基因演算法於污水下水道管網系統管徑組合最佳化之應用

Diameter Combinations Optimization of Sewage Network System with Genetic Algorithms

吳春生(Chun-Sheng Wu) ； 翁建華(Chien-Hua Weng)

《立德學報》 3卷2期 (2006/06) Pp. 39-54

https://doi.org/10.7080/JLU.200606.0039

摘要

本研究於管網埋設路線既定之前提下，建立污水收集系統數學模式，利用MATLAB(上標 ®) 7.0版自行撰寫公認適於搜尋較龐大系統之最佳解的基因演算法(Genetic Algorithms, GAs)的程式，並且使用格雷碼(gray code)編碼、競爭挑選法(Tournament selection, TS)、均等交配(uniform crossover)與倒置突(inverse mutation)等運算元，以改善傳統基因演算法編碼精確度不足與收斂速度緩慢的缺點。將族群大小、交配率和突變率三項參數交叉組合，每一組合都進行世代數10000的搜尋，從中選定尋優效果最佳的一組，得出最經濟的最佳管徑組合，及相關完全符合水力設計準則的管渠水力設計資料。結果顯示，本研究之建造經費約較研究案例低5.2%，足以證明將GAs優異的尋優能力應用於污水下水道管網系統管徑組合之最佳化的確具有不錯的效果。

關鍵字

基因演算法 ； 污水下水道 ； 最佳化 ； 管網系統

並列摘要

A mathematical model on sewage network systems was developed based on the current pipeline networks. In the model, a Genetic Algorithms (Gas) based program, which was considered to be best suited for large system optimization, was constructed with 7.0 edition of MATLAB. Furthermore, gray code and operators of tournament selection, uniform crossover, and inverse mutation were adopted to improve problems' inaccurate encoding and slow convergence, commonly found in traditional GAs. The three parameters, population size, crossover probability and mutation probability were cross-combined in calculation for 10000 generations in searching for the best combination, the least-cost pipe diameter combinations, and related design data were obtained which a re consistent with those acquired by hydraulic design standards. In comparison with the total cost of conventional design, the best GAs design achieved a cost saving of 5.2 percent in this study. The GAs was validated its excellence in optimization. Accordingly, the application of GAs has shown great effectiveness on determining the optimization of pipe diameters combinations in sewage network systems.

並列關鍵字

Genetic Algorithms ； Sewage Systems ； Optimization ； Network Systems