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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (1): 92-96.  DOI: 10.11908/j.issn.0253-374x.2019.01.012 0

### 引用本文

TAO Tao, XIAO Tao, WANG Linsen, YAN Hexiang. Multi-objective Optimization Design of Low-impact Development Plan in Sponge City Construction[J]. Journal of Tongji University (Natural Science), 2019, 47(1): 92-96. DOI: 10.11908/j.issn.0253-374x.2019.01.012

### 文章历史

Multi-objective Optimization Design of Low-impact Development Plan in Sponge City Construction
TAO Tao , XIAO Tao , WANG Linsen , YAN Hexiang
College of Environmental Science and Engineering, Tongji University, Shanghai 200092, China
Abstract: In order to reduce the economic cost effectively and maximize the effect of low-impact development technology in the low-impact development technology design, the total cost of low impact development program is taken as the objective function of economic judgment, and with the volume capture ratio of annual rainfall as the control target, the area of low-impact development as a constraint, the multi-objective optimization mathematical model of low-impact development was established, and the non-dominated sorting genetic algorithms-Ⅱ(NSGA-Ⅱ) was used to solve the multi-objective mathematical model analysis. Finally, a case study was made of a low-impact development project and the Pareto optimal curves of the total cost and the volume capture ratio of annual rainfall was obtained, which could provide decision-makers with multiple sets of different optimization schemes. The combination of low-impact development technologies was more scientific for a clear and reasonable decision-making.
Key words: low-impact development    multi-objective optimization    non-dominated sorting genetic algorithms-Ⅱ (NSGA-Ⅱ)

1 低影响开发多目标优化设计模型构建

 图 1 低影响开发多目标优化 Fig.1 Schematic diagram for low-impact development multi-objective optimization
1.1 年径流总量控制率 1.1.1 设计降雨量的计算

 $V = 10H\varphi F$ (1)

 $V = {V_{\text{s}}} + {W_{\text{p}}}$ (2)

 ${W_{\text{p}}} = KJ{A_{\text{s}}}{t_{\text{s}}}$ (3)

 $H = \frac{{{V_{\text{s}}} + KJ{A_{\text{s}}}{t_{\text{s}}}}}{{10\varphi F}}$ (4)

1.1.2 年径流总量控制率的推求

 图 2 上海市设计降雨量和年径流总量控制率关系曲线 Fig.2 The curve of the relationship between the design precipitation and the volume capture ratio of annual rainfall in Shanghai
1.2 低影响开发技术总费用

 $z = \left( {a + b} \right) \times {s_{{\text{brc}}}} + \left( {c + d} \right) \times {s_{{\text{pp}}}}$ (5)

1.3 约束条件

 $\left\{ \begin{gathered} 0 \leqslant {s_{{\text{brc}}}} \leqslant {A_{{\text{brc}}}} \hfill \\ 0 \leqslant {s_{{\text{pp}}}} \leqslant {A_{{\text{pp}}}} \hfill \\ \end{gathered} \right.$ (6)

2 模型求解

(1) 首先在可行解域内产生个体规模为N的初始种群P0;

(2) 对初始种群进行交叉和变异操作产生N个子代;

(3) 将N个父代和N个子代合并, 并进行非支配排序和计算拥挤度;

(4) 根据每个个体的非支配排序等级和拥挤度选出N个个体组成新的父代种群P1;

(5) 重复过程(2)~(4), 直到遗传代数满足设定的要求.

NSGA-Ⅱ算法流程如图 3所示.NSGA-Ⅱ对于解决多目标优化问题是一种有效的解决方法, 但算法本身的参数对结果有着很大的影响.在应用该方法解决问题时, 需要合理的设定种群规模、遗传代数、交叉和变异操作的概率以保证最终获取的曲线接近于Pareto最优, 在每一步交叉和变异操作过程中应当考虑新生子代是否满足约束条件.

 图 3 年径流总量控制率与总费用优化算法流程 Fig.3 Optimization algorithm flow chart of the volume capture ratio of annual rainfall and total cost
3 工程案例

LID设施的参数设置参照SWMM模型用户手册[14], 生物滞留单元蓄水层厚度取300mm, 孔隙比取0.6, 渗透系数K取1.51×10-5m·s-1, 透水铺装的径流系数取0.2.当每种低影响开发雨水设施的设计参数确定后, 设计降雨量可以认为仅是面积函数, 利用式(4)可求得该区域不同LID设施面积对应的设计降雨量, 然后利用图 2可计算相应的年径流总量控制率.上述两个目标函数可表示为

 $\begin{gathered} \min z = \left( {470 + 40} \right) \times {s_{{\text{brc}}}} + \left( {160 + 8} \right) \times {s_{{\text{pp}}}} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\max y = f\left( {{s_{{\text{brc}}}}, {s_{{\text{pp}}}}} \right) \hfill \\ \end{gathered}$

 图 4 年径流总量控制率与总费用的Pareto最优曲线 Fig.4 Pareto optimal curve of the volume capture ratio of annual rainfall and total cost

4 结论

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