Joint Optimization of Route and Speed for Methanol Dual-Fuel Powered Ships Based on Improved Genetic Algorithm
Abstract
1. Introduction
2. Literature Review
3. Problem Description
4. Mathematical Model
4.1. Model Assumptions
4.2. Model Variables and Parameters
4.3. Ship Sailing Total Costs
4.3.1. Ship Fuel Consumption Cost
4.3.2. Time Cost
4.3.3. Carbon Emissions Cost
4.3.4. Constraint Conditions of the Model
4.3.5. Objective Model
5. Solution Method
5.1. Model Analysis
5.2. Algorithm Overview
5.3. Model Reformulation
5.4. Solution Steps
6. Case Studies
6.1. Definition of Cases
6.2. Results and Discussion
6.3. Comparative Experiment
6.4. Sensitivity Analysis
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Regulations | Requirements | Application Area |
---|---|---|
ECAs | Ships must use fuels with a sulfur content of no more than 0.1% | Baltic Sea, North Sea and English Channel, North American, US Caribbean coasts, China coasts, Specific ports of South Korea |
SLO | Ships must use fuels with a sulfur content of no more than 0.5% | Outside the ECA applicable area |
CTS | Ships need to pay tax on carbon dioxide above a certain threshold. | Europe |
Port Number | Ports | Service Time/Days |
---|---|---|
1 | Tianjin | 2.0 |
2 | Weihai | 2.5 |
3 | Lianyungang | 3.0 |
4 | Busan | 2.0 |
5 | Kaohsiung | 1.0 |
6 | Manila | 1.5 |
7 | Bintulu | 2.5 |
8 | Singapore | 2.5 |
9 | Shenzhen | 1.5 |
10 | Shanghai | 2.0 |
1 | Tianjin | 1.0 |
Ports | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 216 | 490 | 685 | 1187 | 1735 | 2425 | 2749 | 1396 | 632 |
2 | 216 | 0 | 269 | 453 | 961 | 1507 | 2191 | 2533 | 1180 | 414 |
3 | 490 | 269 | 0 | 490 | 813 | 1340 | 2039 | 2388 | 1033 | 271 |
4 | 685 | 453 | 490 | 0 | 898 | 1400 | 2113 | 2498 | 1124 | 437 |
5 | 1187 | 961 | 813 | 898 | 0 | 552 | 1142 | 1608 | 336 | 57 |
6 | 1735 | 1507 | 1340 | 1400 | 552 | 0 | 834 | 1293 | 623 | 1089 |
7 | 2425 | 2191 | 2039 | 2113 | 1142 | 834 | 0 | 555 | 1148 | 1783 |
8 | 2749 | 2533 | 2388 | 2498 | 1608 | 1293 | 555 | 0 | 1413 | 2130 |
9 | 1396 | 1180 | 1033 | 1124 | 336 | 623 | 1148 | 1413 | 0 | 777 |
10 | 632 | 414 | 271 | 437 | 557 | 1089 | 1783 | 2130 | 777 | 0 |
Parameters | Symbols | Value |
---|---|---|
Ship displacement (ton) | W | 55,000 |
Admiralty constant | B | 250 |
Power index in fuel consumption function | ω | 3.5 |
The price of methanol bunkering for ships (USD) | PM | 350 |
The price of LSFO bunkering for ships (USD) | PL | 800 |
Lower limit of ship’s sailing speed (kn) | vmin | 15 |
Upper limit of ship’s sailing speed (kn) | vmax | 25 |
Daily cost of the ship (USD/day) | τ | 8000 |
Ship engine energy consumption rate of LSFO (g/kwh) | ηL | 170.5 |
Lower calorific values of methanol (MJ/kg) | LCM | 22.7 |
Lower calorific values of LSFO (MJ/kg) | LCL | 41.8 |
Methanol tank capacity (ton) | QM | 1000 |
Fuel oil tank capacity (ton) | QL | 2000 |
CO2 emission factor of methanol | EFMCO2 | 1.50 |
CO2 emission factor of LSFO | EFLCO2 | 3.30 |
SOx emission factor of methanol | EFMSOx | 0 |
SOx emission factor of LSFO | EFLSOx | 0.011 |
NOx emission factor of methanol | EFMNOx | 0.013 |
NOx emission factor of LSFO | EFLNOx | 0.101 |
PM emission factor of methanol | EFMPM | 0 |
PM emission factor of LSFO | EFLPM | 0.003 |
CO emission factor of methanol | EFMCO | 0.014 |
CO emission factor of LSFO | EFLCO | 0.006 |
Cases | Methanol Tank Capacity (Ton) | Total Cost (USD) |
---|---|---|
1 | 1000 | 3,840,094 |
2 | 1500 | 3,582,746 |
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Li, Z.; Zhang, H.; Zhang, J.; Wu, B. Joint Optimization of Route and Speed for Methanol Dual-Fuel Powered Ships Based on Improved Genetic Algorithm. Big Data Cogn. Comput. 2025, 9, 90. https://doi.org/10.3390/bdcc9040090
Li Z, Zhang H, Zhang J, Wu B. Joint Optimization of Route and Speed for Methanol Dual-Fuel Powered Ships Based on Improved Genetic Algorithm. Big Data and Cognitive Computing. 2025; 9(4):90. https://doi.org/10.3390/bdcc9040090
Chicago/Turabian StyleLi, Zhao, Hao Zhang, Jinfeng Zhang, and Bo Wu. 2025. "Joint Optimization of Route and Speed for Methanol Dual-Fuel Powered Ships Based on Improved Genetic Algorithm" Big Data and Cognitive Computing 9, no. 4: 90. https://doi.org/10.3390/bdcc9040090
APA StyleLi, Z., Zhang, H., Zhang, J., & Wu, B. (2025). Joint Optimization of Route and Speed for Methanol Dual-Fuel Powered Ships Based on Improved Genetic Algorithm. Big Data and Cognitive Computing, 9(4), 90. https://doi.org/10.3390/bdcc9040090