Two-Stage Optimization on Vessel Routing and Hybrid Energy Output for Marine Debris Collection
Abstract
1. Introduction
2. Literature Review
2.1. Vessel Routing Problem
2.2. Vessels with HES
2.3. Cross-Research on VRP and EMS
3. Two-Stage Optimization Approach
3.1. Problem Description
3.2. First Stage
3.2.1. Drifting Time Window
3.2.2. Logistics Space–Time Network
3.2.3. VRPDTW and Speed Optimization Model
3.3. Second Stage
3.3.1. Power Demand
3.3.2. PV Output
3.3.3. OPF Model
4. Solution Algorithm for VRPDTW
4.1. Removal Operators
4.2. Insertion Operators
4.3. Speed Optimization
4.4. Adaptive Operator Selection Mechanism
4.4.1. Selection Probability
4.4.2. Operator Score
4.4.3. Elitist Strategy
Algorithm 1 ALNSES algorithm |
|
Generate an initial feasible solutions population Find the best solution |
Initialize and |
while |
for |
Select removal operator and insertion operator according to and , respectively |
Perform operators and on a feasible solution to obtain |
Perform SO algorithm on to obtain |
if |
if |
else |
end |
else |
end |
if mod = 0 |
Update and according to Equation (46) |
Update and according to Equation (47) |
end |
end |
Merge parent population and offspring population to obtain population |
Update population : Perform Elite strategy on to obtain new parent population |
end |
5. Numerical Experiment
5.1. Experiment Data
5.2. Algorithm Performance
5.3. HES
5.3.1. Data
- Scenario A: maximum likely output. In the historical data greater than the most likely one, the illumination intensity that occurs the most is selected, and the PV output calculated from this is the maximum likely output.
- Scenario B: most likely output. In all historical data, the illumination intensity with the highest occurrence is taken as the most likely one, and the PV output calculated is thus regarded as the most likely output. This scenario is used as the baseline for further analysis.
- Scenario C: minimum likely output. In the historical data less than the most likely one, the illumination intensity with the most occurrence times is selected, and the PV output calculated from this is the minimum possible PV output.
5.3.2. OPF Analysis
- The reason there is no Diesel-Battery in the OPF is that the cost of the battery powering load after diesel has charged the battery is higher than if diesel powers the load directly. Thus, to save costs, diesel does not charge the battery.
- According to the length of the travel time, all vessels can be divided into two categories, the first three vessels with 14 periods (Category 1) and the last three vessels with no more than 6 periods (Category 2). On the one hand, the two categories share some characteristics. (1) There is no separate output of diesel at any period; (2) there are only three kinds of energy output at most, i.e., Diesel-Load, PV-Load, and PV-Battery, which only occurs in the first two periods; (3) PV-Battery and Battery-Load do not occur in the same period; and (4) PV-Battery must occur simultaneously with PV-Load, which indicates that the condition for PV to charge the battery is when PV supplies power to the load and there is surplus. On the other hand, each category presents different characteristics.
- In Category 1, due to the long trip, PV-Battery and Battery-Load have more outputs except PV-Load. PV-Load runs through almost all of the periods except the last period where the load is completely powered by battery. It is easy to see from Table 14 that PV output in the last period is 0. Diesel-Load occurs in the first three periods, ranging from 15.33% to 59.03%. PV-Battery appears in the front and middle periods (from 1 to 9), reaching a maximum of 83.31%. Battery-Load is mainly located in the later period (from 10 to 14), and the later the period, the higher the proportion.
- In Category 2, the short-trip results in the load being mostly supplied by PV, and the other energy outputs are extremely low. Diesel-Load only appears in period 1, ranging from 3.45% to 21.46%. PV-Battery and Battery-Load are, respectively, no more than 22% and 13% in each period.
