水库水沙联合调度优化方法与应用研究
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摘要
我国是一个水资源严重匮乏、水利发展相对滞后的国家,如何加快水利改革发展,最大限度的合理开发利用水资源是关系到社会、经济、生态环境系统可持续发展和人民生活水平提高的迫切问题。水库作为增加水利支撑保障能力、实现水资源科学配置的关键性工程,提高其运行管理水平是未来加快水利改革发展的重要举措。泥沙淤积与水库运用同步存在,泥沙淤积严重制约水库综合效益的发挥,威胁水库的使用寿命。为充分发挥水库的综合效益,必须综合考虑水库防洪、兴利和排沙减淤等目标,开展水库水沙联合调度优化方法与应用研究,这是目前水库运用管理模式的发展方向。
与一般水库调度相比,水库水沙联合调度不仅要考虑水量的合理调配,还要对泥沙的蓄泄及时间做出合理的安排,对梯级水库而言还要考虑上下游水库的运用要求和上游梯级对下游水库的累积性调节作用。水库水沙联调涉及到水库调度和泥沙冲淤计算两个方面,这两个方面相互联系、相互影响,全面认识泥沙冲淤和水库防洪、发电等目标之间的对立统一关系,从理论上将泥沙冲淤计算和水库调度更好的结合起来,实现水沙联合调度,将进一步丰富水库调度和水库泥沙的基本理论,具有重要的理论意义和实际应用价值。
水库水沙联合调度是一个典型的复杂大系统多目标问题。由于泥沙冲淤计算与水库调度计算是两种性质完全不同、决策时段差异甚大的系统,且梯级水库联合调度本身是一个具有大量约束条件、动态、复杂的最优化控制问题,其优化求解一直受到“维数灾”、“容易陷入局部最优解”等缺点的制约,因此在水库调度中考虑泥沙冲淤,构建能全面反映水沙综合效益的多目标决策模型,实现模型的联合求解,具有很大的难度。基于此,论文分别从水库优化调度、水库泥沙冲淤计算、水沙联调多目标决策模型的构建与求解以及非劣解的生成与评价决策、水沙调度实例等方面对水库水沙联合调度优化方法与应用进行了系统深入研究。取得了如下主要成果：
(1)水库调度与泥沙冲淤规律研究。为从宏观和微观两个层面探索水库调度与泥沙冲淤之间的规律,首先分析了四种水库宏观运用方式对泥沙淤积速率、淤积分布以及淤积平衡形态三方面的影响,给出调水调沙的宏观运用框架；其次研究了汛限水位和蓄水时间调整对泥沙淤积的影响,得出蓄水时间只改变泥沙淤积速率,而汛限水位则会改变整个淤积平衡的结论；再者分析了三种水库宏观排沙方式的排沙机理,讨论其高效排沙方式；最后对初步平衡后的水库冲淤特点进行分析,总结出根据不同冲淤特点进行蓄水排沙的规律。
(2)基于鲶鱼效应粒子群算法的水库优化调度。针对求解水库群优化调度问题时,粒子群优化算法容易陷入局部最优和后期收敛速度慢等缺点,将“鲶鱼效应”机制引入到粒子群算法中,提出基于鲶鱼效应粒子群算法,并给出其求解水库优化调度问题的实现步骤；该算法中的鲶鱼启发器实现了对种群多样性的动态跟踪和鲶鱼粒子的自动引入,通过鲶鱼粒子的驱赶和高素质动态调节作用激活进化中陷入惰性的群体并提高收敛速度；最后通过单库防洪优化调度和梯级水库发电优化调度两个实例证明了算法的可行性和高效率。
(3)水库水沙联合多目标优化调度。针对水库调度涉及防洪、兴利、生态和排沙减淤等综合效益的多个目标,以一维泥沙冲淤计算数学模型为基础,整合目标和决策变量建立全面反映水沙综合效益的单库多目标决策模型；通过对多目标问题非劣解生成技术的深入研究,在介绍向量优化理论权重法和约束法特点的基础上,重点提出基于鲶鱼效应多目标粒子群算法,相比于向量优化理论,该方法计算效率高,能同时获得多个非劣解；最后通过三峡水库水沙优化调度实例证明了该算法的有效性和可行性,并与基于泥沙约束的三峡水库蓄水时间优化实例进行了对比分析。
(4)梯级水库水沙联合调度多目标决策模型及求解方法。从梯级水库水沙联调的目的出发,分别建立梯级水库防洪、发电和泥沙冲淤计算子模型；在此基础上,构建梯级水库水沙联合调度多目标决策模型,该模型能较好的反映梯级水库间的水沙联系以及各目标利益之间的协调；为实现模型的求解,运用约束法将多目标决策模型转化为单目标优化模型,在给定的约束阈值下采用基于鲶鱼效应粒子群算法对单目标优化模型寻优,通过不断变换约束阂值水平生成问题的非劣解集；最后根据层次分析法计算的主观权重和熵权法计算的客观权重,结合理想点评价法,构建基于组合权重的理想点评价模型,该模型在一定程度上改善了单一赋权法的不足,使评价结果更符合客观实际。
(5)溪洛渡-向家坝梯级水库水沙联合调度实例。以溪洛渡-向家坝梯级水库为研究对象,首先在分析梯级水库蓄水时间优化必要性和前提条件的基础上,研究梯级组合蓄水方案调整对发电、航运和泥沙淤积的影响,结果表明：梯级水库蓄水时间应以相互错开为有利蓄水发电原则,并且蓄水提前将增加泥沙淤积,蓄水推后则会减少泥沙淤积,梯级水库的蓄水调整将改变梯级水库的泥沙分配；然后,以计算期内梯级水库多年平均发电最大和库容淤损率最小为目标,建立溪洛渡-向家坝梯级水库水沙联调多目标决策模型,采用约束法获取其非劣解,非劣解分析表明发电量的增加以增加库容淤损率为代价：最后,采用不同的权重对非劣方案集进行评价决策,结果表明：权重不同,评价得到的最优方案不同,最优方案是一个考虑了发电量和库容淤损率的均衡水沙解,从而验证了方法和模型的可行性和有效性。
China is a country which is seriously lack of water resources and lagging of water conservancy development. So how to speed up the development of water conservancy reform and rationally utilize water resources to maximum limit are the urgent problems that related to the sustainable development of the society, economy and ecological environment system, and related to the improvement of people's living standards. As reservoir is the key project that can increase water conservancy support ability and realize the scientific allocation of water resources, improving the level of its operation and management is the important measure to accelerate the development of water conservancy reform in the future. Sediment deposition is synchronous with reservoir operation, which restricts the comprehensive benefits and threats to the service life of reservoir. So in order to give full play to the comprehensive benefits of reservoir, we must study on reservoir water-sediment coordinative operation which take comprehensive consideration of flood control and irrigation and sand sedimentation reduction of reservoir. This is the development direction of reservoir management pattern at present.
