A Hybrid Estimation of Distribution Algorithm for Multi-Objective Multi-Sourcing Intermodal Transportation Network Design Problem Considering Carbon Emissions
Abstract
:1. Introduction
2. Literature Review
3. Problem Description and Model Formulation
3.1. Formulation of Proposed Mathematical Model
An infinite number; | |
Amount of freight from sourcing place i, ; | |
Set of available nodes of stage j, ; | |
Available nodes of stage 0 and =N; | |
Available node of stage M and =1; | |
Set of available transportation modes of stage j, ; | |
The handling capacity for the kth node of stage j, , , ; | |
Carbon emission cost of freight i from the lth node in stage to the hth node in stage j under the transportation mode w, , , ; | |
Transportation cost of freight i from the lth node in stage to the hth node in stage j under the transportation mode w, , , ; | |
Transportation time of freight i from the lth node in stage to the hth node in stage j under the transportation mode w, , , , ; | |
Switch cost of freight i from transportation mode w to v for the kth node of stage j, , , , ; | |
Switch time of freight i from transportation mode w to v for the kth node of stage j, , , , ; and | |
. |
; |
; |
the start time at the stage j for freight i; and |
the leave time at the stage j for freight i. |
3.2. Modification of Established Model
4. HEDA for MO_MSITNDP
4.1. Solution Representation
4.2. Multi-Objective Handling Method
4.3. The Proposed Heterogeneous Probability Model and Update Mechanism
4.4. New Population Generation Method
4.5. Problem-Dependent Local Search
4.6. Procedure of HEDA
5. Computational Results and Comparisons
5.1. Experimental Setup
5.2. Performance Metrics
5.3. Comparisons Results
5.3.1. Comparison with Existing Algorithms
5.3.2. Comparison with Optimization Solver
5.4. Case Study
5.5. Management Insights
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Instance | HEDA vs. NSGAII | HEDA vs. PGA | HEDA vs. HEDA_noLS | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
NSGAII | HEDA | PGA | HEDA | HEDA_noLS | HEDA | |||||||||||||
MAX | AVG | SD | MAX | AVG | SD | MAX | AVG | SD | MAX | AVG | SD | MAX | AVG | SD | MAX | AVG | SD | |
44 | 20.24 | 14.45 | 5 | 3.71 | 0.63 | 3 | 1.57 | 0.79 | 5 | 3.81 | 0.59 | 4 | 2.52 | 1.26 | 4 | 2.81 | 0.96 | |
53 | 6.29 | 13.99 | 8 | 5.48 | 1.65 | 2 | 0.10 | 0.43 | 6 | 4.57 | 1.22 | 8 | 2.76 | 2.04 | 8 | 3.81 | 2.38 | |
52 | 3.76 | 12.22 | 10 | 5.81 | 1.87 | 0 | 0.00 | 0.00 | 12 | 6.52 | 2.34 | 9 | 2.43 | 2.57 | 9 | 5.67 | 2.40 | |
36 | 6.81 | 12.55 | 9 | 4.86 | 2.05 | 1 | 0.14 | 0.35 | 9 | 4.62 | 2.08 | 6 | 2.00 | 1.90 | 6 | 3.43 | 1.47 | |
0 | 0.00 | 0.00 | 9 | 3.81 | 1.94 | 0 | 0.00 | 0.00 | 9 | 4.24 | 1.82 | 4 | 0.71 | 1.16 | 7 | 4.00 | 1.57 | |
0 | 0.00 | 0.00 | 8 | 3.67 | 1.98 | 0 | 0.00 | 0.00 | 9 | 3.86 | 1.61 | 2 | 0.52 | 0.73 | 7 | 3.95 | 1.43 | |
0 | 0.00 | 0.00 | 8 | 4.38 | 1.76 | 0 | 0.00 | 0.00 | 8 | 3.76 | 1.69 | 6 | 1.19 | 1.82 | 8 | 3.71 | 1.91 | |
