應用遺傳演算法於多目標區域性水資源規劃模式之發展

Abstract

應用遺傳演算法於多目標區域性水資源規劃模式之發展 摘要 本研究首先結合多目標遺傳演算法與限制型微分動態規劃理論發展一新的多目標演算法，並進而以此演算法開發一水資源多目標規劃模式，此規劃模式之目標函數包含建水庫之固定成本與營運之操作成本，固定成本為庫容大小之函數而操作成本則以常用之缺水指標(Shortage Index)代表。此兩種成本原本互相競爭，在本研究中並未以權重係數將其結合成單一目標函數，而以新發展的多目標演算法計算其完整的非劣勢解集合。 此多目標規劃問題之決策變數包括各水庫庫容及對應之放水操作策略。在新發展之多目標演算法中，各水庫庫容乃以二進位編碼之染色體表示，每一染色體代表一組可能的水庫群容量方案，而其對應的最佳操作策略則以限制型微分動態規劃求解，如此各方案之固定成本及操作成本即可求得，再透過遺傳演算法的演算機制則可計算出所有非劣解集合。本研究為驗證此水資源多目標規劃模式之適用性，選定一個具有三個水庫系統之案例驗證本模式，根據本案例結果顯示，在可容許的計算資源下，本模式確能求得完整的非劣勢解，並且顯示固定成本與操作成本(缺水指標)確有明確的競爭關係，同時若規劃期距較短，水庫大小與缺水指標競爭情形受水文狀況影響甚大。 綜合言之，本模式能提供水資源開發規劃時完整的投資成本與未來營運成本間完整的競爭關係，可為提高水資源規劃效益之良好輔助工具。

Development of multi-objective water resource planning model using genetic algorithms and differential dynamic programming Abstract The study proposes a new multi-objective programming algorithm by integrating a genetic algorithms (GA) with constrained differential dynamic programming (CDDP), and develops a multi-objective model for water resources planning using the algorithm. The multi-objective planning model considers the fixed cost of reservoirs construction and management cost. The fixed cost is assumed to be linear increased with the reservoirs size and the Shortage Index (SI) surrogates the management cost. These objectives are competed to each other. However, instead of combining the objectives using a weighting factor, the planning model generates the non-inferior solutions set by the proposed multi-objective algorithm. The decision variables of the multi-objective planning model include the reservoirs size and operating policy (amount of water release). As computing the non-inferior solutions by the planning model, the chromosomes represent the combinations of reservoirs size and the associated optimal operating policy for each chromosome is computed by the CDDP algorithm. Therefore, the fixed and management cost for each chromosome can be obtained and the multi-objective genetic algorithm generates the non-inferior set based on the values of two objectives. To verify the capability of the planning model, a water resources system planning problem with three reservoirs is solved by the planning model. The result demonstrates that the model can indeed generates the complete non-inferior set under an affordable computation resources. The non-inferior set clearly indicates the competition of the two objectives, and, for a short planning horizon, the non-inferior solutions are strongly affected by the stream flow hydrograph. In summary, the proposed multi-objective planning model can provide a complete competition relationship. Therefore, it is a valuable tool to facilitate the decisions making on a multi-objective water resources planning problem.