Compared with the ordinary reservoir operation, reservoir water-sediment coordinative operation should consider not only the reasonable allocation of water, but also making reasonable arrangement of the storage and discharge time of sediment. For cascade reservoirs, operation requirements of upstream and downstream reservoirs and cumulative adjustment effect that upstream cascade do to downstream reservoirs should take into consideration. Reservoir water-sediment coordinative operation refers to the two aspects of reservoir operation and sediment deposition calculation, which mutual contacts and mutual influences. Comprehensive understanding the relationship between sediment deposition and targets such as flood control and power generation and theoretically combining sediment deposition calculation and reservoir operation that realize water-sediment coordinative operation will further enrich the basic theory of reservoir operation and sediment, it has important theoretical significance and practical application value.
Reservoir water-sediment coordinative operation is a typical complex large system multi-objective problem. Due to reservoir operation calculation and sediment deposition calculation are two different systems of both properties and decision-making period, and the study on cascade reservoirs coordinative operation itself is a optimal control problem that has a lot of constraint conditions, dynamic and complicated nonlinear systems, whose optimal solution had been affected by the dimension disaster and the problem of local optimal solution, thus it has great difficulty to construct and jointly solve a multi-objective decision model that can comprehensively reflect comprehensive benefits of water-sediment coordinative operation in the optimal problem of water-sediment coordinative operation of reservoir. Based on this, the paper deeply researches on the method and application of reservoir water-sediment coordinative operation in system, the main content respectively contain reservoir operation, sediment deposition calculation, the construction and solution of the multi-objective decision model on the water-sediment coordinative operation, the generation of non inferior solutions, evaluation decision and case study of water-sediment coordinative operation. The major achievements are as following:
(1) Research on regulation of reservoir operation and the scouring and silting of sediment deposition. In order to explore the regulation between the scouring and silting and reservoir operation from macro and micro aspects, firstly the influence of four types of macro mode reservoir operation on sediment deposition rate, deposition distribution and type of deposition balance is analyzed, which can give the macro use frame of water and sediment regulation. By studying in impact on sediment by limited water level and storage time adjustment, the conclusion is that storage time only changes the sediment deposition rate but limited water level can change the whole deposition balance. And the sediment ejection mechanism for three types of macro mode on reservoir sediment ejection is analyzed and the efficient way for sediment ejection is discussed. At last, the characteristics of sediment scouring after the initial deposition balance are discussed and the regulation of water storage and sediment ejection according to different characteristics of scouring and silting is summarized.
