Solving Bi-Objective Vehicle Routing Problems with Driving Risk Consideration for Hazardous Materials Transportation
Abstract
:1. Introduction
2. Driving Risk Evaluation
2.1. Driving Risk Impact Index
2.2. Weights of Criterion
3. Problem Formulation
3.1. Assumption
3.2. Symbols Definition
3.3. Risk and Cost
3.4. Mathematical Model
4. Solution Methodology
4.1. NSGA-II Algorithm
4.2. Encoding and Decoding
4.2.1. Encoding
4.2.2. Decoding
4.3. Crossover Operator
4.4. Mutation Operator
5. Numerical Experiments
5.1. Road Network
5.2. Driving Risk and Cost
5.3. Solution by NSGA-II
5.4. Results and Discussion
6. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Criterion | Weight | Plan (Level 1) | Plan (Level 2) | ||
---|---|---|---|---|---|
Criterion | Weight | Criterion | Weight | ||
Driver’s characteristics | 0.4425 | Age | 0.4039 | 25–30 | 0.1060 |
30–35 | 0.0665 | ||||
35–40 | 0.1646 | ||||
40–45 | 0.2698 | ||||
≥45 | 0.3931 | ||||
Driving experience/years | 0.3404 | 3–7 | 0.4265 | ||
7–11 | 0.2537 | ||||
11–15 | 0.1507 | ||||
15–19 | 0.0867 | ||||
≥19 | 0.0824 | ||||
Educational background | 0.1391 | Uneducated | 0.4743 | ||
Primary | 0.2781 | ||||
Junior school | 0.1184 | ||||
High school | 0.0832 | ||||
Higher education | 0.0460 | ||||
Gender | 0.1166 | Male | 0.3333 | ||
Female | 0.6667 | ||||
Driving habits | 0.5575 | Driving Speed/km·h−1 (on urban roads) | 0.4182 | <45 | 0.0320 |
45–55 | 0.0583 | ||||
55–65 | 0.1031 | ||||
65–75 | 0.2976 | ||||
≥75 | 0.5089 | ||||
Rapid acceleration/km·h−2 | 0.1906 | <5 | 0.0330 | ||
5–10 | 0.0627 | ||||
10–15 | 0.1401 | ||||
15–20 | 0.2626 | ||||
≥20 | 0.5016 | ||||
Rapid deceleration/km·h−2 | 0.2707 | <5 | 0.0458 | ||
5–10 | 0.0907 | ||||
10–15 | 0.1343 | ||||
15–20 | 0.2515 | ||||
≥20 | 0.5326 | ||||
Heavy vehicle mileage/km·d−1 | 0.1205 | 120–150 | 0.1248 | ||
150–180 | 0.0778 | ||||
180–210 | 0.3506 | ||||
>210 | 0.4918 |
Vehicle | Customer Node | Service Order |
---|---|---|
1 | 5, 7 | 1→5→7→1 |
2 | 10 | 1→10→1 |
ID | Road Segment | Distance/km | Population Density/Person·km−2 | Accident Probability |
---|---|---|---|---|
1 | 1-4 | 26.36 | 300 | 0.0042 |
2 | 1-8 | 25.80 | 400 | 0.0040 |
3 | 2-3 | 26.12 | 120 | 0.0031 |
4 | 2-6 | 28.40 | 75 | 0.0032 |
5 | 3-1 | 25.62 | 180 | 0.0034 |
6 | 3-7 | 21.29 | 360 | 0.0036 |
7 | 4-5 | 30.09 | 320 | 0.0062 |
8 | 4-9 | 25.09 | 290 | 0.0035 |
9 | 5-10 | 30.06 | 260 | 0.0065 |
10 | 6-11 | 30.89 | 200 | 0.0042 |
11 | 6-7 | 23.19 | 690 | 0.0040 |
12 | 7-12 | 24.14 | 660 | 0.0042 |
13 | 7-8 | 21.35 | 400 | 0.0044 |
