 17; 22-24; 20-19 | |||
DC5 | 23-25; 21-18; 15-14 |
Number | Distribution Center | Distribution Route | Number of Vehicles | Distance (m) |
---|---|---|---|---|
Test-01A | DC1 | 5-1; 9-4 | 10 | 282.322 |
DC2 | 8-10-14; 7-3-2-6 | |||
DC3 | 15-18; 12-16-17 | |||
DC4 | 20-21; 22;24 | |||
DC5 | 19-13-11; 23-25 | |||
Test-01B | DC1 | 5-1; 9-4 | 11 | 259.177 |
DC2 | 8-10-14; 7-3-2-6 | |||
DC3 | 15-18; 12; 17-13-11 | |||
DC4 | 22-24; 21 | |||
DC5 | 19-20-16; 23-25 | |||
Test-01C | DC1 | 9; 5-1; 4 | 12 | 257.177 |
DC2 | 8-10-14; 7-3-2-6 | |||
DC3 | 15-18; 12; 17-13-11 | |||
DC4 | 22-24; 21 | |||
DC5 | 19-20-16; 23-25 |
NSGAII | HO-NSGAII | Distance Gap | Optimization Rate | |||||
---|---|---|---|---|---|---|---|---|
m | D1 | D2 | m | D3 | D4 | |||
Test01 | 10 | 297.166 | 313.129 | 10 | 282.322 | 282.322 | 30.807 | 9.8% |
11 | 268.431 | 279.614 | 11 | 259.177 | 259.177 | 20.437 | 7.3% | |
12 | 267.611 | 278.794 | 12 | 257.177 | 257.177 | 21.617 | 7.8% | |
Test02 | 10 | 264.747 | 266.757 | 10 | 257.671 | 257.671 | 9.086 | 3.4% |
11 | 260.156 | 264.145 | 11 | 247.409 | 247.409 | 16.736 | 6.3% | |
12 | 258.336 | 261.426 | 12 | 243.066 | 243.066 | 18.36 | 7.0% | |
Test03 | 9 | 396.447 | 426.526 | 9 | 356.199 | 356.199 | 70.327 | 16.4% |
10 | 293.853 | 303.414 | 10 | 255.034 | 255.034 | 48.38 | 15.9% | |
11 | 282.503 | 292.064 | 11 | 242.796 | 242.796 | 49.268 | 16.8% | |
12 | 275.586 | 285.147 | 12 | 233.884 | 233.884 | 51.263 | 17.9% | |
13 | 273.586 | 283.147 | 13 | 232.884 | 232.884 | 50.263 | 17.8% |
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Li, J.; Huang, W.; Wu, X.; Dong, R.; Lin, P. An Optimization Method for Location-Routing of Cruise Ship Cabin Materials Considering Obstacle Blocking Effects. Appl. Sci. 2024, 14, 7510. https://doi.org/10.3390/app14177510
Li J, Huang W, Wu X, Dong R, Lin P. An Optimization Method for Location-Routing of Cruise Ship Cabin Materials Considering Obstacle Blocking Effects. Applied Sciences. 2024; 14(17):7510. https://doi.org/10.3390/app14177510
Chicago/Turabian StyleLi, Jinghua, Wenhao Huang, Xiaoyuan Wu, Ruipu Dong, and Pengfei Lin. 2024. "An Optimization Method for Location-Routing of Cruise Ship Cabin Materials Considering Obstacle Blocking Effects" Applied Sciences 14, no. 17: 7510. https://doi.org/10.3390/app14177510