本研究於地下水之水量管理與污染整治模式中，同時考量整數型態之鑿井固定成本與時變抽水量所引致之操作成本。傳統演算法如線性規劃或非線性規劃對於目標函數中包含整數型態之變數如設井之位置與數量並不容易考量，而離散型態之演算法如整數規劃或離散動態規劃，雖可求解整數型態變數問題，然若求解之問題中包含時變之變數，如水井隨時間改變抽水量，則有變數過多與產生大量計算量之問題，因此雖然系統開發總成本理應包括固定成本與操作成本，以往並未有任何地下水管理規劃模式能同時考量之。本研究乃藉由遺傳演算法（GA）與限制型微分動態規劃（CDDP），將整數型態與時變非線性之變數同時整合於一個模式（GCDDP）中。GA染色體之二進位編碼方式可非常容易的考量設井之位置與數量，然採用GA求解時變抽水量時，則亦有計算量大之問題，故CDDP乃用於求解每一條染色體所對應之時變最佳抽水量與操作成本。拘限含水層與非拘限含水層分別用於驗證本優選模式可應用於地下水之水量管理與污染整治系統中。由數值之優選結果顯示，鑿井固定成本對最佳方案的決定有顯著的影響，當固定成本愈高時，所需之設井數就愈少，因此可節省許多總成本支出。另一方面，含水層地質參數的變化亦影響抽水井的位置與數目，此一優選結果對於採用傳統梯度型演算法並不容易考量。由於本模式能真正考量系統總成本，因此可作為提昇地下水資源管理效率的有力工具，並可將優選結果提供決策者作決策時之參考。

Obtaining optimal solutions for groundwater management and remediation problems, while simultaneously considering both fixed costs and time-varying pumping rates, is a challenging task. Application of conventional optimization algorithms such as linear and nonlinear programming is difficult due to the discontinuity of the fixed cost function in the objective function and the combinatorial nature of assigning discrete well locations. Use of conventional discrete algorithms such as integer programming or discrete dynamic programming is hampered by the large computational burden caused by varying pumping rates over time. A novel procedure that integrates a genetic algorithm (GA) and constrained differential dynamic programming (CDDP), calculates optimal solutions for a groundwater planning problem while simultaneously considering fixed costs and time-varying pumping rates. GA can easily incorporate the fixed costs associated with the installation of wells. However, using GA to solve for time-varying policies would dramatically increase the computational resources required. Therefore, the CDDP is used to handle the sub-problems associated with time-varying operating costs. Numerical experiment for confined and unconfined aquifer that incorporates fixed and time-varying operating costs is presented to demonstrate the effectiveness of the proposed algorithm. Simulation results indicate that the fixed costs can significantly influence the number and locations of wells and a notable total cost saving can be realized by applying the novel algorithm.

封面
中文摘要
英文摘要
志謝
目錄
圖目錄
表目錄
一、緒論
1.1研究目的
1.2文獻回顧
1.2.1線性規則
1.2.2非線性規則
1.2.3微分動態規則
1.2.4遺傳演算法
1.3研究方法
