《计算机应用》唯一官方网站 ›› 2025, Vol. 45 ›› Issue (6): 1945-1953.DOI: 10.11772/j.issn.1001-9081.2024060757
• 先进计算 • 上一篇
收稿日期:
2024-06-07
修回日期:
2024-07-19
接受日期:
2024-07-24
发布日期:
2024-09-06
出版日期:
2025-06-10
通讯作者:
顾播宇
作者简介:
刘树东(1965—),男,黑龙江哈尔滨人,教授,博士,主要研究方向:图像处理、无线传感网络基金资助:
Shudong LIU, Hao WU, Jia CONG, Boyu GU()
Received:
2024-06-07
Revised:
2024-07-19
Accepted:
2024-07-24
Online:
2024-09-06
Published:
2025-06-10
Contact:
Boyu GU
About author:
LIU Shudong, born in 1965, Ph. D., professor. His research interests include image processing, wireless sensor networks.Supported by:
摘要:
随着全球气候变化问题的日益严峻,我国提出了“双碳”目标(碳达峰和碳中和)。而港口作为物流枢纽和货物集散地,它的碳排放问题尤为突出。针对港口作业调度优化问题,考虑船舶到港时间、货物装卸需求、岸桥作业能力及碳排放成本等关键因素,构建最小化碳排放成本和码头运营成本的作业调度优化模型,并提出一种“双碳”目标下基于改进型非支配排序遗传算法(NSGA-Ⅱ)(E-NSGA-Ⅱ)的港口作业调度优化算法。首先,调整算法的编码策略、种群初始化方法和交叉变异操作;其次,设计不可行解的基因修复算子,并引入自适应交叉与变异概率机制。实验结果表明,与FCFS (First Come First Service)调度算法相比,所提算法在模型求解中的总成本下降了7.9%,碳排放成本下降了19.7%,码头运营成本下降了6.5%。以上研究结果丰富了多目标优化算法和港口作业调度理论,并为港口企业实现绿色调度、降低运营成本和提升经济效益提供了有力支持。
中图分类号:
刘树东, 吴昊, 丛佳, 顾播宇. “双碳”目标下基于改进型NSGA-Ⅱ的港口作业调度优化算法[J]. 计算机应用, 2025, 45(6): 1945-1953.
Shudong LIU, Hao WU, Jia CONG, Boyu GU. Port operation scheduling algorithm based on enhanced NSGA-Ⅱ under goals of carbon peaking and carbon neutrality[J]. Journal of Computer Applications, 2025, 45(6): 1945-1953.
参数 类型 | 符号 | 含义 |
---|---|---|
码头 参数 | B | 泊位集合 |
Q | 岸桥集合 | |
Qtotal | 码头岸桥总数 | |
L | 岸线总长度 | |
l | 泊位间距 | |
lbj | 泊位j的长度 | |
Dbj | 泊位j的水深 | |
E0 | 岸桥台时效率 | |
C1 | 岸桥单位时间作业成本 | |
C2 | 岸桥单位时间碳排放成本 | |
C3 | 集卡单位运输距离的碳排放成本 | |
船舶 参数 | S | 抵港船舶集合 |
mi | 船舶i的待装卸货物量 | |
船舶i可配置的最小岸桥数 | ||
船舶i可配置的最大岸桥数 | ||
bpi | 船舶i的偏好停泊泊位 | |
lsi | 船舶i的长度 | |
Dsi | 船舶i的吃水深度 | |
决策 变量 | λ | 集卡实际运行距离与船舶i停泊偏好泊位和 实际停泊泊位之间距离差的比值 |
P1 | 等待泊位单位时间惩罚成本 | |
P2 | 延期离港单位时间惩罚成本 | |
bi | 船舶i的靠泊泊位序号 | |
qi | 船舶i配置的岸桥数 | |
Tai | 船舶i的抵港时间 | |
Tbi | 船舶i的靠泊时间 | |
Tei | 船舶i的预计离港时间 | |
Tdi | 船舶i的实际离港时间 | |
Twi | 船舶i的开始作业时间 | |
αijk | 船舶i在泊位j上以顺序k被服务时的状态。 被服务时取值1,否则为0 | |
βit | 船舶i在t时刻被服务时的状态。 被服务时取值1,否则为0 | |