(2) Particle swarm optimization algorithm based on catfish effect for reservoir optimal operation. Aim at the shortcoming of particle swarm optimization algorithm that easy to fall into local optimum and slow convergence when solving reservoir optimal operation problem, catfish effect mechanism is introduced into it. So particle swarm optimization based on catfish effect is proposed and its implementation step of solving reservoir optimal operation problem is given. The catfish device in the algorithm realizes the dynamic tracing of particle diversity and automatically introduction of catfish particle, which can activate particles that get lazy in evolution. And the convergence rate is improved through driven effect and high-quality dynamic regulating of catfish particle. Finally the algorithm's feasibility and high efficiency are verified through the two examples that are single reservoir flood-control optimal operation and cascade reservoirs power generation optimal operation.
(3) The multi-objective optimization of the reservoir water-sediment coordinative operation. In view of reservoir operation related to multiple objectives for comprehensive benefits, such as flood control, irrigation, ecological and sediment regulation, after integrating objectives and decision variables, the multi-objective decision-making model for single reservoir is established that can reflect the comprehensive water-sediment benefits basing on the calculation mathematics model of one-dimensional sediment scouring and silting. By deeply researching on generating technology of multi-objective problem's non inferior solution and introducing characteristics of weighting method and constraint method in vector optimization theory, multi-objective particle swarm optimization algorithm based on catfish effect is proposed. Compared with the vector optimization theory, it can compute more efficiency and gain multiple non inferior solutions at the same time. Finally, the validity and feasibility of the proposed algorithm are proved through the application of water-sediment optimal operation of Three Gorges Reservoir. And the comparation between the application of storage time optimization on sediment constraints of Three Gorges Reservoir and the above one is discussed.
(4) The multi-objective decision-making model of water-sediment coordinative operation of cascade reservoirs and its solving method. In view of the purpose of cascade reservoirs water-sediment coordinative operation, the three calculation sub-models of flood control, power generation and sediment deposition are established. On this basis, the multi-objective decision-making model of water-sediment coordinative operation in cascade reservoirs is constructed, which can better reflect the links between water and sediment and coordination with every objective interest of cascade reservoirs. For the realization of the model solving, the multi-objective decision-making model is transformed into single objective optimization model by using the constraint method. With a given constraint threshold, the single objective optimization model can be solved by particle swarm optimization algorithm based on catfish effect. The non-inferior sets of the multi-objective problem can be achieved by changing constraint threshold level. At last, according to the subjective weight from analytic hierarchy process and objective weight from entropy method, and combined with the ideal point evaluation method, the evaluation model of ideal point based on combination weight is proposed, which remedies the defects of single-weighing to some extent and make evaluation result more objective.
(5) The application of water-sediment coordinative operation of Xiluodu-Xiangjiaba cascade reservoirs. Take Xiluodu-Xiangjiaba cascade reservoirs as the research object. First of all, on the basis of analyzing the necessity and prerequisites of cascade reservoirs storage time optimization, the impact on power generation and navigation and sediment deposition for cascade reservoirs by combination storage time adjustment is researched. It shows that staggered cascade reservoirs storage time is beneficial for principles of storage and power generation, and storage time adjustment on cascade reservoirs will change the sediment distribution which means advanced storage time would increase sediment deposition and put-back storage time would decrease sediment deposition. Then, aim at the maximum annual average power generation and minimum storage capacity loss rate about sediment of cascade reservoirs in calculate period, the multi-objective decision model of water-sediment coordinative operation on Xiluodu-Xiangjiaba cascade reservoirs is built, and the non inferior solutions is obtained by constraint method. Finally, the non inferior solution sets are evaluated by using different weights. It shows that evaluation of the optimal solution is different if the weight is different and the optimal solution is a balanced one of of water and sediment multi-objective decision model. Case study verifies the feasibility and effectiveness of the method and model.
