應用遺傳演算法與最佳控制於非拘限含水層之水量管理營運

Abstract

本研究利用動態控制理論與遺傳演算法發展非拘限含水層之最佳水量管理營運規劃模式，此管理模式之目標函數包含鑿井成本與營運成本。鑿井成本受井位與井數的影響的離散型變數，惟營運成本卻是隨抽水量變化的連續變數。若兩者同時考量，將使目標函數具有離散與連續兩種性質的變數，此種混合型態的目標函數不易以單一演算法求解，而以往之研究亦鮮少有同時考量兩種成本的例子，因此，本研究乃結合遺傳演算法與動態控制理論，發展新的演算法，以解決上述問題並開發新的管理模式。本研究利用二進位編碼的方式來處理水井之位置與數量，其中每一條基因即代表一組可能設井之位置與數量。對每一條基因，可以動態控制理論來求得此基因對應之最佳操作成本，此時水井之動態抽水量為系統之決策變數。因此本研究所提出之方法具有同時蒐尋最佳抽水井網與動態抽水量之特性，此點為與過去研究最重要的差異之一。根據本研究之結果顯示，水井之設置成本對於最佳總成本具有很大的影響，因此欲合理的反應整個系統的總成本，應將水井之設置成本整合於地下水之管理規劃模式中。

This study utilizes dynamic optimal control and Genetic Algorithms(GAs) to solve a management of unconfined aquifer problem considering the fixed costs and the operating costs. Because of the discrete property, the gradient-based algorithms are difficult to solve a problem with fixed costs such as the installation costs of wells. The Genetic Algorithms used here is to determine the number and locations of pumping wells which are the decision variable of GAs. In GAs, one chromosome represents a possible number and locations of pumping well. When the pumping wells are determined, the fixed cost can be determined. The operating cost will be evaluated by used the dynamic optimal control in which the hydraulic head and pumping rate are the decision variable. According to this study, the fixed costs of drilling well have great impact on groundwater management design even though the fixed costs are relatively small. This work demonstrates that fixed costs of drilling well may significantly impact a groundwater management system and these fixed costs should be explicitly incorporated into a groundwater management model.