铁路施工多目标均衡优化模型与改进NSGA-Ⅲ算法

张燕; 刘佶祯; 秦佳良; 杨兰; 张洪

doi:10.19818/j.cnki.1671-1637.2024.04.013

铁路施工多目标均衡优化模型与改进NSGA-Ⅲ算法

doi: 10.19818/j.cnki.1671-1637.2024.04.013

1.
华东交通大学土木建筑学院，江西南昌 330013
2.
华东交通大学交通运输工程学院，江西南昌 330013

基金项目:

国家重点研发计划 2022YFB2602200

详细信息

作者简介:
张燕(1974-)，女，贵州遵义人，华东交通大学副教授，从事铁路工程项目优化研究

中图分类号: U29
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- 被引次数: 0
出版历程
- 收稿日期: 2024-03-15
- 网络出版日期: 2024-09-26
- 刊出日期: 2024-08-28

Multi-objective equilibrium optimization model and improved NSGA-Ⅲ algorithm of railway construction

1.
School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, Jiangxi, China
2.
School of Transportation Engineering, East China Jiaotong University, Nanchang 330013, Jiangxi, China

Funds:

National Key Research and Development Program of China 2022YFB2602200

More Information

Author Bio:
ZHANG Yan(1974-), female, associate professor, 893872972@qq.com

摘要

摘要: 分析了铁路基础设施建设施工方案的特点、优化模型与优化算法，绘制双代号网络图，以工序所需时间为自变量计算了总工期，提出一种考虑资金时间价值的施工成本计算方法；引入系统可靠性理论对施工质量进行量化评估，探讨施工质量安全水平与时间、成本之间相互关系，计算了施工质量安全水平，提出铁路基础设施施工质量-安全-工期-成本多目标均衡优化模型；引入随机整数基因编码方式与惩罚函数法改进NSGA-Ⅲ算法，以求得模型的帕累托解集，对比了改进NSGA-Ⅲ算法与NSGA-Ⅱ算法的求解性能，并利用轨道工程施工案例对模型进行验证。分析结果表明：设定种群数量为140，迭代次数为900，试验次数为40时，改进NSGA-Ⅲ算法对NSGA-Ⅱ算法的每代平均覆盖率均值比算法NSGA-Ⅱ对改进NSGA-Ⅲ算法的每代平均覆盖率均值提高了将近27倍，改进NSGA-Ⅲ算法的每代平均超体积均值比NSGA-Ⅱ算法的每代平均超体积均值提高了将近54%，表明改进NSGA-Ⅲ算法明显优于传统的NSGA-Ⅱ算法；提出的铁路施工多目标均衡优化模型与改进NSGA-Ⅲ算法能很好地适用于铁路施工管理的多目标均衡优化，在轨道工程施工案例中，当设定种群数量为140，迭代次数为900，每个维度上参考点个数为8时，求解得到140个帕累托解，其中质量水平最大优化0.112 1，安全水平最大优化0.107 3，工期最大优化36 d，成本最大优化将近720万元，可以更好地指导决策者进行施工安排。
- 铁路基础设施 /
- 施工方案 /
- 多目标均衡优化模型 /
- 改进NSGA-Ⅲ算法 /
- 算法对比
Abstract: The characteristics, optimization models and optimization algorithms of railway infrastructure construction schemes were analysis, the double code-network diagrams were drawn, the time required for the construction process was taken as independent variable, and a method for calculating the construction cost was proposed under considering the time cost of capital. The system reliability theory was introduced to quantitatively assess the construction quality, the interrelationship between the safety level, time and cost of construction quality was explored, the safety level was calculated, and a multi-objective equilibrium optimization model of quality-safety-duration-cost for railway infrastructure construction was put forward. The NSGA-Ⅲ algorithm was improved by introducing the random integer genetic coding method and penalty function method to solve the Pareto solution set of the model, the solution performance of the improved algorithm was compared with the NSGA-Ⅱ algorithm, and the model was verified by using a railway construction case. Analysis results show that when the population number is 140, the iteration number is 900, and the test number is 40, the average coverage rate per generation of the improved NSGA-Ⅲ algorithm to the NSGA-Ⅱ algorithm is nearly 27 times higher than that of the NSGA-Ⅱ algorithm to the improved NSGA-Ⅲ algorithm, and the mean supervolume per generation of the improved NSGA-Ⅲ algorithm is nearly 54% higher than that of the NSGA-Ⅱ algorithm, therefore, the improved NSGA-Ⅲ algorithm is obviously superior to the traditional NSGA-Ⅱ algorithm. The proposed model and improved NSGA-Ⅲ algorithm are well applied to the multi-objective equilibrium optimization of railway construction management. In the construction case of track engineering, when the population number is 140, the iteration number is 900, and the reference point number in each dimension is 8, 140 Pareto solutions are obtained, and the maximum optimizations of quality level, safety level, duration and cost of the engineering are 0.1121, 0.1073, 36 days and nearly 7.2 million yuan, which can better guide the decision makers to arrange the construction.
- railway infrastructure /
- construction scheme /
- multi-objective equilibrium optimization model /
- improved NSGA-Ⅲ algorithm /
- algorithm comparison