与一般水库调度相比,水库水沙联合调度不仅要考虑水量的合理调配,还要对泥沙的蓄泄及时间做出合理的安排,对梯级水库而言还要考虑上下游水库的运用要求和上游梯级对下游水库的累积性调节作用。水库水沙联调涉及到水库调度和泥沙冲淤计算两个方面,这两个方面相互联系、相互影响,全面认识泥沙冲淤和水库防洪、发电等目标之间的对立统一关系,从理论上将泥沙冲淤计算和水库调度更好的结合起来,实现水沙联合调度,将进一步丰富水库调度和水库泥沙的基本理论,具有重要的理论意义和实际应用价值。
水库水沙联合调度是一个典型的复杂大系统多目标问题。由于泥沙冲淤计算与水库调度计算是两种性质完全不同、决策时段差异甚大的系统,且梯级水库联合调度本身是一个具有大量约束条件、动态、复杂的最优化控制问题,其优化求解一直受到“维数灾”、“容易陷入局部最优解”等缺点的制约,因此在水库调度中考虑泥沙冲淤,构建能全面反映水沙综合效益的多目标决策模型,实现模型的联合求解,具有很大的难度。基于此,论文分别从水库优化调度、水库泥沙冲淤计算、水沙联调多目标决策模型的构建与求解以及非劣解的生成与评价决策、水沙调度实例等方面对水库水沙联合调度优化方法与应用进行了系统深入研究。取得了如下主要成果：
(1)水库调度与泥沙冲淤规律研究。为从宏观和微观两个层面探索水库调度与泥沙冲淤之间的规律,首先分析了四种水库宏观运用方式对泥沙淤积速率、淤积分布以及淤积平衡形态三方面的影响,给出调水调沙的宏观运用框架；其次研究了汛限水位和蓄水时间调整对泥沙淤积的影响,得出蓄水时间只改变泥沙淤积速率,而汛限水位则会改变整个淤积平衡的结论；再者分析了三种水库宏观排沙方式的排沙机理,讨论其高效排沙方式；最后对初步平衡后的水库冲淤特点进行分析,总结出根据不同冲淤特点进行蓄水排沙的规律。
(2)基于鲶鱼效应粒子群算法的水库优化调度。针对求解水库群优化调度问题时,粒子群优化算法容易陷入局部最优和后期收敛速度慢等缺点,将“鲶鱼效应”机制引入到粒子群算法中,提出基于鲶鱼效应粒子群算法,并给出其求解水库优化调度问题的实现步骤；该算法中的鲶鱼启发器实现了对种群多样性的动态跟踪和鲶鱼粒子的自动引入,通过鲶鱼粒子的驱赶和高素质动态调节作用激活进化中陷入惰性的群体并提高收敛速度；最后通过单库防洪优化调度和梯级水库发电优化调度两个实例证明了算法的可行性和高效率。
(3)水库水沙联合多目标优化调度。针对水库调度涉及防洪、兴利、生态和排沙减淤等综合效益的多个目标,以一维泥沙冲淤计算数学模型为基础,整合目标和决策变量建立全面反映水沙综合效益的单库多目标决策模型；通过对多目标问题非劣解生成技术的深入研究,在介绍向量优化理论权重法和约束法特点的基础上,重点提出基于鲶鱼效应多目标粒子群算法,相比于向量优化理论,该方法计算效率高,能同时获得多个非劣解；最后通过三峡水库水沙优化调度实例证明了该算法的有效性和可行性,并与基于泥沙约束的三峡水库蓄水时间优化实例进行了对比分析。
(4)梯级水库水沙联合调度多目标决策模型及求解方法。从梯级水库水沙联调的目的出发,分别建立梯级水库防洪、发电和泥沙冲淤计算子模型；在此基础上,构建梯级水库水沙联合调度多目标决策模型,该模型能较好的反映梯级水库间的水沙联系以及各目标利益之间的协调；为实现模型的求解,运用约束法将多目标决策模型转化为单目标优化模型,在给定的约束阈值下采用基于鲶鱼效应粒子群算法对单目标优化模型寻优,通过不断变换约束阂值水平生成问题的非劣解集；最后根据层次分析法计算的主观权重和熵权法计算的客观权重,结合理想点评价法,构建基于组合权重的理想点评价模型,该模型在一定程度上改善了单一赋权法的不足,使评价结果更符合客观实际。
(5)溪洛渡-向家坝梯级水库水沙联合调度实例。以溪洛渡-向家坝梯级水库为研究对象,首先在分析梯级水库蓄水时间优化必要性和前提条件的基础上,研究梯级组合蓄水方案调整对发电、航运和泥沙淤积的影响,结果表明：梯级水库蓄水时间应以相互错开为有利蓄水发电原则,并且蓄水提前将增加泥沙淤积,蓄水推后则会减少泥沙淤积,梯级水库的蓄水调整将改变梯级水库的泥沙分配；然后,以计算期内梯级水库多年平均发电最大和库容淤损率最小为目标,建立溪洛渡-向家坝梯级水库水沙联调多目标决策模型,采用约束法获取其非劣解,非劣解分析表明发电量的增加以增加库容淤损率为代价：最后,采用不同的权重对非劣方案集进行评价决策,结果表明：权重不同,评价得到的最优方案不同,最优方案是一个考虑了发电量和库容淤损率的均衡水沙解,从而验证了方法和模型的可行性和有效性。
China is a country which is seriously lack of water resources and lagging of water conservancy development. So how to speed up the development of water conservancy reform and rationally utilize water resources to maximum limit are the urgent problems that related to the sustainable development of the society, economy and ecological environment system, and related to the improvement of people's living standards. As reservoir is the key project that can increase water conservancy support ability and realize the scientific allocation of water resources, improving the level of its operation and management is the important measure to accelerate the development of water conservancy reform in the future. Sediment deposition is synchronous with reservoir operation, which restricts the comprehensive benefits and threats to the service life of reservoir. So in order to give full play to the comprehensive benefits of reservoir, we must study on reservoir water-sediment coordinative operation which take comprehensive consideration of flood control and irrigation and sand sedimentation reduction of reservoir. This is the development direction of reservoir management pattern at present.