γij | 船舶i停靠在泊位j上时的状态。 在泊位上时取值1,否则为0 |
表1 符号说明
Tab.1 Description of symbols
参数 类型 | 符号 | 含义 |
---|---|---|
码头 参数 | B | 泊位集合 |
Q | 岸桥集合 | |
Qtotal | 码头岸桥总数 | |
L | 岸线总长度 | |
l | 泊位间距 | |
lbj | 泊位j的长度 | |
Dbj | 泊位j的水深 | |
E0 | 岸桥台时效率 | |
C1 | 岸桥单位时间作业成本 | |
C2 | 岸桥单位时间碳排放成本 | |
C3 | 集卡单位运输距离的碳排放成本 | |
船舶 参数 | S | 抵港船舶集合 |
mi | 船舶i的待装卸货物量 | |
船舶i可配置的最小岸桥数 | ||
船舶i可配置的最大岸桥数 | ||
bpi | 船舶i的偏好停泊泊位 | |
lsi | 船舶i的长度 | |
Dsi | 船舶i的吃水深度 | |
决策 变量 | λ | 集卡实际运行距离与船舶i停泊偏好泊位和 实际停泊泊位之间距离差的比值 |
P1 | 等待泊位单位时间惩罚成本 | |
P2 | 延期离港单位时间惩罚成本 | |
bi | 船舶i的靠泊泊位序号 | |
qi | 船舶i配置的岸桥数 | |
Tai | 船舶i的抵港时间 | |
Tbi | 船舶i的靠泊时间 | |
Tei | 船舶i的预计离港时间 | |
Tdi | 船舶i的实际离港时间 | |
Twi | 船舶i的开始作业时间 | |
αijk | 船舶i在泊位j上以顺序k被服务时的状态。 被服务时取值1,否则为0 | |
βit | 船舶i在t时刻被服务时的状态。 被服务时取值1,否则为0 | |
γij | 船舶i停靠在泊位j上时的状态。 在泊位上时取值1,否则为0 |
船名 | 船长/m | 船宽/m | 吃水深度/m | 预计抵港时间 | 装卸货量(箱数) | 最小岸桥数 | 最大岸桥数 | 净吨位/t |
---|---|---|---|---|---|---|---|---|
HONG TAI 96 | 134 | 19 | 4.6 | 00:30 | 4 250 | 3 | 5 | 11 006 |
XIN HAI KOU | 263 | 32 | 9.4 | 01:50 | 2 730 | 2 | 4 | 52 212 |
BERING GAS | 160 | 27 | 6.5 | 04:20 | 1 500 | 2 | 4 | 24 244 |
GRANDIS | 201 | 34 | 6.7 | 07:30 | 980 | 1 | 3 | 62 353 |
ZHONGGUGUANGZHOU | 180 | 33 | 10.8 | 09:20 | 3 140 | 2 | 5 | 41 200 |
HUA HAI DA 58 | 98 | 16 | 3.5 | 10:00 | 750 | 1 | 2 | 4 979 |
ANJI 7 | 133 | 20 | 5.5 | 11:50 | 2 420 | 2 | 4 | 4 066 |
GREBE ARROW | 200 | 23 | 9.9 | 15:40 | 1 697 | 1 | 3 | 55 777 |
HUA XIN 878 | 116 | 16 | 6.1 | 18:10 | 1 020 | 1 | 2 | 6 381 |
LIAO TONG YOU 9 | 117 | 17 | 5.2 | 19:40 | 2 060 | 2 | 4 | 7 030 |
HENG JUN 806 | 137 | 20 | 5.6 | 23:20 | 1 450 | 1 | 2 | 13 417 |
JIN XIU HE | 181 | 26 | 8.1 | 00:40 | 4 300 | 3 | 5 | 29 105 |
YUE DAN | 111 | 18 | 5.5 | 03:50 | 1 243 | 1 | 2 | 7 379 |
WINDS 3 | 120 | 19 | 5.1 | 08:40 | 2 980 | 2 | 5 | 11 759 |
XIN YI HAI 3 | 159 | 24 | 5.5 | 11:30 | 1 400 | 2 | 3 | 23 540 |
JINRUN 168 | 95 | 15 | 4.5 | 13:40 | 1 750 | 3 | 4 | 4 403 |
RENJIANQUANZHOU | 180 | 28 | 10.1 | 15:20 | 1 320 | 1 | 3 | 27 662 |