5.3.3. Carbon Emissions
5.4. Time Windows
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ALNS | Adaptive Large Neighborhood Search |
ALNSES | ALNS embedded with Elitist Strategy |
ECA | Emission Control Areas |
EMS | Energy Management Strategies |
GNOME | General NOAA Operational Modeling Environment |
HES | Hybrid Energy System |
MD | Marine Debris |
MDL | MD Location |
MILP | Mixed Integer Linear Programming |
NOAA | National Oceanic and Atmospheric Administration |
OPF | Optimal Power Flow |
PV | Photovoltaic |
SOA | Speed Optimization Algorithm |
SOC | State of Charge |
VRP | Vessel Routing Problem |
VRPDTW | VRP with Drifting Time Window |
Appendix A
Speed Optimization Algorithm
Algorithm A1 Speed optimization algorithm |
Input: . Output: Speed vector . for if else if end end end |
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Sets: | ||
---|---|---|
Set of time window for origin, | ||
Set of time windows of MDs, | ||
Set of time window for destination, | ||
Set of all vertices, | ||
Set of origin, | ||
Set of MDs, | ||
Set of destination, | ||
Set of edges, | ||
Set of origin with time window, | ||
Set of MDLs, | ||
Set of destination with time window, | ||
Set of all edges, | ||
Set of edges from origin with time window to an MDL, | ||
Set of edges from one MDL to another, | ||
Set of edges from an MDL to destination with time window, | ||
Set of vessels | ||
Parameters: | ||
MD collection time at vertex | ||
MD volume at vertex | ||
MD density at vertex | ||
Time window of vertex , and are the earliest time and the latest time, respectively | ||
Maximum design speed of the vessel | ||
Weight capacity of vessel | ||
Volume capacity of vessel | ||
Distance of edge | ||
Decision variables: | ||
1 if vessel transfers edge ; 0 otherwise | ||
Cumulative loaded volume of vessel at vertex | ||
Cumulative loaded weight of vessel at vertex | ||
The speed of vessel on edge | ||
Arrival time of vessel at vertex |
Set: | |
---|---|
Set of all periods, | |
Parameters: | |
Loss cost of PV power generation | |
Cost of diesel | |
Loss cost of battery charging and discharging | |
Carbon tax rate | |
Carbon emission factor | |
Diesel intercept coefficient | |
Diesel slope coefficient | |
Power required for load of vessel in period | |
Maximum output power of PV in period | |
Battery charging efficiency | |
Battery discharge efficiency | |
Maximum value of battery SOC | |
Minimum value of battery SOC | |
Rated power of PV power | |
Rated power of diesel generator | |
Maximum power of PV to vessel load | |
Maximum power of PV to battery | |
Maximum power of diesel generator to vessel load | |
Maximum power of diesel generator to battery | |
Maximum power of storage battery to vessel load | |
Decision Variables: | |
Power of PV to load of vessel in period | |
Power of PV to battery of vessel in period | |
Power of diesel generator to load of vessel in period | |
Power of diesel generator to battery in period | |