Compared with the ordinary reservoir operation, reservoir water-sediment coordinative operation should consider not only the reasonable allocation of water, but also making reasonable arrangement of the storage and discharge time of sediment. For cascade reservoirs, operation requirements of upstream and downstream reservoirs and cumulative adjustment effect that upstream cascade do to downstream reservoirs should take into consideration. Reservoir water-sediment coordinative operation refers to the two aspects of reservoir operation and sediment deposition calculation, which mutual contacts and mutual influences. Comprehensive understanding the relationship between sediment deposition and targets such as flood control and power generation and theoretically combining sediment deposition calculation and reservoir operation that realize water-sediment coordinative operation will further enrich the basic theory of reservoir operation and sediment, it has important theoretical significance and practical application value.
Reservoir water-sediment coordinative operation is a typical complex large system multi-objective problem. Due to reservoir operation calculation and sediment deposition calculation are two different systems of both properties and decision-making period, and the study on cascade reservoirs coordinative operation itself is a optimal control problem that has a lot of constraint conditions, dynamic and complicated nonlinear systems, whose optimal solution had been affected by the dimension disaster and the problem of local optimal solution, thus it has great difficulty to construct and jointly solve a multi-objective decision model that can comprehensively reflect comprehensive benefits of water-sediment coordinative operation in the optimal problem of water-sediment coordinative operation of reservoir. Based on this, the paper deeply researches on the method and application of reservoir water-sediment coordinative operation in system, the main content respectively contain reservoir operation, sediment deposition calculation, the construction and solution of the multi-objective decision model on the water-sediment coordinative operation, the generation of non inferior solutions, evaluation decision and case study of water-sediment coordinative operation. The major achievements are as following:
(1) Research on regulation of reservoir operation and the scouring and silting of sediment deposition. In order to explore the regulation between the scouring and silting and reservoir operation from macro and micro aspects, firstly the influence of four types of macro mode reservoir operation on sediment deposition rate, deposition distribution and type of deposition balance is analyzed, which can give the macro use frame of water and sediment regulation. By studying in impact on sediment by limited water level and storage time adjustment, the conclusion is that storage time only changes the sediment deposition rate but limited water level can change the whole deposition balance. And the sediment ejection mechanism for three types of macro mode on reservoir sediment ejection is analyzed and the efficient way for sediment ejection is discussed. At last, the characteristics of sediment scouring after the initial deposition balance are discussed and the regulation of water storage and sediment ejection according to different characteristics of scouring and silting is summarized.