AN SHENG 26 | 146 | 21 | 8.1 | 19:30 | 2 470 | 2 | 5 | 13 259 |
AURIGA OCEAN | 235 | 38 | 14.2 | 22:40 | 1 190 | 1 | 2 | 93 549 |
YONG YE 67 | 65 | 16 | 4.9 | 23:50 | 1 230 | 1 | 2 | 1 933 |
表2 到港船舶的基本数据
Tab.2 Basic data of arriving ships
船名 | 船长/m | 船宽/m | 吃水深度/m | 预计抵港时间 | 装卸货量(箱数) | 最小岸桥数 | 最大岸桥数 | 净吨位/t |
---|---|---|---|---|---|---|---|---|
HONG TAI 96 | 134 | 19 | 4.6 | 00:30 | 4 250 | 3 | 5 | 11 006 |
XIN HAI KOU | 263 | 32 | 9.4 | 01:50 | 2 730 | 2 | 4 | 52 212 |
BERING GAS | 160 | 27 | 6.5 | 04:20 | 1 500 | 2 | 4 | 24 244 |
GRANDIS | 201 | 34 | 6.7 | 07:30 | 980 | 1 | 3 | 62 353 |
ZHONGGUGUANGZHOU | 180 | 33 | 10.8 | 09:20 | 3 140 | 2 | 5 | 41 200 |
HUA HAI DA 58 | 98 | 16 | 3.5 | 10:00 | 750 | 1 | 2 | 4 979 |
ANJI 7 | 133 | 20 | 5.5 | 11:50 | 2 420 | 2 | 4 | 4 066 |
GREBE ARROW | 200 | 23 | 9.9 | 15:40 | 1 697 | 1 | 3 | 55 777 |
HUA XIN 878 | 116 | 16 | 6.1 | 18:10 | 1 020 | 1 | 2 | 6 381 |
LIAO TONG YOU 9 | 117 | 17 | 5.2 | 19:40 | 2 060 | 2 | 4 | 7 030 |
HENG JUN 806 | 137 | 20 | 5.6 | 23:20 | 1 450 | 1 | 2 | 13 417 |
JIN XIU HE | 181 | 26 | 8.1 | 00:40 | 4 300 | 3 | 5 | 29 105 |
YUE DAN | 111 | 18 | 5.5 | 03:50 | 1 243 | 1 | 2 | 7 379 |
WINDS 3 | 120 | 19 | 5.1 | 08:40 | 2 980 | 2 | 5 | 11 759 |
XIN YI HAI 3 | 159 | 24 | 5.5 | 11:30 | 1 400 | 2 | 3 | 23 540 |
JINRUN 168 | 95 | 15 | 4.5 | 13:40 | 1 750 | 3 | 4 | 4 403 |
RENJIANQUANZHOU | 180 | 28 | 10.1 | 15:20 | 1 320 | 1 | 3 | 27 662 |
AN SHENG 26 | 146 | 21 | 8.1 | 19:30 | 2 470 | 2 | 5 | 13 259 |
AURIGA OCEAN | 235 | 38 | 14.2 | 22:40 | 1 190 | 1 | 2 | 93 549 |
YONG YE 67 | 65 | 16 | 4.9 | 23:50 | 1 230 | 1 | 2 | 1 933 |
方案 | 碳排放成本/元 | 码头运营成本/元 | 总成本/元 |
---|---|---|---|
1 | 11 519.4 | 113 801.9 | 125 321.3 |
2 | 13 186.7 | 112 774.3 | 125 961.0 |
3 | 22 974.2 | 111 757.0 | 134 731.1 |
4 | 37 269.4 | 111 507.1 | 148 776.5 |
5 | 48 036.9 | 111 195.7 | 159 232.6 |
6 | 60 129.7 | 110 644.7 | 170 774.4 |
7 | 71 952.2 | 110 415.9 | 182 368.0 |