Power of storage battery to load of vessel in period | |
Battery SOC of vessel at the beginning of period | |
1 if the battery of vessel is charged in period ; 0 otherwise | |
1 if the battery of vessel is discharged in period ; 0 otherwise | |
1 if the diesel generator of vessel is on in period ; 0 otherwise |
Debris No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Weight (tons) | 1.91 | 2.16 | 2.55 | 1.27 | 1.59 | 1.01 | 1.13 | 2.07 | 1.37 | 2.64 |
Volume (m3) | 2.67 | 2.81 | 3.57 | 1.78 | 1.91 | 1.31 | 1.69 | 2.48 | 1.92 | 3.17 |
Collection time (h) | 1.1 | 1.1 | 1.5 | 0.9 | 0.9 | 0.8 | 0.9 | 1.0 | 0.9 | 1.3 |
Debris No. | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Weight (tons) | 2.15 | 2.52 | 1.24 | 1.87 | 0.53 | 0.71 | 2.92 | 2.09 | 0.97 | 2.07 |
Volume (m3) | 2.80 | 3.78 | 1.86 | 2.81 | 0.69 | 0.92 | 3.8 | 2.51 | 1.26 | 3.1 |
Collection time (h) | 1.1 | 1.6 | 0.9 | 1.1 | 0.6 | 0.9 | 1.6 | 1.0 | 0.8 | 1.2 |
Debris No. | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
Weight (tons) | 2.67 | 1.09 | 1.91 | 1.60 | 0.33 | 1.83 | 1.01 | 1.12 | 0.66 | 2.87 |
Volume (m3) | 3.47 | 1.31 | 2.87 | 2.24 | 0.39 | 2.38 | 1.31 | 1.35 | 0.98 | 3.45 |
Collection time (h) | 1.5 | 0.8 | 1.1 | 1.0 | 0.5 | 1.0 | 0.8 | 0.8 | 0.7 | 1.4 |
Time Window | [7, 10] | [13, 15] | [17.5, 19.5] | |||
---|---|---|---|---|---|---|
Debris No. | Latitude | Longitude | Latitude | Longitude | Latitude | Longitude |
0 | 30.5922 | 122.0746 | 30.5922 | 122.0746 | 30.5922 | 122.0746 |
1 | 30.5443 | 121.8925 | 30.5497 | 121.9043 | 30.5403 | 121.9154 |
2 | 30.5735 | 121.9392 | 30.5130 | 121.9491 | 30.5280 | 121.9523 |
3 | 30.5284 | 121.7923 | 30.5736 | 121.8362 | 30.4521 | 121.9460 |
4 | 30.4722 | 121.9415 | 30.6140 | 121.9462 | 30.6576 | 121.9503 |
5 | 30.7940 | 122.0825 | 30.8051 | 121.9833 | 30.8706 | 122.1567 |
6 | 30.5745 | 122.0054 | 30.5816 | 121.9981 | 30.5639 | 122.0362 |
7 | 30.4397 | 122.0351 | 30.5124 | 122.0778 | 30.7127 | 122.0831 |
8 | 30.6824 | 122.1027 | 30.7435 | 122.1245 | 30.8020 | 122.1727 |
9 | 30.7625 | 122.1340 | 30.7987 | 122.1095 | 30.8261 | 122.1435 |
10 | 30.8226 | 122.1530 | 30.6455 | 122.1468 | 30.9182 | 122.1572 |
11 | 30.8695 | 122.1593 | 30.9207 | 122.1681 | 30.7218 | 122.1558 |
12 | 30.9958 | 122.1649 | 30.8834 | 122.1763 | 30.7876 | 122.2613 |
13 | 30.4125 | 122.2102 | 30.7941 | 122.2481 | 30.6881 | 122.2506 |
14 | 30.9061 | 122.2715 | 31.0390 | 122.2595 | 30.8971 | 122.2920 |
15 | 30.8272 | 122.3001 | 30.9263 | 122.3102 | 30.8544 | 122.3215 |
16 | 30.7945 | 122.3210 | 30.9369 | 122.3321 | 30.9719 | 122.3321 |
17 | 30.7571 | 122.3516 | 30.7753 | 122.3685 | 30.7811 | 122.3885 |
18 | 30.5500 | 122.3907 | 30.8887 | 122.3936 | 30.9011 | 122.3853 |
19 | 31.3781 | 122.3890 | 31.0267 | 122.4047 | 31.0695 | 122.4168 |
20 | 31.1228 | 122.4172 | 31.1103 | 122.4354 | 31.1205 | 122.4775 |
21 | 31.2529 | 122.4611 | 31.2005 | 122.5079 | 31.2359 | 122.5070 |
