Location of Logistics Distribution Center Based on Improved Bald Eagle Algorithm
Abstract
:1. Introduction
2. Related Work
2.1. Original Bald Eagle Search Algorithm
2.1.1. Select the Search Space
2.1.2. Search Space Prey
2.1.3. Subduction Stage
2.2. Location of Logistics Center
- (1)
- There is regard for the size of logistics centers and other economic issues;
- (2)
- The distribution centers must meet the requirements of all locations, i.e., the sum of the product of the distance between the center and each node and the volume of goods is the minimum;
- (3)
- There is no regard to other costs
3. Algorithm Improvements
3.1. Chaos Map Initialization
3.2. Improvements to the Search Phase
4. Experiments and Analysis
4.1. Test Algorithm Description
4.2. Test Functions
4.3. Test Environment Setting
5. Application in Location of Logistics Center
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Serial Number | Function | Dimension | Search Range | Minimum |
---|---|---|---|---|
1 | 50 | [−100, 100] | 0 | |
2 | 50 | [−10, 10] | 0 | |
3 | 50 | [−100, 100] | 0 | |
4 | 50 | [−100, 100] | 0 | |
5 | 50 | [−30, 30] | 0 | |
6 | 50 | [−100, 100] | 0 | |
7 | 50 | [−1.28, 1.28] | 0 | |
8 | 50 | [−500, 500] | −12,659.5 | |
9 | 50 | [−5.12, 5.12] | 0 | |
10 | 50 | [−32, 32] | 0 |
Test Function | Index | PSO | WCA | WOA | BES | LSCBES |
---|---|---|---|---|---|---|
f1 | Average Value | 1.78 × 101 | 7.65 × 10−11 | 3.46 × 10−14 | 2.35 × 10−36 | 0 |
Standard Deviation | 3.26 × 100 | 4.37 × 10−11 | 2.15 × 10−14 | 1.27 × 10−36 | 0 | |
f2 | Average Value | 2.33 × 101 | 6.38 × 10−7 | 9.26 × 10−13 | 4.96 × 10−183 | 0 |
Standard Deviation | 4.37 × 100 | 4.96 × 10−7 | 4.13 × 10−12 | 1.49 × 10−185 | 0 | |
f3 | Average Value | 1.16 × 102 | 2.87 × 101 | 7.31 × 10−10 | 3.67 × 10−223 | 0 |
Standard Deviation | 4.46 × 100 | 1.74 × 100 | 2.33 × 10−10 | 0 | 0 | |
f4 | Average Value | 2.45 × 100 | 5.43 × 10−1 | 8.39 × 10−13 | 3.21 × 10−226 | 0 |
Standard Deviation | 7.46 × 101 | 2.76 × 10−1 | 2.91 × 10−13 | 1.23 × 10−227 | 0 | |
f5 | Average Value | 7.29 × 103 | 7.77 × 102 | 2.15 × 101 | 3.45 × 10−6 | 1.43 × 10−6 |
Standard Deviation | 3.18 × 103 | 6.45 × 102 | 1.46 × 101 | 2.94 × 10−6 | 4.36 × 10−6 | |
f6 | Average Value | 2.44 × 101 | 8.14 × 10−10 | 6.45 × 10−9 | 3.77 × 10−6 | 7.92 × 10−22 |
Standard Deviation | 5.73 × 100 | 5.37 × 10−10 | 2.78 × 10−9 | 8.73 × 10−7 | 6.45 × 10−22 | |
f7 | Average Value | 6.26 × 101 | 9.46 × 10−3 | 7.26 × 10−3 | 2.33 × 10−5 | 3.92 × 10−6 |
Standard Deviation | 2.91 × 101 | 3.42 × 10−2 | 5.42 × 10−3 | 4.26 × 10−5 | 2.35 × 10−6 | |
f8 | Average Value | −7.65 × 103 | −5.64 × 103 | −2.15 × 103 | −2.13 × 103 | −7.94 × 102 |
Standard Deviation | 2.45 × 103 | 4.94 × 102 | 8.92 × 101 | 7.96 × 10−3 | 4.32 × 102 | |
f9 | Average Value | 1.66 × 102 | 7.86 × 10−6 | 5.45 × 10−16 | 6.57 × 10−98 | 2.15 × 10−199 |
Standard Deviation | 2.74 × 101 | 3.82 × 10−6 | 4.37 × 10−16 | 5.42 × 10−99 | 4.37 × 10−199 | |