8 | 84 034.7 | 110 093.2 | 194 127.8 |
9 | 90 852.2 | 109 605.4 | 200 457.6 |
10 | 97 737.2 | 109 286.4 | 207 023.5 |
表3 Pareto前沿解集方案
Tab.3 Pareto frontier solution set schemes
方案 | 碳排放成本/元 | 码头运营成本/元 | 总成本/元 |
---|---|---|---|
1 | 11 519.4 | 113 801.9 | 125 321.3 |
2 | 13 186.7 | 112 774.3 | 125 961.0 |
3 | 22 974.2 | 111 757.0 | 134 731.1 |
4 | 37 269.4 | 111 507.1 | 148 776.5 |
5 | 48 036.9 | 111 195.7 | 159 232.6 |
6 | 60 129.7 | 110 644.7 | 170 774.4 |
7 | 71 952.2 | 110 415.9 | 182 368.0 |
8 | 84 034.7 | 110 093.2 | 194 127.8 |
9 | 90 852.2 | 109 605.4 | 200 457.6 |
10 | 97 737.2 | 109 286.4 | 207 023.5 |
抵港 船舶编号 | 靠泊 泊位编号 | 分配 岸桥数 | 抵港 船舶编号 | 靠泊 泊位编号 | 分配 岸桥数 |
---|---|---|---|---|---|
2 | 2 | 4 | 11 | 6 | 2 |
6 | 1 | 2 | 13 | 5 | 2 |
12 | 1 | 3 | 7 | 6 | 3 |
16 | 1 | 3 | 9 | 3 | 2 |
4 | 6 | 3 | 3 | 4 | 3 |
8 | 2 | 3 | 14 | 2 | 3 |
17 | 2 | 2 | 10 | 4 | 3 |
1 | 3 | 3 | 20 | 6 | 2 |
5 | 5 | 3 | 15 | 4 | 3 |
19 | 3 | 2 |
表4 泊位岸桥调度最优方案
Tab.4 Optimal scheme for berth and quay crane scheduling
抵港 船舶编号 | 靠泊 泊位编号 | 分配 岸桥数 | 抵港 船舶编号 | 靠泊 泊位编号 | 分配 岸桥数 |
---|---|---|---|---|---|
2 | 2 | 4 | 11 | 6 | 2 |
6 | 1 | 2 | 13 | 5 | 2 |
12 | 1 | 3 | 7 | 6 | 3 |
16 | 1 | 3 | 9 | 3 | 2 |
4 | 6 | 3 | 3 | 4 | 3 |
8 | 2 | 3 | 14 | 2 | 3 |
17 | 2 | 2 | 10 | 4 | 3 |
1 | 3 | 3 | 20 | 6 | 2 |
5 | 5 | 3 | 15 | 4 | 3 |
19 | 3 | 2 |
算法 | 碳排放成本/元 | 码头运营成本/元 | 总成本/元 |
---|---|---|---|
FCFS | 14 336.9 | 121 671.0 | 136 007.9 |
E-NSGA-Ⅱ | 11 519.4 | 113 801.9 | 125 321.3 |
表5 调度算法的对比
Tab.5 Comparison of scheduling algorithms
算法 | 碳排放成本/元 | 码头运营成本/元 | 总成本/元 |
---|---|---|---|
FCFS | 14 336.9 | 121 671.0 | 136 007.9 |
E-NSGA-Ⅱ | 11 519.4 | 113 801.9 | 125 321.3 |
C2 / (元·h-1) | C3/ (元·km-1) | 碳排放 成本/元 | 码头运营 成本/元 | 总成本/元 |
---|---|---|---|---|
1.22 | 0.012 00 | 8 797.2 | 105 934.6 | 114 731.8 |
1.30 | 0.012 75 | 9 510.6 | 106 873.5 | 116 384.1 |
1.37 | 0.013 50 | 10 246.2 | 108 314.4 | 118 560.6 |
1.45 | 0.014 25 | 10 968.7 | 111 439.6 | 122 408.3 |
