﻿ 基于EDA与GA算法的水库群短期防洪优化调度研究 Optimal Operation Research of Reservoirs Short-Time Flood Control Based on EDA and GA Algorithms

Journal of Water Resources Research
Vol.04 No.05(2015), Article ID:16192,9 pages
10.12677/JWRR.2015.45049

Optimal Operation Research of Reservoirs Short-Time Flood Control Based on EDA and GA Algorithms

Wang Zhang1,2, Pan Liu1,2, Zejun Li1,2, Zhuowei Shen1,2, Maoyuan Feng1,2

1State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan Hubei

2Hubei Provincial Collaborative Innovation Center for Water Resources Security, Wuhan Hubei

Email: zhangwang@whu.edu.cn

Received: Sep. 23rd, 2015; accepted: Oct. 7th, 2015; published: Oct. 21st, 2015

ABSTRACT

Since the Muskingum flood routing is used in reservoir operation for short-time flood control, the curse of dimensionality is aggravated due to the time-lags of food routing. In order to solve this problem, a reservoirs optimal flood control operation model is established to minimize the flood peak of the downstream flood control station with the formula of Muskingum as the additional constraints. The Longtan and Bose reservoirs in the Xijiang Basin are used as a case study. The Estimation of Distribution Algorithm (EDA) is proposed to solve the optimal model, and the results are compared with that of the Genetic Algorithm (GA). The experiment demonstrates that the EDA outperforms the GA in terms of the convergence rate and the flood peak reduction.

Keywords:Reservoirs Optimal Operation, Muskingum, Estimation of Distribution Algorithm, Genetic Algorithm

1武汉大学水资源与水电工程科学国家重点实验室，湖北 武汉

2水资源安全保障湖北省协同创新中心，湖北 武汉

Email: zhangwang@whu.edu.cn

1. 引言

2. 水库群短期防洪优化调度问题

2.1. 目标函数

(1)

2.2 约束条件

1) 水量平衡约束

(2)

2) 水库库容约束

(3)

3) 下游河道安全泄量约束

(4)

4) 水库泄流能力约束

(5)

5) 泄量变幅约束

(6)

6) 边界条件约束

(7)

7) 马斯京根流量演算约束

(8)

2.3 滞时问题

3. 优化算法

(9)

(10)

3.1. 遗传算法(GA)

GA算法应用在水库群优化调度中，可直接采用各水库在调度期各时刻的库容或水位进行实数编码，每个染色体是由N*T(N个水库、T个时段)个基因组成。公式(9)的总体目标函数E直接作为适应度函数。GA算法的基本步骤如下：

1) 初始化种群：每个个体的单个基因由该位置对应的特定水库、特定时刻库容上下限范围内，即搜索空间内以均匀分布随机产生；

2) 适应度计算：计算各个染色体的目标函数即适应度函数；

3) 选择运算：水库群调度中选用比例选择和最优保存策略，个体适应度大的被选择的概率高；

4) 交叉运算：把两个父代个体的部分基因结构相互交叉、替换而生成新个体；

5) 变异运算：通过变异引入新的基因，保持种群的多样性，防止早熟；

6) 迭代终止：算法开始计算之前设置迭代终止的进化代数或者达到的精度要求，当迭代达到终止条件的时候停止迭代并输出最优解及对应的最优适应度值。

3.2. 分布估计算法(EDA)

Figure 1. Flow chart of the GA and the EDA

4. 实例研究

4.1. 百色、龙滩并联水库群概况

Figure 2. Flood control reservoirs and cities in the Xijiang River basin

Table 1. Parameters of the Bose and Longtan reservoirs

4.2. 结果对比分析

1) 对比算法的计算效率。比较算法在计算过程中收敛于最优值的速度。

2) 对比最优值大小。通过10次求解最终目标函数值，比较梧州站削峰效果。

3) 对比每次求解结果的变异性。比较10次结果的标准方差和四分位范围。

GA与EDA10次计算平均每一代求解的最优个体适应度值结果如图4所示。

Figure 3. Wuzhou station discharge curve

Figure 4. The average best values of the objective of each generation

Figure 5. The empirical cumulative distribution function

Figure 6. Box plot of the best solution

EDA10次计算得到的最优结果的标准方差为522,385.3，而GA10次计算得到的最优结果标准方差为174,108，EDA结果的标准方差大。图6是EDA和GA的最优结果四分位分布图，图中看出EDA的四分位范围比GA范围大。由标准差和箱状图结果可知，EDA求解的最优结果离散程度高，但即使最差的解，也与GA最优解相当。

5. 结论

Optimal Operation Research of Reservoirs Short-Time Flood Control Based on EDA and GA Algorithms[J]. 水资源研究, 2015, 04(05): 395-403. http://dx.doi.org/10.12677/JWRR.2015.45049

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