1.4數學符號
1.5本文架構
二、地下水管理模式之建立
2.1地下水流與污染輿控制方程式
2.1.1拘限含水層
2.1.2非拘限含水層
2.2地下水水量管理模式
2.3地下水污染整治模式
三、理論基礎
3.1遺傳演算法
3.2微分動態規劃
3.2.1無限制式微分動態規則(DDP)
3.2.2限制型微分動態規則（CDDP）
3.3遺傳演算法無限制型微分動態規則之結合(GCDDP)
四、限制型微分動態規則相關問題處理
4.1系統轉換之微分
4.2限制型微分動態規則之修正
4.3稀疏矩陣(Mansfield et al.,1998)
4.4初始軌足跡之求得
4.5非拘限含水層水位下限之處理
五、地下水水量管理規則模式之應用與範例演算
5.1拘限含水層之水量管理規則
5.1.1不考慮設井成本
5.1.2考慮單位固定設井成本
5.1.3總成本比較
5.1.4考慮地質條件不同之設井成本
5.2非拘限含水層之水量管理規則
5.2.1總成本之比較
5.2.2厚含水層及薄含水層之比較
5.2.3水位下限對水量管理之影響
5.2.4接近最佳解集合之染色體設井組合分析
六、地下水污染整治規則模式之應用與範例演算
6.1拘限含水層之污染整治
6.1.1不考慮設井成本
6.1.2考慮單位固定設井成本
6.1.3考慮地質條件不同之設井成本
6.1.4總成本分析
6.1.5GCDDP演算法性能分析
6.2非拘限含水層之污染整治
6.2.1考慮固定單位設井成本
6.2.2考慮地質條件不同之設井成本
6.2.3非拘限含水層採用拘限含水層來模擬之污染整治結果比較
七、結論與建議
7.1結論
7.1.1水量管理模式
7.1.2污染整治模式
7.2建議
參考文獻
作者簡歷

徐享崑、李朝晉，「序率水資源系統離散型微分動態規劃模式之初步研究」，水利工程第十一卷，第三期，第43-58頁(1984)。
徐享崑、李朝晉，「串聯水庫系統離散型微分動態規劃模式之應用研究」，第三屆水利工程研討會論文集(1986)。
郭振泰、朱文生、徐年盛、林永禎、萬象，「淡水河流域水庫系統即時優選操作模式之發展與應用（一）」，經濟部水資會／台大土木研究所，臺北(1988)。
萬象、陳昶憲、郭振泰，「水庫防洪操作最佳控制模式之研究」，第五屆水利工程研討會論文集，第186-199頁(1990)。
黃寄萍、郭振泰，「最佳序率控制應用於水庫旬即時操作之研究」，博士論文，臺灣大學土木工程研究所，臺北(1991)。
楊智霖，「水庫聯合操作系統之研究」，碩士論文，國立中興大學土木工程研究所(1993).
陳德源，「最佳控制理論在並聯水庫防洪操作之應用」，碩士論文，成功大學水利及海洋工程研究所，臺南(1993)。
郭嘉真，「抽注率敏感方程法在地下水管理上之研究」，中國土木水利工程學刊，第三卷第三期，第199-207頁(1993)。
蕭金財，「序率最佳控制理論應用於水庫系統之優選操作」，碩士論文，國立交通大學土木工程研究所(1994)。
金維仁，「水庫群最佳聯合防洪操作分析方法之比較」，碩士論文，國立成功大學水利及海洋工程學系(1995)。
林挺生，「區域性水資源系統之最佳營運特性分析」，碩士論文，國立成功大學水利及海洋工程學系(1995)。
曾振遠、馬國榮，「集合控制理論應用於串聯水庫操作之研究」，臺灣水利，第44卷第4期，第38-46頁(1996)。
劉新達，「類神經網路在水庫操作的應用」，碩士論文，國立交通大學土木工程研究所(1996)。
蘇明道、徐忠寶、陳維英，「石門水庫操作規則之推導及評估」，臺灣水利，第45卷第1期，第58-67頁(1997)。
蕭金財、張良正、許鈺珍，「應用序率最佳控制於水庫系統之優選操作」，中國土木水利工程學刊，第九卷第三期，第449-457頁(1997)。
林妙貞，「遺傳演算法在地下水復育系統的不確定性之應用」，碩士論文，國立中興大學環境工程研究所(1997)。
張斐章、惠士奇，「灰色模糊序率動態規劃於水庫操作之應用」，農業工程學報，第44卷第1期，第34-49頁(1998)。
許維群，「遺傳演算法與非線性規劃混合模式在地下水復育問題上之應用」，碩士論文，國立中興大學環境工程研究所(1998)。
王建勛，「人工湖對屏東平原地下水補注之數值模擬與評估」，碩士論文，屏東科技大學(1999)。
蕭金財、張良正，「應用平行序率最佳控制演算法於多目標水庫系統之優選操作」，中國土木水利工程學刊，第十二卷第三期，第551-560頁(2000)。
許清荃，「濁水溪沖積扇多層地下水調配與管理之研究」，碩士論文，國立成功大學(2000)。
劉志文，「屏東沖積平原地下水資源調配與管理之研究」，碩士論文，國立成功大學(2000)。
Aquado, E., and Remson. I., "Groundwater hydraulics in aquifer management," J. hydr. Div., ASCE, 100(1), 103-118, (1974).
Ahlfeld, D. P., J. M. Mulvey, G. F. Pinder, and E. F. Wood, "Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory, 1, Model development," Water Resour. Res., 24(5), 431-441, (1988a).