14 | 8-9 | 25.12 | 480 | 0.0043 |
15 | 8-13 | 27.48 | 520 | 0.0047 |
16 | 9-10 | 40.20 | 400 | 0.0045 |
17 | 9-14 | 25.60 | 760 | 0.0049 |
18 | 10-15 | 32.50 | 430 | 0.0042 |
19 | 11-12 | 20.67 | 680 | 0.0054 |
20 | 11-16 | 35.60 | 300 | 0.0052 |
21 | 12-13 | 23.50 | 700 | 0.0045 |
22 | 12-17 | 30.20 | 620 | 0.0050 |
23 | 13-14 | 25.29 | 620 | 0.0050 |
24 | 13-18 | 35.55 | 710 | 0.0053 |
25 | 14-15 | 27.35 | 850 | 0.0049 |
26 | 14-19 | 36.78 | 720 | 0.0048 |
27 | 15-20 | 35.70 | 650 | 0.0055 |
28 | 16-17 | 21.10 | 550 | 0.0032 |
29 | 16-21 | 30.12 | 420 | 0.0060 |
30 | 17-18 | 28.50 | 640 | 0.0050 |
31 | 17-21 | 28.56 | 500 | 0.0040 |
32 | 18-19 | 28.30 | 630 | 0.0049 |
33 | 18-22 | 30.58 | 530 | 0.0052 |
34 | 19-20 | 27.08 | 640 | 0.0036 |
35 | 19-23 | 24.16 | 480 | 0.0042 |
36 | 20-23 | 29.46 | 160 | 0.0064 |
37 | 21-22 | 32.60 | 200 | 0.0058 |
38 | 22-23 | 30.60 | 240 | 0.0055 |
Node | Demand/t | Service Duration/h | Time Window |
---|---|---|---|
10 | 10 | 1 | 09:30–11:00 |
11 | 8 | 1 | 13:00–14:30 |
14 | 10 | 1 | 10:30–12:00 |
17 | 7 | 1 | 14:30–16:30 |
23 | 8 | 1 | 12:30–14:00 |
Driver | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
Driving risk () | 0.2129 | 0.1849 | 0.2417 | 0.1370 | 0.1622 | 0.2264 |
1.0965 | 0.9522 | 1.2447 | 0.7055 | 0.8352 | 1.1659 | |
Driving cost/CNY·t−1·km−1 | 0.0881 | 0.0989 | 0.0770 | 0.1173 | 0.1076 | 0.0829 |
Path No. | Vehicle | Path | Distance/km |
---|---|---|---|
1 | 1 | 1→4→9→14→13→12→11→12→17→12→7→3→1 | 624.09 |
2 | 1→4→5→10→15→20→23→19→18→13→8→1 | ||
2 | 1 | 1→4→9→14→13→12→11→16→17→12→7→3→1 | 629.92 |
2 | 1→4→5→10→15→20→23→19→18→13→8→1 | ||
3 | 1 | 1→4→9→14→13→12→11→16→17→12→7→3→1 | 635.06 |
2 | 1→4→9→10→15→20→23→19→18→13→8→1 | ||
4 | 1 | 1→4→9→14→19→23→19→18→17→12→7→3→1 | 639.18 |
2 | 1→4→5→10→9→8→7→6→11→12→7→3→1 | ||
5 | 1 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 649.98 |
2 | 1→4→5→10→9→8→7→6→11→12→7→3→1 | ||
6 | 1 | 1→4→9→14→19→23→19→18→17→12→7→3→1 | 629.91 |
2 | 1→4→5→10→9→8→7→12→11→12→7→3→1 | ||
7 | 1 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 640.71 |
2 | 1→4→5→10→9→8→7→12→11→12→7→3→1 | ||
8 | 1 | 1→8→9→14→19→23→19→18→17→12→7→3→1 | 629.38 |
2 | 1→4→5→10→9→8→7→12→11→12→7→3→1 | ||
9 | 1 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 645.85 |
2 | 1→4→9→10→9→8→7→6→11→12→7→3→1 |
Solution No. | Path | Driver | Risk | Cost /CNY |
---|---|---|---|---|
1 | 1→8→9→14→19→23→19→18→17→12→7→3→1 | 4 | 402.5062 | 4394.09 |
1→4→5→10→9→8→7→12→11→12→7→3→1 | 5 | |||
59 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 3 | 768.3525 | 3849.75 |
