Abstract: Freshwater resources are the basis for the survival and development of human society, as well as the basic and strategic resources for the healthy and sustainable development of the national economy. According to the statistics, China is a country rich in freshwater resources in the world, and also one of the countries with the poorest per capita freshwater resources. Therefore, the protection and rational use of freshwater resources has attracted the high attention of the Chinese government. On the other hand, the spatiotemporal distribution of freshwater resources in China is extremely uneven, which does not match the distribution of population, cultivated land, minerals and other resources. Therefore, it is necessary to rationally allocate the limited freshwater resources in order to maximize its effectiveness. At present, the joint operation of inter-basin reservoirs has become a feasible and effective means to solve the problem of uneven distribution of water resources in time and space in China. In the existing single objective bilevel programming model for joint operation of inter-basin water supply reservoirs, which is established by the authors in the early stage, the maximum weighted sum of the water supply guarantee rate of the reservoir to each water user is taken as the lower objective function and the weight is a fixed constant. It should be noted that the above approach may not guarantee the optimal regulation of water transfer and supply, because different water transfer and supply rules correspond to different weights. For the above defects, in this paper the semivectorialbilevel programming model for deriving the inter-basin multi-reservoir operating rule is constructed. The semivectorial bilevel programming model constructed in this paper takes the minimum near to the expected water allocation and the abandoned water of the receiving reservoirs as the upper level objective, and the minimum differentials between expected and actual water supply indexes of multi-reservoir system as the lower level objectives. Following the structural characteristics of the constructed model, a parallel population hybrid evolutionary particle swarm optimization algorithm is designed to obtain its “optimistic optimal solution”. In dealing with the constructed model, the weight of the lower level is regarded as the upper level variable. Finally, four water transfer scenarios are taken as examples to verify the feasibility of the model and algorithm built in this paper. In addition, the analysis shows that compared with the existingsingle objective bilevel programming model for joint operation of inter-basin water supply reservoirs, the semivectorial bilevel programming model constructed in this paper can generally reduce the generalized water shortage index of main water users of each reservoir by 15%~25%. This further confirms the validity of the semivectorial bilevel programming model constructed in this paper for deriving the inter-basin multi-reservoir operating rule. It is worth pointing out that the semivectorial bilevel programming model for joint operation of inter-basin water supply reservoirs proposed in this paper provides a new idea for the study of inter-basin water transfer and water supply problem. And at the same time, it is more likely to obtain the optimal water transfer and supply rules. In addition, the acquisition of optimal water regulation and water supply rules is also related to whether the algorithm used can obtain the global optimal solution of the model. The particle swarm optimization algorithm has the defects of precocity and can only obtain the local optimal solution of the problem. How to take a more effective global optimization algorithm to solve the built model is the further research direction.

Key words: inter-basin water transfer, multi-reservoir, joint optimization operation, operation rule, semivectorial bilevel programming

摘要： 跨流域水库群联合调度已成为解决我国水资源时空分配不均问题的一种可行、有效手段。针对已有跨流域水库群联合调度的单目标双层规划模型可能无法得到最优调水规则和供水规则的问题,本文以接近流域间预期调配水量和各受水水库弃水量最小为上层目标函数,水库期望供水质量与实际供水质量的差值最小为下层目标函数,构建了跨流域供水水库群联合调度的半向量双层规划模型,并针对模型的结构特点,设计了求解其“乐观最优解”的并行种群混合进化的粒子群算法。最后,以四种调水情境为例,验证了本文所建模型的可行性;另外,分析表明相比于已有的跨流域水库群联合调度的单目标双层规划模型,本文所构建的半向量双层规划模型可以使各水库主要用水户广义缺水指数降低15%~25%,进一步证实了所建模型的有效性。

关键词: 跨流域调水, 水库群, 联合优化调度, 调度规则, 半向量双层规划