基因演算法在多水庫多目標規劃之應用

Abstract

台灣地區目前較大型水庫多採用多目標的操作運轉，以獲得在蓄水、灌溉、給水、發電、觀光等操作目標下有較大的整體效益，然而在多目標規劃問題(multiobject programming)中，並無一個絕對的最佳解，必須先找出一組非劣勢解集合(Noninferior Solutions)，再由決策者從非劣勢解當中來選取其中一個方案進行操作。有鑒於此,本研究乃應用基因演算法(genetic algorithms)來求得多目標規畫問題的非劣勢解﹐其基本原理為將原問題之決策變數(decision variables)編成染色體，再利用複製、交配、突變等演化元件，配合適當定義之適合度函數，可解得原問題之非劣勢解集合。 在處理水庫系統之限制條件時，本研究利用可行解集合觀念及線性規劃找出決策變數可行解集合，將染色體在決策變數可行解範圍內解碼，如此便可滿足系統之限制條件。 除了模式驗證之外，本研究進一步以三個水庫系統案例驗證模式的收歛效率與實用性，第一個案例為假設之二水庫並聯系統，第二個案例為假設之三水庫串並聯系統，第三個案例為翡翠及石門水庫並聯系統，由案例結果可證明當水庫可用水資源減少時，各目標彼此衝突情形更加嚴重，且本模式的搜尋空間不到所有可行解集合的 分之一，證明本模式確實很有效率。

Most of the large reservoirs in Taiwan were multi-objectives. The objectives may include irrigation, water supply, hydropower and recreations. For a multi-object problem, the solutions are not unique. To obtain the optimal solution, the non-inferior set has to be solved in advance. The decision-maker can then choose a solution from the non-inferior set according to his/her preferences. Basing these considerations, this study applies genetic algorithms (GA) to compute the non-inferior set of a multi-object-programming problem. The procedure can be outline as en-coding of decision variables, selection (reproduction), crossover and mutations. The key is to properly define the fitness function and search the non-inferior set. Beside the model development, this research also solve a example problem to varify the convergent rate and prativility of the algorithm. The model reliability and convergence are verified by applying the framework of a multi-reservoir system of the Tanshui River Basin in northern Taiwan.