22 | 30.9215 | 122.5127 | 30.9489 | 122.5108 | 30.9687 | 122.5315 |
23 | 30.5210 | 122.5411 | 30.9569 | 122.5488 | 30.9795 | 122.5605 |
24 | 30.8596 | 122.5648 | 31.0681 | 122.5711 | 30.8633 | 122.5767 |
25 | 30.9438 | 122.5957 | 31.0588 | 122.6106 | 31.1471 | 122.6150 |
26 | 31.2275 | 122.6325 | 30.9067 | 122.6451 | 31.0919 | 122.6411 |
27 | 30.9562 | 122.6721 | 31.1450 | 122.6862 | 31.1455 | 122.9609 |
28 | 30.4777 | 122.7659 | 30.3808 | 122.7931 | 30.5073 | 122.8421 |
29 | 30.9171 | 122.8444 | 31.1642 | 122.6592 | 31.1774 | 122.6399 |
30 | 31.1789 | 122.6554 | 31.2654 | 122.6695 | 31.3057 | 122.6574 |
Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|
0.2 | 0.2 | 0.7 | |||
0.2 | 6 | 100 | |||
0.2 | 3 | 300 | |||
0.2 | 1 | 200 |
Vessel No. | Route | Speed (km/h) | Travel Time (h) | Loading Weight (tons) | Loading Volume (m3) |
---|---|---|---|---|---|
1 | 0-231-281-262-202-153-123-0 | 40, 40, 17.6946, 40, 16.8217, 40, 40 | 13.56 | 9.98 | 14.17 |
2 | 0-221-301-272-292-212-183-143-0 | 40, 40, 2.4726, 40, 40, 29.6628, 40, 40 | 13.72 | 12.26 | 15.84 |
3 | 0-81-161-171-192-252-242-133-113-0 | 40, 40, 40, 16.8198, 40, 40, 29.7806, 40, 40 | 13.11 | 11.99 | 15.75 |
4 | 0-61-41-71-0 | 40, 40, 40, 40 | 3.68 | 3.41 | 4.78 |
5 | 0-91-101-51-0 | 40, 40, 40, 40 | 4.35 | 5.6 | 7 |
6 | 0-21-11-31-0 | 40, 40, 40, 40 | 5.1 | 6.62 | 9.05 |
Algorithm | Total Travel Time (h) | Running Time (s) | |
---|---|---|---|
ALNSES | Min | 53.52 | 114.23 |
Max | 54.6 | 124.4 | |
Average | 53.81 | 119.91 | |
ALNS | Min | 54.22 | 117.37 |
Max | 57.04 | 128.99 | |
Average | 55.48 | 124.77 |
MDL Scale | Total Travel Time (h) | Running Time (s) |
---|---|---|
90 | 53.81 | 119.91 |
120 | 74.73 | 172.58 |
150 | 98.9 | 270.15 |
180 | 118.7 | 407.84 |
210 | 134.61 | 570.98 |
240 | 160.28 | 811.16 |
270 | 179.09 | 1162.41 |
300 | 202.74 | 1598.78 |
Parameter | Value |
---|---|
Rated power of PV | 180 kW |
Rated power of diesel generator | 200 kW |
Maximum value of battery SOC | 400 kWh |
Minimum value of battery SOC | 120 kWh |
Loss cost of PV power generation | 0.3 CNY/kWh |
Cost of diesel | 6.4 CNY/L |
Loss cost of battery charging and discharging | 0.3 CNY/kWh |
Carbon tax rate | 0.14 CNY/kg |
Carbon emission factor | 3.315 |
Diesel intercept coefficient | 0.01609 |
Diesel slope coefficient | 0.2486 |
Battery charging efficiency | 85% |
Battery discharge efficiency | 100% |
Condition | Period | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
Sailing 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.1 | 1 | 0.5 | 0 | 0 | 0 |
Sailing 2 | 0 | 0 | 0 | 0.42 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Sailing 3 | 1 | 0.13 | 0.55 | 0 | 0 | 0 | 0 | 0.7 | 0 | 0 | 0 | 0.22 | 0.08 | 0.56 |
Working | 0 | 0.87 | 0.45 | 0.58 | 0 | 0 | 1 | 0.3 | 0.9 | 0 | 0.5 | 0.78 | 0.92 | 0 |
Vessel No. | Period | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
1 | 160 | 73.26 | 114.94 | 48.35 | 32.12 | 32.12 | 60 | 130.15 | 57.08 | 30.41 | 45.21 | 81.58 | 68.42 | 90.31 |
