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基于Pareto解集的治沙区非线性分式多目标水土资源优化配置模型 
郭文贤,郭萍,潘琦,罗彪


(中国农业大学 水利与土木工程学院, 北京 100083) 

摘要: 
为提高沙漠治理效益的同时考虑提升水资源利用效率，本研究考虑治沙过程中水、土地和生物资源之间的作用与制约关系，构建以固碳制氧总价值最大和用水效率最大为目标的治沙区非线性分式多目标水土资源优化配置模型，对治沙区植物种植结构和植物生长季灌水量进行联合优化配置；采用遗传算法求解该模型以探究目标之间的博弈过程，并将模型应用于治沙区水土资源优化配置算例，得到Pareto解集，并分析了模型对可供水量的敏感性。结果表明:当配水量增加同时大量种植梭梭时系统的固碳制氧总价值最大，而当配水量减小同时大量种植花棒时系统的用水效率最大，沙拐枣在水土资源优化配置过程中不占优势；Pareto解集可以体现目标之间的博弈关系，通过博弈信息能够有效排除不合理方案；在3组典型方案中，2个目标处于平衡倾向的55号方案在水土资源的配置上更为合理；供水量对Pareto解集存在显著影响，当供水量超过3 500 m^{3}/hm^{2}时会导致水资源浪费，当目标处于平衡倾向时，治沙区最佳供水量为3 000 m^{3}/hm^{2}，该供水量能在获得理想的固碳制氧总价值的同时充分利用水资源。该模型综合考量了治沙过程中的水资源和土地资源，量化了目标之间的博弈关系，可以为沙漠化治理提供有效的决策支持信息。 
关键词: 沙漠治理 水土资源优化 非线性分式规划 多目标规划 Pareto解集 
DOI：10.11841/j.issn.10074333.2023.02.15 
投稿时间：20220518 
基金项目:国家自然科学基金项目(41871199) 

A nonlinear fractional multiobjective optimal allocation model of water and land resources in desert region based on Pareto solution set 
GUO Wenxian,GUO Ping,PAN Qi,LUO Biao

(College of Water Resource & Civil Engineering, China Agricultural University, Beijing 100083, China) 
Abstract: 
In order to improve the efficiency of desertification control and water resources, this study considered the role and restriction relationship between water, land and biological in the process of desertification control, and a nonlinear fractional multiobjective water and land resource model in the desertification control area was developed with the goal of maximizing the total value of carbon sequestration and oxygen production and maximizing water efficiency, using to jointly optimize the planting structure and irrigation water during growth season of plant in the desertification control area; the genetic algorithm was used to solve the model to explore the tradeoff process between goals. The model was applied to the example of optimal allocation of water and land resources in the desertification control area to obtain the Pareto solution set and analyze the sensitivity to the amount of water available. The results show that the total value of the system for carbon fixation and oxygen production is the largest when the water distribution increases and a large number of Haloxylon ammodendron are planted. The water efficiency of the system is maximized when the water distribution is reduced while a large number of Hedysarum scoparium are planted. Calligonum mongolicum has no advantage in the process of optimal allocation of water and land resources. The Pareto solution set can reflect the tradeoff between goals that can effectively eliminate unreasonable solutions; among the three typical schemes, the 55^{th} scheme with two goals in equilibrium is more reasonable in the distribution of water and land resources; water supply has a significant impact on Pareto solution set. When the water supply exceeds 3 500 m^{3}/hm^{2}, water resources will be wasted. When the goals are in equilibrium, the optimal water supply in the desertification control area is 3 000 m^{3}/hm^{2}, which the ideal total value of carbon fixation and oxygen production can be obtained to make full use of water resources. The model comprehensively considers water resources and land resources in the process of desertification control, quantifies the tradeoff relationship between goals, the results can provide effective decision support information for desertification control. 
Key words: desertification control water and land resource optimization nonlinear fractional programming multiobjective programming Pareto solution set 

