建議

1. 本研究發展之地下水量即時管理模式，可進一步發展為污染整治管理模式。因對 於水質問題，污染物濃度因受抽水行為影響，應採用同時考慮抽水與監測之容量 擴張方式設井。

2. 本研究以遺傳演算法(GA)優選不連續變數(井位)，再以退火演算法(SA)優選連續 變數(時變抽水量)，類似遺傳演算法及退火演算法這類啟發式演算法，在於其容 易應用於各種類型的問題，且能同時優選連續與不連續變數，再配合平行運算，

將可應用於求解各類複雜地下水管理問題上。

3. 可將地下水模擬模式不確定性視為另一目標函數，建立同時考量系統不確定性及 總成本二個目標函數之優選模式，並可由多目標遺傳演算法進行解題。

4. 建議於地下水模擬模式之更新機制中，加入由水位監測值逆推水文地質參數。

5. 本研究發展之模式可作為決定原有監測井網設置之工具，可先依第 1 階段初規劃 策略，先設置第 1 階段之監測井，以作為原有之監測井網，使得初始條件之原有 監測井網有較合理之佈設。

6. 本模式在實際應用上，可能會有因考量利率甚低，而提早設置較多之抽水井與監 測井，為以避免提早設置過多之抽水井與監測井，而失去重新調整井網之彈性，

可增加各抽水井之抽水量下限值，以限制模式在早期設井階段不會設置過多之抽 水井。

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附錄 A 遺傳演算法(Genetic algorithm) z 遺傳演算法之介紹

遺傳演算法的理論基礎可回溯自 1859 年達爾文（Charles Darwin）的「物種 演化」（On the Origin of Species by Means of Nature Selection）書中的「物競天擇，

適者生存」的演化及淘汰觀念。在這種由自然選擇的演化機制中，生物界中的每 個個體會把它們的特徵傳遞到下一代，而生物的特徵是由生物細胞內的染色體來 決定的（染色體即是由基因所組成的基因鏈），由於每個個體的特徵都不大相同，

因此不同特徵的個體對環境的適應力也不大一樣，同時生物的突變及交配也會使 得上下代個體之特徵不相同，而適應力較高的個體，即它們的特徵較適合於目前 的環境，在後代的數目上由於競爭的緣故，適應力較高的個體的後代數目會比適 應力較低的後代數目多，因此這會把整個族群的特徵引導向更適合生存於自然環 境的方向發展，在長時間中，這種引導所發生的變異會越來越累積，最後演變至 產生一整個特徵能適應於特別生態環境下的種族。

將這種自然界的選擇方法系統化並發展一可用之模式最早是由密西根大學 的 John Holland 教授在 1975 年於 Adaption in Natural and Artificial System 文中所 提出，發展出遺傳演算法搜尋技術的基本架構，並且由其學生 David Goldberg 成 功地運用在工程問題上。之後，有許多研究亦證實了遺傳演算法在最佳化問題的 求解上是十分有效率的，其有以下幾個優點：

1. 其可優選連續（continuous）及不連續（discrete）的參數。

2. 在優選的過程中，不需要求得目標函數的導數。

3. 搜尋的方式不同於以往的單點搜尋方式，而是採用多點搜尋，因此不容易掉入 局部解（local optimum）。

4. 可以處理多參數的優選問題。

5. 具有隱平行運算的能力，若在平行電腦中，可大量節省運算的時間。

6. 在優選複雜非線性的問題中，其演算機制可跳脫局部最佳解（local optimum）。 7. 演算優選的結果，可提供一組最佳解，而非只有單一最佳解。

8. 參數優選需經由解碼的過程，而整個演算的機制是在解碼後的參數集合中進 行，不是在參數集合本身，因此演算的機制不受問題函數型態的影響。

以上的優點，使得我們發現當傳統的最佳化方法無法解決一個問題或得到令 人滿意的優選結果時，遺傳演算法便是一個很有趣且擁有很大潛力去替代部份傳 統的優選法。

對所有的問題而言，遺傳演算法並非都是一個最佳的方法，例如當在處理一 具有凸函數型態，且僅有少量變數之問題時，一般傳統以微積分為基礎的搜尋 法，即可比遺傳演算法快速的找到最佳解，別外一些簡單優選的問題，傳統的演 算法亦都能很快的解決，然而當我們在處理實際的問題時，經常會遇見的是非凸 函數且多變數型態或更複雜的問題，這是一般演算法不易解決的，而遺傳演算法 就有解決此類問題的能力，且可得到近以全域最佳解。

z 遺傳演算法之架構

遺傳演算法將欲求解的問題變數或參數以一種類似染色體的資料結構

（Chromosome-Like Data Structure）來編碼，並應用一些遺傳運算元（Operators）

如交換（Crossover）、突變（Mutation）對大量的染色體作運算，運算後產生的 子代除了保存親代中具優勢的特質外，也有可能因為基因的交換與突變而比親代 的表現更佳。基本的遺傳演算法包含下列幾個步驟：

一、將問題的變數編碼:

例如可以二進位字串（Binary String）的形式來表示變數，其間的轉換為二 進位與十進位的對應，如將二進位字串 1001 解碼，則可對應於十進位的變數值 9，而 1100 對應於 12，1001 與 1100 可看作是兩條染色體。

二、產生初始群集（Initial Population）

以隨機的方式產生多條染色體作為初始解。

三、計算目標函數值（Evaluation）

將初始群集大量的染色體解碼後對應的變數值一一代入問題模式中，計算函 數或目標函數值。

四、計算適合度

適合度愈高表示該染色體具有較優的特質，將來被複製（Reproduction）的 機會也較大，以搜尋最大化目標值的問題來說，適合度可以目標函數來表示，若 是應用於最小化目標函數之問題時，適合度函數則需由目標函數經適當的轉換而 產生。

五、複製（Reproduction）或選取（Selection）

為演化出更優良的個體，必須從原來族群中篩選出較佳的個體，組成下一代 的族群，這就是複製。因此，擁有較高適應值的染色體，便有較高的機率被選擇 出來進行複製。茲以下列兩種常用的方式說明：

為演化出更優良的個體，必須從原來族群中篩選出較佳的個體，組成下一代 的族群，這就是複製。因此，擁有較高適應值的染色體，便有較高的機率被選擇 出來進行複製。茲以下列兩種常用的方式說明：