應用遺傳演算法與可微分動態規劃於地表地下水聯合營運之多目標規劃

Abstract

水資源規劃往往牽涉到的標的或需求，亦即常常是一個多目標規劃的問題，惟在以往對多目標的問題在計算上最常用的簡化方式為將各目標賦予權重而將問題轉化成單目標型態，再求解之，惟若如此，則往往不能清楚的描述不同目標間的競爭關係，其中代表性的例子之一為系統規模（固定成本）與營運目標（如缺水及其影響）間之競爭關係，有鑑於此，本研究將以微分動態規劃(Differential Dynamic Programming)理論為核心，結合多目標遺傳演算法(Multi-objective Genetic Algorithm) ，來建立新的多目標優選方法，此新的方法不但能計算完整的非劣勢解，並能同時考量系統固定成本與操作成本，後者亦為以往其它相關研究所難以處理者，本研究並進一步以未來台灣南部地區水資源調配可能執行的策略，即地表水資源系統整體營運、地表地下水資源系統聯合營運及考量淨水廠容量擴張之地表水資源系統整體營運等不同的系統架構，發展最佳營運及規劃模式，並進行實例應用。此外，為維持地下水系統的非線性特性及解決模式整體計算量增加的問題，本研究亦將地下水流模擬模式ISOQUAD崁入上述地表地下水資源系統聯合營運發展模式中來計算抽水量或補注量與地下水位之變動關係。

Owing to difficulties in considering fixed cost and time-varying operating cost for conjunctive use of surface and subsurface water at the same time, optimization of water resources planning is a challenging task. Major difficulty is encountered due to the discontinuity of fixed cost in time led the objective function, including fixed cost and operating cost, not to be solved time by time. Moreover, these two objectives conflict with each other. Therefore, instead of combining the objectives using a weighting factor, this study proposes a novel multi-objective programming algorithm by integrating a multi-objective genetic algorithm (MOGA) with constrained differential dynamic programming (CDDP). Using the proposed algorithm, a multi-objective model for water resources planning is also proposed, capable of accurately reflecting how multi-objectives compete with each other and estimating the available releases of surface and subsurface systems. A MOGA is used to generate the various fixed costs of reservoirs’ scale and estimate the non-inferior solutions set, which reflects the impact on the relation between two objectives of fixed cost and operating cost. The optimization model is then adopted to distribute the releases among reservoirs based on CDDP. Additionally, a MOGA is also applied to decide a pattern of pumping / recharge and a groundwater simulation model ISOQUAD is directly embedded to handle the complex dynamic relationship between the groundwater level and the pumping / recharge. Doing so averts an increasing computational time of CDDP if groundwater variables are considered. Next, the results of above releases and pumping / recharge are used to evaluate the fixed cost. Furthermore, effectiveness of the planning model is verified by solving a water resources planning problem of conjunctive use of surface and subsurface water in southern Taiwan. Simulation results demonstrate that the proposed model can generate a complete non-inferior set under an affordable computation resources. This thesis provides a valuable reference for governmental authorities when developing water resource-related management strategies.