0 | 0.00 | 0.00 | 10 | 4.48 | 1.99 | 0 | 0.00 | 0.00 | 8 | 3.48 | 1.94 | 3 | 0.29 | 0.70 | 7 | 3.76 | 1.74 | |
0 | 0.00 | 0.00 | 5 | 2.52 | 1.18 | 0 | 0.00 | 0.00 | 7 | 2.48 | 1.40 | 6 | 0.86 | 1.83 | 7 | 2.48 | 1.65 | |
0 | 0.00 | 0.00 | 7 | 2.38 | 1.40 | 0 | 0.00 | 0.00 | 5 | 2.48 | 1.33 | 3 | 0.67 | 0.99 | 4 | 2.00 | 1.07 | |
0 | 0.00 | 0.00 | 4 | 1.95 | 1.09 | 0 | 0.00 | 0.00 | 5 | 2.33 | 1.28 | 3 | 0.29 | 0.76 | 8 | 2.29 | 1.69 | |
0 | 0.00 | 0.00 | 4 | 2.00 | 1.07 | 0 | 0.00 | 0.00 | 6 | 2.10 | 1.38 | 3 | 0.29 | 0.76 | 3 | 1.67 | 0.64 | |
0 | 0.00 | 0.00 | 12 | 5.33 | 3.48 | 0 | 0.00 | 0.00 | 11 | 4.00 | 2.98 | 2 | 0.10 | 0.43 | 10 | 3.52 | 3.19 | |
0 | 0.00 | 0.00 | 6 | 2.33 | 1.32 | 0 | 0.00 | 0.00 | 6 | 3.14 | 1.39 | 1 | 0.10 | 0.29 | 5 | 1.86 | 1.04 | |
0 | 0.00 | 0.00 | 9 | 2.00 | 1.69 | 0 | 0.00 | 0.00 | 6 | 2.05 | 1.13 | 0 | 0.00 | 0.00 | 10 | 2.48 | 2.15 | |
Average | 12.33 | 2.47 | 3.55 | 7.60 | 3.65 | 1.67 | 0.40 | 0.12 | 0.10 | 7.47 | 3.56 | 1.65 | 4.00 | 0.98 | 1.15 | 6.87 | 3.16 | 1.69 |
Instance | HEDA vs. NSGAII | HEDA vs. PGA | HEDA vs. HEDA_noLS | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
NSGAII | HEDA | PGA | HEDA | HEDA_noLS | HEDA | |||||||||||||
MAX | AVG | SD | MAX | AVG | SD | MAX | AVG | SD | MAX | AVG | SD | MAX | AVG | SD | MAX | AVG | SD | |
0.44 | 0.21 | 0.15 | 1.00 | 1.00 | 0.00 | 0.67 | 0.33 | 0.18 | 1.00 | 1.00 | 0.00 | 1.00 | 0.68 | 0.35 | 1.00 | 0.78 | 0.24 | |
0.53 | 0.07 | 0.14 | 1.00 | 1.00 | 0.00 | 0.25 | 0.01 | 0.05 | 1.00 | 1.00 | 0.00 | 1.00 | 0.55 | 0.38 | 1.00 | 0.69 | 0.34 | |
0.54 | 0.04 | 0.13 | 1.00 | 0.99 | 0.02 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.37 | 0.33 | 1.00 | 0.85 | 0.30 | |
0.36 | 0.07 | 0.13 | 1.00 | 1.00 | 0.00 | 0.25 | 0.04 | 0.09 | 1.00 | 1.00 | 0.00 | 1.00 | 0.43 | 0.38 | 1.00 | 0.99 | 0.05 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.75 | 0.17 | 0.26 | 1.00 | 1.00 | 0.00 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.50 | 0.13 | 0.19 | 1.00 | 0.99 | 0.03 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.20 | 0.30 | 1.00 | 1.00 | 0.00 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.50 | 0.06 | 0.13 | 1.00 | 1.00 | 0.00 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.86 | 0.13 | 0.27 | 1.00 | 1.00 | 0.00 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.17 | 0.26 | 1.00 | 1.00 | 0.00 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.75 | 0.07 | 0.19 | 1.00 | 1.00 | 0.00 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.12 | 0.30 | 1.00 | 1.00 | 0.00 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.05 | 0.21 | 1.00 | 1.00 | 0.00 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.07 | 0.23 | 1.00 | 1.00 | 0.00 | |
0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | 0.00 | |
Average | 0.12 | 0.03 | 0.04 | 1.00 | 1.00 | 0.00 | 0.08 | 0.03 | 0.02 | 1.00 | 1.00 | 0.00 | 0.82 | 0.21 | 0.25 | 1.00 | 0.95 | 0.06 |
Instance | HEDA vs. NSGAII | HEDA vs. PGA | HEDA vs. HEDA_noLS | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