(2) Particle swarm optimization algorithm based on catfish effect for reservoir optimal operation. Aim at the shortcoming of particle swarm optimization algorithm that easy to fall into local optimum and slow convergence when solving reservoir optimal operation problem, catfish effect mechanism is introduced into it. So particle swarm optimization based on catfish effect is proposed and its implementation step of solving reservoir optimal operation problem is given. The catfish device in the algorithm realizes the dynamic tracing of particle diversity and automatically introduction of catfish particle, which can activate particles that get lazy in evolution. And the convergence rate is improved through driven effect and high-quality dynamic regulating of catfish particle. Finally the algorithm's feasibility and high efficiency are verified through the two examples that are single reservoir flood-control optimal operation and cascade reservoirs power generation optimal operation.
(3) The multi-objective optimization of the reservoir water-sediment coordinative operation. In view of reservoir operation related to multiple objectives for comprehensive benefits, such as flood control, irrigation, ecological and sediment regulation, after integrating objectives and decision variables, the multi-objective decision-making model for single reservoir is established that can reflect the comprehensive water-sediment benefits basing on the calculation mathematics model of one-dimensional sediment scouring and silting. By deeply researching on generating technology of multi-objective problem's non inferior solution and introducing characteristics of weighting method and constraint method in vector optimization theory, multi-objective particle swarm optimization algorithm based on catfish effect is proposed. Compared with the vector optimization theory, it can compute more efficiency and gain multiple non inferior solutions at the same time. Finally, the validity and feasibility of the proposed algorithm are proved through the application of water-sediment optimal operation of Three Gorges Reservoir. And the comparation between the application of storage time optimization on sediment constraints of Three Gorges Reservoir and the above one is discussed.
(4) The multi-objective decision-making model of water-sediment coordinative operation of cascade reservoirs and its solving method. In view of the purpose of cascade reservoirs water-sediment coordinative operation, the three calculation sub-models of flood control, power generation and sediment deposition are established. On this basis, the multi-objective decision-making model of water-sediment coordinative operation in cascade reservoirs is constructed, which can better reflect the links between water and sediment and coordination with every objective interest of cascade reservoirs. For the realization of the model solving, the multi-objective decision-making model is transformed into single objective optimization model by using the constraint method. With a given constraint threshold, the single objective optimization model can be solved by particle swarm optimization algorithm based on catfish effect. The non-inferior sets of the multi-objective problem can be achieved by changing constraint threshold level. At last, according to the subjective weight from analytic hierarchy process and objective weight from entropy method, and combined with the ideal point evaluation method, the evaluation model of ideal point based on combination weight is proposed, which remedies the defects of single-weighing to some extent and make evaluation result more objective.
(5) The application of water-sediment coordinative operation of Xiluodu-Xiangjiaba cascade reservoirs. Take Xiluodu-Xiangjiaba cascade reservoirs as the research object. First of all, on the basis of analyzing the necessity and prerequisites of cascade reservoirs storage time optimization, the impact on power generation and navigation and sediment deposition for cascade reservoirs by combination storage time adjustment is researched. It shows that staggered cascade reservoirs storage time is beneficial for principles of storage and power generation, and storage time adjustment on cascade reservoirs will change the sediment distribution which means advanced storage time would increase sediment deposition and put-back storage time would decrease sediment deposition. Then, aim at the maximum annual average power generation and minimum storage capacity loss rate about sediment of cascade reservoirs in calculate period, the multi-objective decision model of water-sediment coordinative operation on Xiluodu-Xiangjiaba cascade reservoirs is built, and the non inferior solutions is obtained by constraint method. Finally, the non inferior solution sets are evaluated by using different weights. It shows that evaluation of the optimal solution is different if the weight is different and the optimal solution is a balanced one of of water and sediment multi-objective decision model. Case study verifies the feasibility and effectiveness of the method and model.
引文
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