Ahlfeld, D. P., J. M. Mulvey, G. F. Pinder, "Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory, 2, Analysis of a field site," Water Resour. Res., 24(5), 443-452, (1988b).
Andricevic, R., and P. K. Kitanidis, "Optimization of the pumping schedule in aquifer remediation under uncertainty," Water Resour. Res., 26(5), 875-885, (1990).
Aly, A. H., and R. C. Peralta, "Comparison of a genetic algorithm and mathematical programming to the design of groundwater cleanup systems," Water Resour. Res., 35(8), 2415-2425, (1999).
Bancha Kwanyuen, Improved multiobjective groundwater planning model, Ph. D. Dissertation, Colorado State University, (1996).
Basagaoglu, H. and Marino, M. A., "Joint Management of Surface and Ground Water Supplies," Ground Water, 37(2), 214-222, (1999).
Chang, S. C., A Hierarchical, Temporal Decomposition Approach to Long Horizon Optimal Control Problems. Ph. D. Disseration, Univ. of Connecticut, (1986).
Chang, L. C., C. A. Shoemaker, and P. L. F. Liu, "Optimal time-varying pumping rates for groundwater remediation: application of a constrained optimal control algorithm," Water Resour. Res., 28(12), 3157-3171, (1992).
Culver, T. B., and C. A. Shoemaker, "Dynamic Optimal Control for Groundwater Remediation with Flexible Management Periods," Water Resour. Res., 28(3), 629-641, (1992).
Culver, T. B., and C. A. Shoemaker, "Optimal control for groundwater remediation by differential dynamic programming with quasi-Newton appeoximations," Water Resour. Res., 29(4), 823-831, (1993).
Cieniawski S. E., Eheart, J. W., and Ranjithan, S., "Using genetic algorithm to solve a multiobjective groundwater monitoring problem." Water Resour. Res., 31(2), 399 - 409, (1995).
Culver, T. B., and C. A. Shoemaker, "Dynamic optimal ground-water reclamation with treatment capital costs." J. Water Resour. Plng. and Mgmt., ASCE, 123(1), 23-29, (1997).
Deninger, R. A., "Systems analysis of water supply systems", Water Resour. Bull., 6(4), 573 - 579, (1970).
DeJong, K. A., "An analysis of the behavior of a class of genetic adaptive systems," Ph.D. dissertation, University of Michigan, Ann Arbor, Mich, (1975).
Dougherty, D. E., and R. A. Marryott, "Optimal Groundwater Management 1. Simulated Annealing." Water Resour. Res., 27(10), 2493 - 2508, (1991).
Gorelick, S. M., " A review of distributed parameter groundwater management modeling methods," Water Resour. Res., 19(2), 305-319, (1983).
Gorelick, S. M., C. I. Voss, P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright, "Aquifer reclamation design: The use of contaminant transport simulation combined with nonlinear programming," Water Resour. Res., 20(4), 415-427, (1984).
Goldberg, D. E., Genetic Algorithm in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, Mass, (1989).
Huang, C., and A. S. Mayer, "Pump-and-treat optimization using well locations and pumping rates as decision variables," Water Resour. Res., 33(5), 1001-1012, (1997).
Hsiao, C. T. and L. C. Chang, "Dynamic Optimal Groundwater Management while considering Fixed Cost," Journal of Water Resources Planning and Management, ASCE, Accepted, 2001
Jones, L., R. Willis and W. W.-G. Yeh, "Optimal Control of Nonlinear Groundwater Hydraulics Using Differential Dynamic Programming," Water Resour. Res., 23(11), 2097-2106, (1987).
Lin, T. W., "Well behaved penalty functions for constrained optimization," J. Chinese Inst. of Eng., 13(2), 157-166, (1990).
Lin, X. and Yang, Y., "The optimization of groundwater supply system in SHI JIAZHUANG city, China," Water Science and Technology, 24(11), 71-76, (1991).
Murray, D. M., and S. J. Yakowitz, "Constrained Differential Dynamic Programming and its Application to Multireservoir Control," Water Resour. Res., 15(5), 1017-1027, (1979).
McKinney, D. C., and M. D. Lin, "Genetic algorithm solution of groundwater management models," Water Resour. Res., 30(6), 1897-1906, (1994).
McKinney, D. C., and M. D. Lin, "Approximate mixed-integer nonlinear programming methods for optimal aquifer remediation design," Water Resour. Res., 31(3), 731-740, (1995).