1→4→9→10→9→8→7→6→11→12→7→3→1 | 6 |
Solution No. | Path | Driver | Risk | Cost /CNY |
---|---|---|---|---|
3 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 4 | 411.1256 | 4343.33 |
1→4→5→10→9→8→7→6→11→12→7→3→1 | 5 | |||
13 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 4 | 465.5105 | 4238.69 |
1→4→5→10→9→8→7→6→11→12→7→3→1 | 1 | |||
26 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 5 | 539.9801 | 4111.56 |
1→4→5→10→9→8→7→6→11→12→7→3→1 | 3 | |||
30 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 1 | 562.9320 | 4082.62 |
1→4→5→10→9→8→7→6→11→12→7→3→1 | 6 | |||
41 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 6 | 611.4671 | 4007.39 |
1→4→5→10→9→8→7→6→11→12→7→3→1 | 3 | |||
49 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 3 | 651.2104 | 3939.51 |
1→4→5→10→9→8→7→6→11→12→7→3→1 | 6 |
Solution No. | Path | Driver | Risk | Cost /CNY |
---|---|---|---|---|
2 | 1→4→9→14→13→12→11→16→17→12→7→3→1 | 4 | 407.4593 | 4367.60 |
1→4→9→10→15→20→23→19→18→13→8→1 | 5 | |||
4 | 1→4→9→14→13→12→11→16→17→12→7→3→1 | 4 | 416.0787 | 4316.85 |
1→4→5→10→15→20→23→19→18→13→8→1 | 5 | |||
7 | 1→4→9→14→13→12→11→12→17→12→7→3→1 | 4 | 433.2476 | 4293.67 |
1→4→5→10→15→20→23→19→18→13→8→1 | 5 |
Solution No. | Path | Driver | Risk | Cost /CNY |
---|---|---|---|---|
3 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 4 | 411.1256 | 4343.33 |
1→4→5→10→9→8→7→6→11→12→7→3→1 | 6 | |||
13 | 1→4→9→14→19→23→19→18→17→12→7→3→1 | 4 | 465.5105 | 4238.69 |
1→4→5→10→9→8→7→12→11→12→7→3→1 | 1 | |||
36 | 1→4→9→14→19→23→22→21→17→12→7→3→1 | 2 | 585.2382 | 4045.60 |
1→4→5→10→9→8→7→12→11→12→7→3→1 | 6 | |||
38 | 1→4→9→14→19→23→19→18→17→12→7→3→1 | 2 | 597.1895 | 4032.59 |
1→4→5→10→9→8→7→12→11→12→7→3→1 | 1 |
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Chai, H.; He, R.; Kang, R.; Jia, X.; Dai, C. Solving Bi-Objective Vehicle Routing Problems with Driving Risk Consideration for Hazardous Materials Transportation. Sustainability 2023, 15, 7619. https://doi.org/10.3390/su15097619
Chai H, He R, Kang R, Jia X, Dai C. Solving Bi-Objective Vehicle Routing Problems with Driving Risk Consideration for Hazardous Materials Transportation. Sustainability. 2023; 15(9):7619. https://doi.org/10.3390/su15097619
Chicago/Turabian StyleChai, Huo, Ruichun He, Ronggui Kang, Xiaoyan Jia, and Cunjie Dai. 2023. "Solving Bi-Objective Vehicle Routing Problems with Driving Risk Consideration for Hazardous Materials Transportation" Sustainability 15, no. 9: 7619. https://doi.org/10.3390/su15097619