NSGAII | HEDA | PGA | HEDA | HEDA_noLS | HEDA | |||||||||||||||
MIN | AVG | SD | MIN | AVG | SD | MIN | AVG | SD | MIN | AVG | SD | MIN | AVG | SD | MIN | AVG | SD | |||
36.64 | 123.36 | 67.77 | 0.00 | 1107.72 | 1012.93 | 61.66 | 116.48 | 74.67 | 0.00 | 60.73 | 51.70 | 0.00 | 15.66 | 19.03 | 0.00 | 25.87 | 53.26 | |||
181.89 | 544.88 | 265.34 | 0.00 | 2286.86 | 5945.60 | 158.87 | 793.87 | 400.31 | 0.00 | 55.16 | 246.67 | 0.00 | 183.72 | 191.64 | 0.00 | 128.18 | 163.28 | |||
269.57 | 1225.25 | 758.57 | 0.00 | 1550.08 | 6811.30 | 647.41 | 1960.32 | 800.04 | 0.00 | 0.00 | 0.00 | 0.00 | 390.81 | 331.60 | 0.00 | 93.72 | 138.05 | |||
1598.90 | 3824.40 | 1870.46 | 0.00 | 9359.46 | 17,387.86 | 2038.44 | 4826.59 | 2376.99 | 0.00 | 203.33 | 504.80 | 32.09 | 829.86 | 593.75 | 0.00 | 652.71 | 968.25 | |||
1054.05 | 2843.73 | 1558.43 | 0.00 | 0.00 | 0.00 | 1954.42 | 4134.30 | 1889.59 | 0.00 | 0.00 | 0.00 | 157.67 | 1649.53 | 1260.86 | 0.00 | 233.46 | 401.39 | |||
1216.20 | 4652.32 | 3060.08 | 0.00 | 0.00 | 0.00 | 2946.40 | 6184.59 | 2407.24 | 0.00 | 0.00 | 0.00 | 1096.54 | 2973.23 | 1518.30 | 0.00 | 404.02 | 581.21 | |||
1650.11 | 5755.40 | 2848.66 | 0.00 | 0.00 | 0.00 | 1967.32 | 7092.64 | 3234.82 | 0.00 | 0.00 | 0.00 | 217.86 | 2257.73 | 1475.94 | 0.00 | 691.68 | 1160.49 | |||
1343.27 | 8610.60 | 3947.62 | 0.00 | 0.00 | 0.00 | 2449.42 | 10,036.65 | 6093.77 | 0.00 | 0.00 | 0.00 | 833.73 | 4881.32 | 2931.44 | 0.00 | 371.87 | 954.23 | |||
2254.08 | 6060.90 | 3079.91 | 0.00 | 0.00 | 0.00 | 2639.69 | 8937.82 | 5210.97 | 0.00 | 0.00 | 0.00 | 1347.68 | 4364.83 | 2613.23 | 0.00 | 1512.26 | 3231.31 | |||
1785.60 | 6760.44 | 4068.56 | 0.00 | 0.00 | 0.00 | 4635.60 | 11,795.78 | 6546.49 | 0.00 | 0.00 | 0.00 | 1730.08 | 4839.59 | 3264.24 | 0.00 | 1572.35 | 2319.77 | |||
3116.28 | 8257.92 | 4925.34 | 0.00 | 0.00 | 0.00 | 5636.08 | 15,186.47 | 8625.25 | 0.00 | 0.00 | 0.00 | 2451.58 | 8163.42 | 6419.59 | 0.00 | 1162.14 | 3194.25 | |||
3917.91 | 9219.88 | 5022.42 | 0.00 | 0.00 | 0.00 | 6149.95 | 15,340.45 | 10,717.45 | 0.00 | 0.00 | 0.00 | 2664.78 | 5933.61 | 2339.85 | 0.00 | 1003.98 | 2603.61 | |||
5795.40 | 19,982.45 | 10,818.12 | 0.00 | 0.00 | 0.00 | 9074.13 | 34,600.99 | 21,887.46 | 0.00 | 0.00 | 0.00 | 4809.12 | 15,213.67 | 10,688.43 | 0.00 | 525.18 | 2348.70 | |||
2128.72 | 7800.28 | 4562.72 | 0.00 | 0.00 | 0.00 | 6379.80 | 20,857.98 | 9415.57 | 0.00 | 0.00 | 0.00 | 3564.77 | 7778.40 | 5030.00 | 0.00 | 439.48 | 1358.51 | |||
4697.53 | 10,692.39 | 6753.19 | 0.00 | 0.00 | 0.00 | 10,426.97 | 22,517.95 | 12,695.50 | 0.00 | 0.00 | 0.00 | 5898.19 | 16,269.53 | 11,700.77 | 0.00 | 0.00 | 0.00 | |||
Average | 2069.74 | 6423.61 | 3573.81 | 0.00 | 953.61 | 2077.18 | 3811.08 | 10,958.86 | 6158.41 | 0.00 | 21.28 | 53.54 | 1653.61 | 5049.66 | 3358.58 | 0.00 | 587.79 | 1298.42 |
Instance | CPLEX | HEDA | ||||||
---|---|---|---|---|---|---|---|---|
ONSN | RNDS | DIR | Time | ONSN | RNDS | DIR | Time | |