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图 1 工序直接成本与时间关系

Figure 1. Relationship of direct cost and time of procedure

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图 2 工序质量水平与时间关系

Figure 2. Relationship of quality level and time of procedure

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图 3 工序安全水平与时间关系

Figure 3. Relationship of safety level and time of procedure

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图 4 工序的安全水平与成本关系

Figure 4. Relationship of safety level and cost of procedure

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图 5 基因编码结构

Figure 5. Genetic coding structure

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图 6 铁路基础设施施工多目标均衡优化模型在NSGA-Ⅲ算法中实现流程

Figure 6. Implementation process of multi-objective equilibrium optimization model of railway infrastructure construction in NSGA-Ⅲ algorithm

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图 7 某铁路轨道工程项目双代号网络

Figure 7. Double-code network of a railway track engineering project

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图 8 工期-成本二维散点图

Figure 8. Duration-cost 2D scatter plot

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图 9 工期-质量二维散点图

Figure 9. Duration-quality 2D scatter plot

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图 10 工期-成本-安全三维散点图

Figure 10. Duration-cost-safety 3D scatter plot

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图 11 平均覆盖率对比

Figure 11. Comparison of average coverages

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图 12 平均超体积对比

Figure 12. Comparison of average supervolumes

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表 1 工序数据与参数

Table 1. Data and parameters of procedures

工序编号	工序名称	t_{s, i}/d	t_{n, i}/d	t_{max, i}/d	C_{n, i}/万元	φ_i	Q_{max, i}	R_{min, i}	R_{max, i}
A	站1至站2左线铺轨	6	8	10	216.8	1.1	0.87	0.05	0.07
B	站1至站2右线铺轨	6	8	10	216.8	1.1	0.87	0.05	0.07
C	站1至站2左线焊接、应力放散与锁定	8	10	12	81.5	1.3	0.89	0.10	0.14
D	站1至站2右线焊接、应力放散与锁定	8	10	12	81.5	1.3	0.89	0.10	0.14
E	站1至站2全线轨道精调	13	15	17	472.7	1.5	0.90	0.08	0.13
F	站2至站3右线铺轨	7	9	11	289.6	1.3	0.90	0.06	0.08
G	站2至站3左线铺轨	7	9	11	289.6	1.3	0.90	0.06	0.08
H	站2至站3右线焊接、应力放散与锁定	10	12	14	108.9	1.6	0.85	0.10	0.13
I	站2至站3左线焊接、应力放散与锁定	10	12	14	108.9	1.6	0.85	0.10	0.13
J	站2至站3全线轨道精调	18	20	22	631.5	1.8	0.83	0.05	0.10
K	站3至站4左线铺轨	8	10	12	302.4	1.5	0.86	0.06	0.09
L	站3至站4右线铺轨	8	10	12	302.4	1.5	0.86	0.06	0.09
M	站3至站4左线焊接、应力放散与锁定	10	12	14	113.7	1.8	0.88	0.10	0.15
N	站3至站4右线焊接、应力放散与锁定	10	12	14	113.7	1.8	0.88	0.10	0.15
O	站3至站4全线轨道精调	19	21	23	659.5	2.0	0.93	0.06	0.12

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表 2 试验1结果

Table 2. Result of experiment 1

维度参考点个数	6	8	10
评价指标平均值	58 161.62	58 286.84	57 655.54

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表 3 试验2结果

Table 3. Result of experiment 2

种群数量	120	130	140
评价指标平均值	50 087.15	50 132.94	58 286.84

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表 4 部分帕累托解集

Table 4. Partial Pareto solution sets

方案编号	工期/d	成本/万元	质量水平	安全水平
1	103	3 616.7	0.918 8	0.946 9
2	119	3 480.5	0.898 7	0.937 3
3	118	3 604.6	0.962 1	0.956 9
4	115	3 617.0	0.960 4	0.957 3
5	99	3 613.7	0.880 0	0.935 7
6	126	3 482.5	0.944 0	0.947 1
7	121	3 540.3	0.960 7	0.956 6
8	113	3 623.3	0.958 4	0.957 0
9	100	3 600.2	0.880 5	0.935 7
10	117	3 483.0	0.905 6	0.938 4

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