2 | 160 | 91.53 | 130.63 | 60 | 28.89 | 20.03 | 67.95 | 97.34 | 60 | 69.35 | 68.55 | 82.41 | 77.59 | 115.66 |
3 | 82.67 | 118.9 | 71.6 | 60 | 43.18 | 30.41 | 80 | 99.75 | 61.82 | 77.78 | 68.89 | 84.15 | 85.85 | 17.36 |
4 | 80 | 86.09 | 83.78 | 78.41 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
5 | 103.29 | 75.13 | 78.26 | 73.33 | 56.23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
6 | 92.8 | 73.22 | 84.35 | 60 | 119.63 | 15.73 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Scenario | Period | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
A | 80 | 90 | 100 | 140 | 160 | 180 | 150 | 120 | 90 | 80 | 60 | 35 | 20 | 0 |
B | 70 | 80 | 90 | 120 | 140 | 160 | 130 | 100 | 80 | 70 | 50 | 30 | 15 | 0 |
C | 40 | 50 | 60 | 90 | 110 | 130 | 100 | 70 | 50 | 40 | 30 | 15 | 5 | 0 |
Scenario | Vessel No. | Total | |||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | ||
A | 572.17 | 680.93 | 445.89 | 98.49 | 163.17 | 166.28 | 2126.93 |
B | 634.59 | 739.67 | 514.24 | 137.43 | 181.83 | 180.35 | 2388.1 |
C | 918.93 | 1127.79 | 820.8 | 344.94 | 343.62 | 331.5 | 3887.58 |
Item (kW) | Period | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
Load demand | 160 | 73.26 | 114.94 | 48.35 | 32.12 | 32.12 | 60 | 130.15 | 57.08 | 30.41 | 45.21 | 81.58 | 68.42 | 90.31 |
PV-Load | 59.16 | 73.26 | 90 | 48.35 | 32.12 | 32.12 | 60 | 100 | 57.08 | 30.41 | 45.21 | 30 | 15 | 0 |
PV-Battery | 10.84 | 6.74 | 0 | 71.65 | 100 | 100 | 5.35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Diesel-Load | 100.84 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Battery-Load | 0 | 0 | 24.94 | 0 | 0 | 0 | 0 | 30.15 | 0 | 0 | 0 | 51.58 | 53.42 | 90.31 |
SOC | 139.21 | 144.94 | 120 | 180.91 | 265.91 | 350.91 | 355.46 | 325.31 | 325.31 | 325.31 | 325.31 | 273.73 | 220.31 | 130 |
Case | Time Windows |
---|---|
1.1 | [7, 10] |
1.2 | [13, 15] |
1.3 | [17.5, 19.5] |
2.1 | [13, 15], [17.5, 19.5] |
2.2 | [7, 10], [17.5, 19.5] |
2.3 | [7, 10], [13, 15] |
3 (baseline) | [7, 10], [13, 15], [17.5, 19.5] |
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Chen, L.; Duan, G.; Cao, J.; Wang, J. Two-Stage Optimization on Vessel Routing and Hybrid Energy Output for Marine Debris Collection. Sustainability 2025, 17, 3425. https://doi.org/10.3390/su17083425
Chen L, Duan G, Cao J, Wang J. Two-Stage Optimization on Vessel Routing and Hybrid Energy Output for Marine Debris Collection. Sustainability. 2025; 17(8):3425. https://doi.org/10.3390/su17083425
Chicago/Turabian StyleChen, Li, Gang Duan, Jie Cao, and Jinhua Wang. 2025. "Two-Stage Optimization on Vessel Routing and Hybrid Energy Output for Marine Debris Collection" Sustainability 17, no. 8: 3425. https://doi.org/10.3390/su17083425
APA StyleChen, L., Duan, G., Cao, J., & Wang, J. (2025). Two-Stage Optimization on Vessel Routing and Hybrid Energy Output for Marine Debris Collection. Sustainability, 17(8), 3425. https://doi.org/10.3390/su17083425