NSGA-Ⅲ算法在水资源多目标优化配置中的应用

Application of NSGA-Ⅲ Algorithm in Multi-objective Optimization Allocation of Water Resources

针对红延河调水工程规划中多水源、多受水子区、多决策者间相互协调难的问题,建立了考虑经济、社会和环境效益的红延河调水工程的水资源多目标优化配置数学模型,采用基于参考点选择机制的遗传算法NSGA-Ⅲ得到受水区水资源多目标配置的Pareto解集。遗传算法NSGA-Ⅲ的SP值总是小于NSGA-Ⅱ的SP值,说明NSGA-Ⅲ更能提高Pareto解集分布的均匀性,进而维持种群的多样性;分析了经济、社会、环境效益3个目标中任意2个目标解集的分布情况,得出NSGA-Ⅲ对3个目标函数的优选能力更强。表明NSGA-Ⅲ算法适用于求解水资源多目标优化配置问题,可为决策者选择方案提供依据。

Aiming at the difficulty to coordinate multi-source,multi-demand area and multi-decision-maker in water resources allocation of Hongyanhe river water diversion project,the mathematical model of multi-objective optimization allocation of water resources was established considering economic benefit,social benefit and environmental benefit.The NSGA-Ⅲ based on the reference point selection mechanism was used to obtain multi-objective Pareto solution set of water resources allocation.The SP value of NSGA-Ⅲ is always smaller than the that of NSGA-Ⅱ,indicating that NSGA-Ⅲ can improve the uniformity of Pareto solution set distribution and maintain the diversity of the population.By analyzing the distribution of the solution sets of any two of the three objectives,it shows that NSGA-Ⅲ is more capable of optimizing the three objective functions of economic benefit,social benefit and environmental benefit.The results show that the NSGA-Ⅲ algorithm is suitable for solving the problem of multi-objective optimal allocation of water resources,which can provide the basis for decision maker to choose the scheme.