f10 | Average Value | 1.08 × 101 | 7.12 × 10−7 | 6.64 × 10−12 | 8.42 × 10−16 | 2.41 × 10−19 |
Standard Deviation | 2.32 × 100 | 2.34 × 10−8 | 4.33 × 10−12 | 2.11 × 10−18 | 0 |
Serial Number | Coordinate | Cargo Volume | Serial Number | Coordinate | Cargo Volume |
---|---|---|---|---|---|
1 | (1625, 2413) | 20 | 17 | (4027, 2106) | 90 |
2 | (3710, 924) | 90 | 18 | (4135, 2419) | 70 |
3 | (4213, 2256) | 90 | 19 | (3864, 2217) | 100 |
4 | (3694, 1403) | 60 | 20 | (3655, 2543) | 50 |
5 | (3476, 1537) | 70 | 21 | (4122, 2795) | 50 |
6 | (3319, 1558) | 70 | 22 | (4257, 2931) | 50 |
7 | (3238, 1231) | 40 | 23 | (3429, 1908) | 80 |
8 | (2793, 1546) | 90 | 24 | (3507, 2376) | 70 |
9 | (2894, 1793) | 90 | 25 | (3451, 2712) | 80 |
10 | (3154, 1425) | 70 | 26 | (3275, 3014) | 40 |
11 | (2857, 2236) | 60 | 27 | (3167, 3455) | 40 |
12 | (2346, 1498) | 40 | 28 | (3345, 3716) | 60 |
13 | (2476, 1154) | 40 | 29 | (2296, 2437) | 70 |
14 | (1819, 1479) | 40 | 30 | (3004, 3152) | 50 |
15 | (1684, 829) | 20 | 31 | (2754, 3666) | 30 |
16 | (3729, 1683) | 80 |
Algorithm | Site Selection Plan | Distance ∗ Cargo Volume | Number of Iterations |
---|---|---|---|
LSCBES | (5, 9, 12, 18, 25, 27) | 6.1069 × 105 | 33 |
BES | (3, 5, 9, 12, 20, 27) | 6.1934 × 105 | 28 |
WOA | (5, 11, 14, 18, 25, 27) | 6.3114 × 105 | 30 |
WCA | (5, 8, 14, 18, 20, 27) | 6.2412 × 105 | 52 |
PSO | (4, 6, 12, 18, 25, 27) | 6.4463 × 105 | 42 |
LSCBES | BES | WOA | WCA | PSO | |||||
---|---|---|---|---|---|---|---|---|---|
Distribution Centera | Distribution Range | Distribution Centera | Distribution Range | Distribution Centera | Distribution Range | Distribution Centera | Distribution Range | Distribution Centera | Distribution Range |
5 | 2, 4, 6, 7, 10, 16, 23 | 3 | 17, 18, 21, 22 | 5 | 2, 4, 6, 7, 10, 16, 23 | 5 | 2, 4, 6, 7, 10, 16, 23 | 4 | 2, 16 |
9 | 8, 11, 29 | 5 | 2, 4, 6, 7, 16, 23 | 11 | 8, 9, 29 | 8 | 9, 11, 12, 13 | 6 | 5, 7, 8, 9, 11, 23 |
12 | 1, 13, 14, 15 | 9 | 8, 10, 11 | 14 | 1, 12, 13, 15 | 14 | 1, 15, 29 | 12 | 1, 13, 14, 15, 29 |
18 | 3, 17, 19, 21, 22 | 12 | 1, 13, 14, 15, 29 | 18 | 3, 17, 19, 21, 22 | 18 | 3, 17, 21, 22 | 18 | 3, 17, 19, 21, 22 |
25 | 20, 24, 26 | 20 | 19, 24, 25 | 25 | 20, 24, 26 | 20 | 19, 24, 25 | 25 | 20, 24, 26 |
27 | 28, 30, 31 | 27 | 26, 30, 31, 28 | 27 | 28, 30, 31 | 27 | 26, 28, 30, 31 | 27 | 28, 30, 31 |
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Tong, Y.; Cheng, X. Location of Logistics Distribution Center Based on Improved Bald Eagle Algorithm. Sustainability 2022, 14, 9036. https://doi.org/10.3390/su14159036
Tong Y, Cheng X. Location of Logistics Distribution Center Based on Improved Bald Eagle Algorithm. Sustainability. 2022; 14(15):9036. https://doi.org/10.3390/su14159036
Chicago/Turabian StyleTong, Yanfen, and Xianbao Cheng. 2022. "Location of Logistics Distribution Center Based on Improved Bald Eagle Algorithm" Sustainability 14, no. 15: 9036. https://doi.org/10.3390/su14159036