47 * | 1.00 | 0.00 | <0.1 | 7 | 0.47 | 107.47 | <0.1 | |
55 * | 1.00 | 0.00 | 1.23 | 10 | 0.58 | 645.23 | <0.1 | |
61 * | 1.00 | 0.00 | 2.37 | 13 | 0.89 | 961.30 | <0.1 | |
38 * | 1.00 | 0.00 | 5.24 | 8 | 0.91 | 809.26 | <0.1 | |
8 | 0.88 | 879.01 | 8.78 | 10 | 0.98 | 2.54 | 1.38 | |
11 | 0.87 | 669.25 | 25.33 | 11 | 1.00 | 0.00 | 2.56 | |
9 | 0.74 | 420.21 | 38.36 | 10 | 1.00 | 0.00 | 5.25 | |
7 | 0.89 | 321.52 | 1 h limit | 9 | 1.00 | 0.00 | 6.24 | |
4 | 0.77 | 264.67 | 2 h limit | 7 | 1.00 | 0.00 | 10.62 | |
7 | 0.74 | 74.45 | 2 h limit | 6 | 1.00 | 0.00 | 11.23 | |
3 | 0.52 | 254.91 | 2 h limit | 5 | 1.00 | 0.00 | 12.08 | |
4 | 0.69 | 141.12 | 2 h limit | 6 | 1.00 | 0.00 | 12.21 | |
5 | 0.56 | 957.76 | 4 h limit | 11 | 1.00 | 0.00 | 13.45 | |
- | - | - | - | 7 | 1.00 | 0.00 | 17.77 | |
- | - | - | - | 10 | 1.00 | 0.00 | 19.25 |
Stage | Stage 1 | Stage 2 | Stage 3 | Stage 4 | Stage 5 |
---|---|---|---|---|---|
Nodes | Hong Kong (1) Fuzhou (2) Wenzhou (3) Shanghai (4) | Wuhan (1) Nanjing (2) | Zhengzhou (1) Jinan (2) | Beijing (1) Tianjin (2) | Jilin (1) |
Sourcing Place | Tokyo | America | Australia | Manila |
---|---|---|---|---|
Supply/TEU | 80 | 50 | 50 | 120 |
Mode | Waterway | Railway | Road | |
---|---|---|---|---|
Transportation cost ($/TEU-km) | 0.2 (Ship) | 0.18 (Barge) | 0.5 | 2 |
Carbon emission cost ($/TEU-km) | 0.018 (Ship) | 0.015 (Barge) | 0.03 | 0.05 |
Average speed (km/h) | 40 (Ship) | 30 (Barge) | 70 | 70 |
Solution | Tokyo | America | Australia | Manilas | TTC/$ | MFT/h | CEC/$ | Feasibility (Yes/No) |
---|---|---|---|---|---|---|---|---|
1 | 1-4-2-1-1-1-2-2-2 | 1-1-3-2-1-1-1-1-3 | 1-1-2-2-1-2-3-2-2 | 1-1-2-2-1-2-2-1-2 | 110,799 | 601 | 2330 | Yes |
2 | 1-1-2-2-1-2-2-2-2 | 1-1-2-2-1-1-3-2-3 | 1-1-2-2-1-1-2-2-2 | 1-1-2-2-1-2-2-2-2 | 99,097 | 614 | 2041 | Yes |
3 | 1-1-2-1-1-2-2-2-2 | 1-1-2-2-1-2-3-1-3 | 1-1-2-2-1-2-2-1-2 | 1-1-2-1-1-2-2-1-2 | 92,188 | 617 | 1854 | Yes |
4 | 1-4-2-2-1-2-2-1-2 | 1-1-2-2-1-1-2-2-2 | 1-1-2-1-1-2-3-2-2 | 1-1-2-2-1-2-2-1-2 | 92,141 | 662 | 1850 | Yes |
5 | 1-1-2-2-1-2-3-2-2 | 1-1-2-2-1-1-3-1-3 | 1-1-2-1-1-2-2-1-2 | 1-1-2-2-1-2-2-1-2 | 103,661 | 610 | 2106 | Yes |
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Ji, S.-f.; Luo, R.-j. A Hybrid Estimation of Distribution Algorithm for Multi-Objective Multi-Sourcing Intermodal Transportation Network Design Problem Considering Carbon Emissions. Sustainability 2017, 9, 1133. https://doi.org/10.3390/su9071133
Ji S-f, Luo R-j. A Hybrid Estimation of Distribution Algorithm for Multi-Objective Multi-Sourcing Intermodal Transportation Network Design Problem Considering Carbon Emissions. Sustainability. 2017; 9(7):1133. https://doi.org/10.3390/su9071133
Chicago/Turabian StyleJi, Shou-feng, and Rong-juan Luo. 2017. "A Hybrid Estimation of Distribution Algorithm for Multi-Objective Multi-Sourcing Intermodal Transportation Network Design Problem Considering Carbon Emissions" Sustainability 9, no. 7: 1133. https://doi.org/10.3390/su9071133