1.52 | 0.015 00 | 11 519.4 | 113 801.9 | 125 321.3 |
1.60 | 0.015 75 | 11 525.3 | 115 435.1 | 126 960.4 |
1.68 | 0.016 50 | 12 295.1 | 124 376.7 | 136 671.8 |
1.75 | 0.017 25 | 13 859.7 | 125 634.8 | 139 494.5 |
1.82 | 0.018 00 | 15 381.5 | 126 876.3 | 142 257.8 |
表6 基于碳排放成本变化的敏感性分析
Tab.6 Sensitivity analysis based on changes in carbon emission cost
C2 / (元·h-1) | C3/ (元·km-1) | 碳排放 成本/元 | 码头运营 成本/元 | 总成本/元 |
---|---|---|---|---|
1.22 | 0.012 00 | 8 797.2 | 105 934.6 | 114 731.8 |
1.30 | 0.012 75 | 9 510.6 | 106 873.5 | 116 384.1 |
1.37 | 0.013 50 | 10 246.2 | 108 314.4 | 118 560.6 |
1.45 | 0.014 25 | 10 968.7 | 111 439.6 | 122 408.3 |
1.52 | 0.015 00 | 11 519.4 | 113 801.9 | 125 321.3 |
1.60 | 0.015 75 | 11 525.3 | 115 435.1 | 126 960.4 |
1.68 | 0.016 50 | 12 295.1 | 124 376.7 | 136 671.8 |
1.75 | 0.017 25 | 13 859.7 | 125 634.8 | 139 494.5 |
1.82 | 0.018 00 | 15 381.5 | 126 876.3 | 142 257.8 |
岸桥台时效率/(标准箱·h-1) | 碳排放 成本/元 | 码头运营 成本/元 | 总成本/元 |
---|---|---|---|
35 | 11 519.4 | 113 801.9 | 125 321.3 |
40 | 11 296.6 | 110 643.5 | 121 940.1 |
45 | 11 077.2 | 108 543.7 | 119 620.9 |
50 | 10 965.1 | 105 316.4 | 116 281.5 |
55 | 10 861.3 | 103 871.1 | 114 732.4 |
60 | 10 647.9 | 102 137.8 | 112 785.7 |
75 | 10 437.6 | 98 716.5 | 109 154.1 |
70 | 10 043.1 | 95 675.4 | 105 718.5 |
75 | 9 943.5 | 91 473.9 | 101 417.4 |
80 | 9 846.8 | 87 734.6 | 97 581.4 |
表7 基于岸桥台时效率变化的敏感性分析
Tab.7 Sensitivity analysis based on changes in machine-hour quay crane efficiency
岸桥台时效率/(标准箱·h-1) | 碳排放 成本/元 | 码头运营 成本/元 | 总成本/元 |
---|---|---|---|
35 | 11 519.4 | 113 801.9 | 125 321.3 |
40 | 11 296.6 | 110 643.5 | 121 940.1 |
45 | 11 077.2 | 108 543.7 | 119 620.9 |
50 | 10 965.1 | 105 316.4 | 116 281.5 |
55 | 10 861.3 | 103 871.1 | 114 732.4 |
60 | 10 647.9 | 102 137.8 | 112 785.7 |
75 | 10 437.6 | 98 716.5 | 109 154.1 |
70 | 10 043.1 | 95 675.4 | 105 718.5 |
75 | 9 943.5 | 91 473.9 | 101 417.4 |
80 | 9 846.8 | 87 734.6 | 97 581.4 |
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