McKinney, D. C., and M. D. Lin, "Pump-and-treat ground-water remediation system optimization," J. Water Resour. Plng. and Mgmt., ASCE, 122(2), 128-136, (1996).
Mansfield, C. M., C. A. Shoemaker and L. Z. Liao, "Utilizing sparsity in time-varying optimal control of aquifer cleanup," J. Water Resour. Plng. and Mgmt., ASCE, 124(1), 15-21, (1998).
Mansfield, C. M., and C. A. Shoemaker, "Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations," Water Resour. Res., 35(5), 1455-1469, (1999).
Molz, F. J., and L. C. Bell, "Head gradient control in aquifers used for fluid storage," Water Resour. Res., 13(14), 795-798, (1977).
Murtagh, B. A., and Saunders, M. A., "A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints," Mathematical programming study 16, North-Holland Publishing Company, Amsterdam, The Netherlands, (1982).
Morshed, J. and Kaluarachchi, J. J., "Enhancements to genetic algorithm for optimal ground-water management," Journal of hydrologic engineering, 5(1), 67-73, (2000).
Pinder, G. F., Galerkin finite element models for aquifer simulation, Rep. 78-WR-5, Dept. of Civ. Eng., Princeton Univ., Princeton, N. J., (1978).
Ritzel, B. J., Eheart J. W. and S. Ranjithan, "Using genetic algorithm to solve a multiple objective groundwater pollution containment problem," Water Resour. Res., 30(5), 1589-1603, (1994).
Rizzo, D. M., and D. E. Dougherty, "Design optimization for multiple management period groundwater remediation," Water Resour. Res., 32(8), 2549-2561, (1996).
Pezeshk, S., Helweg, O. J. and Oliver, K. E., "Optimal operation of ground-water supply distribution systems," J. Water Resour. Plng. and Mgmt., ASCE, 120(5), 573-585, (1994).
Philbrick, C. R. and P. K. Kitanidis, "Optimal conjunctive-use operations and plans," Water Resour. Res., 34(5), 1307-1316, (1998).
Rosenwald. G. W., and Green, D. W., "A method for determining the optimum location of wells in a reservoir using mixed-integer programming," Society of Petroleum Engrs. J., 14(1), 44-54, (1974).
Sawyer, C. S., D. P. Ahlfed, and A. J. King, "Groundwater remediation design using a three-dimensional simulation model and mixed-integer programming," Water Resour. Res., 31(5), 1373-1385, (1995).
Taghavi, S. A., Howitt, R. E. and Marino, M. A., "Optimal control of ground-water quality management: nonlinear programming approach," J. Water Resour. Plng. and Mgmt., ASCE, 120(6), 962-982, (1994).
Takahashi, S. and Peralta, R. C., "Optimal perennial yield planning for complex nonlinear aquifers: Methods and examples," Advances in Water Resources, 18(1), 49-62, (1995).
Willis, R., and Liu, P., "Optimization model for ground-water planning," J. Water Resour. Plng. and Mgmt., ASCE, 110(3), 333-347, (1984).
Whiffen, G. J., Optimal control for deterministic and uncertain groundwater remediation , Ph. D. thesis, Cornell Univ. School of Civ. and Environ. Eng., Ithaca, N. Y., (1995).
Wang, M., and C. Zheng, "Optimal remediation policy selection under general conditions," Ground Water, 35(5), 757-764, (1997).
Wang, M., and C. Zheng, "Ground Water management optimization using genetic algorithms and simulated annealing: formulation and comparison," Journal of the American water Resources Association, 34(3), 519-530, (1998).
Watkins, Jr, D. W., and D. C. McKinney, "Decomposition methods for water resources optimization models with fixed costs," Advances in Water Resources, 21(4), 283-295, (1998).
Wardlaw, R. and Sharif, M., "Evaluation of Genetic Algorithms for Optimal Reservoir System Operation," J. Water Resour. Plng. and Mgmt., ASCE, 125(1), 25-33, (1999).
Yeh, W. W-G., "System Analysis in ground-water planning and management," J. Water Resour. Plng. and Mgmt., ASCE, 118(3), 224-237, (1992).
Zheng, C., and P. P. Wang, "An integrated global and local optimization approach for remediation system design," Water Resour. Res., 35(1), 137-148, (1999).