天然气管网稳态运行优化模型的非线性界增强方法

doi:10.15960/j.cnki.issn.1007-6093.2024.01.008

运筹学学报 ›› 2024, Vol. 28 ›› Issue (1): 101-111.doi: 10.15960/j.cnki.issn.1007-6093.2024.01.008

天然气管网稳态运行优化模型的非线性界增强方法

张晴¹, 陈亮³, 艾文宝¹^,², 寇彩霞¹^,²^,*()

1. 北京邮电大学理学院, 北京 100876
2. 数学与信息网络教育部重点实验室(北京邮电大学), 北京 100876
3. 中国科学院数学与系统科学研究院, 北京 100190

收稿日期:2022-03-25 出版日期:2024-03-15 发布日期:2024-03-15
通讯作者: 寇彩霞 E-mail:koucx@bupt.edu.cn
基金资助:
国家自然科学基金(11971073);国家自然科学基金(12171052);国家自然科学基金(12201620)

A nonlinear bound strengthing method for the steady-state operation optimization model of gas pipeline networks

Qing ZHANG¹, Liang CHEN³, Wenbao AI¹^,², Caixia KOU¹^,²^,*()

1. College of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China
2. Laboratory of Mathematics and Information Networks of Ministry of Education(Beijing University of Posts and Telecommunications), Beijing 100876, China
3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received:2022-03-25 Online:2024-03-15 Published:2024-03-15
Contact: Caixia KOU E-mail:koucx@bupt.edu.cn

摘要/Abstract

摘要：

天然气管网稳态运行优化问题在提升能源使用效率、降低运行成本等多方面发挥着重要的作用。该问题由于网络结构复杂、规模大、非线性程度高, 所以建模成的混合整数非线性规划模型求解难度非常大。本文基于混合整数线性规划的界增强方法, 提出了适用于该问题结构的非线性界增强方法, 能够缩紧变量的上下界, 使得在线性化方法中更好地逼近原混合整数非线性规划模型。数值结果显示新的方法能够得到更优的可行解, 并且加快了天然气管网稳态运行优化问题的求解。

关键词: 天然气管网运行优化, 混合整数非线性规划, 界增强方法

Abstract:

The gas pipeline network steady-state operation optimization problem plays an important role in improving energy use efficiency and reducing operation cost in many aspects. It is extremely challenging to solve its mixed integer nonlinear programming model, because of the complex network structure, large scale and high nonlinearity. In this paper, based on the bound strengthing method of mixed integer linear programming, we propose a nonlinear bound strengthing method for the structure of this problem, which can tighten the upper and lower bounds of variables and more approximate to the original mixed integer nonlinear programming model in the linearization method. Numerical results show that this method can obtain better feasible solutions and speed up the solution of the optimization problem for the steady-state operation of gas pipeline networks.

Key words: gas pipeline network operation optimization, mixed integer nonlinear programming, bound strengthing method

中图分类号:

O221

张晴, 陈亮, 艾文宝, 寇彩霞. 天然气管网稳态运行优化模型的非线性界增强方法[J]. 运筹学学报, 2024, 28(1): 101-111.

Qing ZHANG, Liang CHEN, Wenbao AI, Caixia KOU. A nonlinear bound strengthing method for the steady-state operation optimization model of gas pipeline networks[J]. Operations Research Transactions, 2024, 28(1): 101-111.

图/表 3

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区间个数	无界增强			有界增强
$ q*T $	耗气量/($ {\rm m^{3}\cdot d^{-1}} $)	时间/s	迭代次数	耗气量/($ {\rm m^{3}\cdot d^{-1}} $)	时间/s	迭代次数
$ 8*2 $	22 599.52	7.88	5	22 086.85	2.50	3
$ 8*6 $	22 735.79	4.83	3	22 530.23	4.19	3
$ 8*12 $	22 935.86	5.75	5	22 693.73	4.41	4
$ 16*2 $	22 567.87	7.30	6	22 053.90	3.80	3
$ 16*6 $	22 721.67	5.77	3	22 307.06	9.59	6
$ 16*12 $	22 929.92	62.31	4	22 566.93	45.04	5
$ 32*2 $	22 234.35	14.26	8	22 091.72	7.15	4
$ 32*6 $	22 357.72	4.70	2	22 131.44	9.55	4
$ 32*12 $	22 699.35	93.15	5	22 257.01	53.37	4

天然气管网稳态运行优化模型的非线性界增强方法

A nonlinear bound strengthing method for the steady-state operation optimization model of gas pipeline networks

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