污水下水道管網系統規劃設計最佳化模式之研究

A Study on Optimization Models for sewer Systems Planning and Design

翁煥廷(Huahn-Tyng Weng)

指導教授 ： 廖述良

國立中央大學/工學院/環境工程研究所/博士(2006年)

摘要

最佳化污水管網系統方案，較符合投資成本效益。傳統人工設計方法，僅能對少數的替代方案評估，無法保證是最佳的設計結果, 啟發電腦化的污水系統規劃設計最佳化模式方面之探討。本研究乃根據經驗工程師規劃設計程序，以系統分析方法，分成兩階段來發展實用的「污水管網系統規劃與設計最佳化模式」： (1) 首先，建置「都市污水下水道系統水力設計最佳化模式(SSOM)」，並發展為通用的水理分析模組。主要係在「固定配置」系統下，求取最小成本管徑與管線坡度，採用0-1整數規劃（MIP）方法建構最佳化模式，運用簡單又有效率的「界限隱式列舉法(BIE)」達成最佳化演算，特別考量的是提供一套設計變數，可因應都市污水管網設計問題，選用各種不同施工工法；(2)接著，建置「污水管網系統配置最佳化模式(SSOM/LH)」，係在「非固定配置」系統下，考量計畫區域的人口、流量、街區和地形等，鋪設廢污水收集及輸送的管網系統，求解最佳化「系統配置」的目標。
SSOM/LH被建構為組合演算模式，先以全列舉法(TE)演算「管網配置」產生程序，結合已發展SSOM通用模組，作為最佳化水力設計程序，並共同執行此篩選求解程序，可同時達成最佳化「管線配置與水力設計」，且保證求解為「全域最佳解」；然而，最佳化搜尋過程，產生「管網配置」的組合數，隨著「人孔階段數」增加，以指數函數關係增加，當系統太龐大時，卻面臨N-P complete問題。為改善以上SSOM/LH之時效性問題，乃應用遺傳演算法(GA)重新建置污水管網系統配置最佳化模式(GA/SSLOM)。GA的演化程序，係採「整個管網系統」為最佳化之演算子代，以「一條染色體」表示「一個系統配置」，二元編碼方式排成一條字串，直接演化此字串參數，得到較佳的系統配結果，可確保更「快速」接近全域的最佳解，但存在可能產生局部最佳解之問題。
本研究首次應用「混合演算法」的概念，建構「2-混合污水管網系統配置最佳化模式」(2-Hybrid SSLOM)，將包含上述已發展完成的兩個「污水管網系統配置最佳化模式」之特點，以一個混合執行程式，達成最小成本的目標。最後，經由幾個研究案例之推導，驗證本研究發展的2-Hybrid SSLOM，確實比SSOM/LH更有效率的搜尋得到全域最佳解，未來可發展為污水系統規劃模式，方便使用於解決較複雜管線系統最佳化的問題。

關鍵字

界限隱式列舉法 ； 遺傳演算法 ； 多階段多選項系統 ； 系統配置 ； 混合演算 ； 水力設計

並列摘要

The optimal design of new sewer systems becomes an important issue for the necessary of cost-effectiveness analysis. However the result of traditional design approach is only a very small number of the alternatives can be evaluated; therefore the final design is sometimes deficient and there is no guarantee that it is the best design. This has more inspired the research on computerized optimization models for sewer systems planning and design. In this study, according to the design procedure of experience engineer, the practical Optimization Models for Sewer Systems Planning and Design are developed with system analysis approach and divided into two phases: (1) at first, an urban Sewer System Optimization Model (SSOM) for hydraulic design is established and has become a general module for being applied to hydraulic design, which can be employed to determine the size and slope of the sewer pipes for a “fixed layout” sewer system design problem. The SSOM model uses a 0-1 mixed integer programming (MIP) and an efficient screening algorithm, the bounded implicit enumeration (BIE) algorithm. The particular consideration is to provide a set of design variables for urban sewer system design problems corresponding to the various construction modes; and (2) then the Sewer System Optimization Model for Layout & Hydraulic design
(SSOM/LH) is established to find the optimal “system layout” for an “unfixed layout” sewer system. The goal of the optimal system layout process is to arrange a network of sewer pipes for collecting and transporting the wastewater considering the populations, the discharge flow-rate, street layout and topography of the area. Thus, the SSOM/LH was constructed as a combinatorial model to combine the Total Enumeration (TE) algorithm for a “network layout” generating procedure with the general module of developed SSOM for an optimal hydraulic design procedure. Both of the procedures perform a screening role to achieve the optimization of the “network layout” and “hydraulic design” simultaneously, and ensuring ensure that the solution obtained is globally optimal. However, in the search for optimality, the number of feasible network layout combinations increases exponentially as the number of manholes increases. This would predictably lead to an N-P complete problem if a huge sewer system is planned. To remedy the flaws in SSOM/LH, a genetic algorithm (GA) will be applied to reestablish this optimization model namely GA/SSOM/LH. “one system layout parameter in the GA evolutionary process is coded to represent one chromosome”. The specific coding strings for the “parameters” are then operated directly, resulting in a more efficient search for the optimal sewer system layout and ensuring a solution closer to the global optimum in a ‘fast’ manner. The optimality of GA/SSLOM obtained could possibly be in a local optimum.
In this study, a concept of hybrid algorithm is first applied to establish a Two-Hybrid Sewer System Layout Optimization Model (2-Hybrid SSLOM) involving this couple of developed model’s advantages in a hybrid role for the minimum cost objective. Finally, several of case studies are conducted to verify that this developed 2-Hybrid SSLOM can indeed search for the global optimum solution with the more increased efficiency than SSOM/LH and develop as a future sewer system planning model for the convenience of solving more complicated pipeline system optimization problems.

並列關鍵字

system layout ； hydraulic design ； bounded implicit enumeration algorithm ； hybrid algorithm ； genetic algorithm ； multi-stage multi-option system

參考文獻

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