考慮容量擴張之非拘限含水層水量管理規劃模式

Abstract

一般而言，用水需求皆隨著經濟及人口的成長而與時俱增，因此水資源開發最經濟而合理的方式應該是隨著需求增加而逐步增大其規模，對於地下水管理而言，因為地下水抽取容量直接與水井數相關，因此更適合於此種容量逐漸擴增的營運方式，惟此問題就計算上而言，包含了離散型變數、非線性及動態等特性，以往並未有演算法或模式，可完整的解此問題。本研究乃應用遺傳演算法與最佳控制理論針對二維非拘限含水層系統，發展考量容量擴增下之地下水最佳水量管理規劃模式，模式特色在基於容量逐步擴增的原則下，能完整考量不同階段包括固定成本及操作成本的系統總成本。模式乃以遺傳演算法為主要演算架構，其中每一條染色體代表一組所有階段之設井數量與位置，對於每一條染色體再以可微分動態規劃求其最佳抽水量與操作成本。研究結果顯示，考慮容量擴張的影響而分階段的增建井，不但較符合實際現況，也大幅降低設井成本及總成本。由於本模式考量的容量擴增為更合理的規劃型態，並能在可接受的計算資源下求得其最佳解，因此可為提昇地下水資源管理效率的有力工具。

Generally speaking, the demand of water resources is gradually increasing according to the increase of population and economic development. Therefore, a cost-effective investment strategy is to expand the capacity of a water resources project with the augment of water demand. The system capacity of a groundwater supply system depends on the total number of wells and the capacity of each well. Since each well is installed independently, the total capacity of the system is convenient to expand according the increase of demand. However, since the problem of capacity expansion is a discrete, nonlinear and transient optimization problem,no optimization algorithms have been developed to resolve the problem. This study utilizes dynamic optimal control and Genetic Algorithms (GAs) to solve the groundwater management problem considering the system capacity expansion. The total cost of the problem including fixed and operating costs, and both are computed under the consideration interest rates. In GAs, one chromosome represents a possible network design which consists the well number and the location and developing schedule for each production well. The fixed cost can then be computed according to the network design.The optimal operating cost is evaluated by using the dynamic optimal control algorithm in which the pumping rates are the decision variables. According to this study, the consideration of system capacity expansion have significant impact on the fixed cost and the network design. This work also demonstrates that fixed costs of drilling well may significantly influence a design of groundwater production network. Therefore, the strategy of capacity expansion and fixed costs should be explicitly incorporated into a groundwater management model.