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浙江大学学报(工学版)
浙江大学学报(工学版)  2023, Vol. 57 Issue (12): 2501-2512    DOI: 10.3785/j.issn.1008-973X.2023.12.017
土木工程、水利工程     
基于改进哈里斯鹰算法的梯级泵站优化调度
张雷克1(),侯笑鹏1,刘小莲1,*(),田雨2
1. 太原理工大学 水利科学与工程学院，山西 太原 030024
2. 中国水利水电科学研究院 流域水循环模拟与调控国家重点实验室，北京 100038
Optimal scheduling of cascade pumping stations based on improved Harris hawks optimization algorithm
Lei-ke ZHANG1(),Xiao-peng HOU1,Xiao-lian LIU1,*(),Yu TIAN2
1. College of Water Resources Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
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摘要：

为了提高梯级泵站系统运行效率，节约工程运行成本，以梯级泵站运行效率最大化为目标，建立梯级泵站优化调度模型，提出基于改进哈里斯鹰算法（HUHHO）的梯级泵站优化调度方法. 将饥饿率引入哈里斯鹰算法（HHO）以更好地实现探索与开发之间的平衡；在探索阶段添加1个偏移项以考虑哈里斯鹰饥饿感强弱对搜寻猎物能力的影响，提高算法的寻优能力、避免陷入局部最优. 通过基准测试函数验证HUHHO寻优性能的优越性. 将HUHHO应用于北京市某三级泵站优化调度中，对HUHHO求解梯级泵站优化调度问题的可行性与有效性进行验证. 结果表明：相较于现状方案，基于HUHHO的优化方案可使梯级泵站运行效率提高0.11个百分点，年运行成本节约42 187元，优于利用粒子群优化算法（PSO）、遗传算法（GA）、HHO得到的运行效率及节约成本.
关键词： 梯级泵站;  优化调度;  经济运行;  改进哈里斯鹰算法（HUHHO）;  大系统;  分解协调模型    
Abstract:

The optimal operation model of cascade pumping stations was established with the objective function of maximizing the total operation efficiency. An optimized scheduling method based on improved Harris hawks optimization (HUHHO) was proposed to raise the operation efficiency of the system and save the cost. Firstly, the starvation rate was introduced in order to control the balance between exploration and exploitation. Secondly, considering the effect of hunger intensity on prey hunting ability, an offset item was added in the exploration stage to enhance the search capability and avoid falling into the local optimum. Then, the superior performance of HUHHO was demonstrated by the benchmark functions. In addition, the proposed method was applied to the optimal operation of a three-stage pumping station in Beijing. Finally, the feasibility and effectiveness of HUHHO for solving the optimal scheduling problem in cascade pumping stations were verified. Results show that compared with the current scheme, the optimization scheme based on HUHHO can increase the operation efficiency of the system by 0.11 percentage points and save 42 187 yuan in annual operating costs, which are better than those obtained by using particle swarm optimization (PSO), genetic algorithm (GA) and Harris hawks optimization (HHO).
Key words: cascade pumping station    optimal scheduling    economic operation    improved Harris hawks optimization algorithm (HUHHO)    large-scale system    decomposition-coordination model
收稿日期: 2023-02-06 出版日期: 2023-12-27
CLC:  TV 675  
基金资助: 国家重点研发计划项目(2021YFC3001000)；国家自然科学基金资助项目(51879273)
通讯作者: 刘小莲     E-mail: zhangleike@tyut.edu.cn;liuxiaolian@tyut.edu.cn
作者简介: 张雷克（1984—），男，副教授，从事水工建筑物稳定性分析研究. orcid.org/0000-0003-1840-9579. E-mail： zhangleike@tyut.edu.cn
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引用本文:

张雷克,侯笑鹏,刘小莲,田雨. 基于改进哈里斯鹰算法的梯级泵站优化调度[J]. 浙江大学学报(工学版), 2023, 57(12): 2501-2512.

Lei-ke ZHANG,Xiao-peng HOU,Xiao-lian LIU,Yu TIAN. Optimal scheduling of cascade pumping stations based on improved Harris hawks optimization algorithm. Journal of ZheJiang University (Engineering Science), 2023, 57(12): 2501-2512.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.12.017    或    https://www.zjujournals.com/eng/CN/Y2023/V57/I12/2501

图 1  梯级泵站优化调度模型结构图
图 2  改进哈里斯鹰算法的算法流程图
算法 Rastrigin Ackley Foxholes Kowalik
Mean Std Mean Std Mean Std Mean Std
PSO 4.014×10 9.711 4.856 9.542×10?1 1.950 1.495 8.020×10?4 3.957×10?4
GA 1.098×10 2.267 2.942 2.046×10?1 1.576 1.526 1.631×10?2 1.988×10?2
GWO 2.802 3.459 1.053×10?13 1.658×10?14 3.935 4.106 3.730×10?3 7.568×10?3
HHO 0 0 1.007×10?15 6.486×10?16 1.164 3.768×10?1 4.138×10?4 2.468×10?4
HUHHO 0 0 8.882×10?16 0 1.031 1.815×10?1 4.048×10?4 2.035×10?4
表 1  不同算法优化性能测试
图 3  不同算法在测试函数中的收敛过程曲线
图 4  基于改进哈里斯鹰算法的梯级泵站优化调度模型求解流程图
图 5  某三级泵站工程平面图
泵站 Ht/m h/m Qj，k/（m3·s?1） ηj, k Hn h/Hn ηj,max/% ηc,max/%
k=1 k=2 k=3 k=1 k=2 k=3
1 1.03 6.47 6.47 6.47 0.37 0.37 0.37 37.04
0.51
2 1.60 6.47 6.47 6.47 0.51 0.51 0.51 4.84 0.33 51.00 34.09
0.11
3 2.21 6.47 6.47 6.47 0.63 0.63 0.63 62.66
表 2  某三级泵站调水系统现状方案表
图 6  基于不同算法的优化效果对比
优化方案 泵站 Ht/m h/m Qj，k/（m3·s?1） ηj, k Hn/m h/Hn ηj,max/% ηc,max/%
k=1 k=2 k=3 k=1 k=2 k=3
基于PSO 1 1.04 6.30 6.80 6.30 0.36 0.39 0.36 4.84 0.334 5 37.31 34.11
0.56
2 1.62 6.80 6.80 5.80 0.54 0.54 0.46 51.64
1.06
3 2.18 6.50 6.40 6.50 0.62 0.61 0.62 61.92
基于GA 1 1.14 6.30 6.58 6.52 0.40 0.42 0.41 4.79 0.327 3 41.17 34.12
0.52
2 1.45 6.80 6.37 6.23 0.49 0.46 0.45 46.29
1.05
3 2.19 6.49 6.49 6.41 0.62 0.62 0.62 62.20
基于HHO 1 1.12 6.98 6.34 6.08 0.43 0.40 0.38 4.80 0.328 6 40.29 34.15
0.56
2 1.50 6.30 6.58 6.52 0.47 0.49 0.49 48.24
1.02
3 2.17 6.60 6.40 6.40 0.63 0.61 0.61 61.50
基于HUHHO 1 1.23 6.47 6.47 6.7 0.45 0.45 0.45 4.74 0.320 8 44.71 34.20
0.44
2 1.31 6.43 6.47 6.50 0.41 0.42 0.42 41.70
1.08
3 2.20 6.50 6.41 6.49 0.63 0.62 0.63 62.47
表 3  基于不同优化算法的梯级泵站优化结果
图 7  哈里斯鹰算法改进前后收敛过程对比
N ηc,max
Th=50、Tq=50 Th=100、Tq=50 Th=50、Tq=100 Th=100、Tq=100 Th=100、Tq=150 Th=150、Tq=150
30 0.341 6 0.342 0 0.342 0 0.342 0 0.342 1 0.342 2
50 0.341 6 0.342 1 0.342 1 0.342 1 0.342 3 0.342 3
100 0.341 8 0.342 2 0.342 2 0.342 2 0.342 4 0.342 4
150 0.342 0 0.342 4 0.342 4 0.342 5 0.342 5 0.342 5
表 4  改进哈里斯鹰算法于不同种群规模与最大迭代次数下的优化结果
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