基于鲸鱼优化算法与投影寻踪耦合的云南省初始水权分配

论文基于公平性、效率性和可持续性原则,选取水资源开发用率等17个分水指标建立云南省初始水权分配指标体系,运用投影寻踪（Projection Pursuit, PP）技术确定云南省各州市初始水权分配水量。针对PP技术最佳投影方向难以确定的不足,利用一种新型群智能算法——鲸鱼优化算法（Whale Optimization Algorithm, WOA）寻优PP模型最佳投影方向,构建WOA-PP耦合的初始水权分配模型。通过6个典型测试函数对WOA进行仿真验证,仿真结果与文化算法（Cultural Algorithm, CA）、差分进化（Differential Evolution, DE）算法、混合蛙跳算法（Shuffled Frog Leaping Algorithm, SFLA）、布谷鸟搜索（Cuckoo Search, CS）算法、粒子群优化（Particle Swarm Optimization, PSO）算法和人工蜂群（Artificial Bee Colony, ABC）算法的寻优结果进行比较。结果表明：1）无论是单峰还是多峰函数,WOA能够探索不同的搜索空间,具有良好的开发和勘探能力,对Sphere等6个函数的寻优精度高于CA、DE、SFLA、CS、PSO和ABC算法,表现出较好的寻优精度、收敛速度、全局寻优能力与收敛稳定性。2）从WOA-PP模型初始水权分配结果及目前实行的综合法水量分配结果对比来看,2015年昭通、丽江、临沧、红河、文山、怒江两种方法的分配结果相差最小,在0.11亿~0.41亿m³之间;玉溪、普洱、大理、德宏和迪庆两种方法的分配结果相差最大,在2.06亿~4.38亿m³之间;其余州市两种方法的分配结果在1.12亿~1.61亿m³之间。2020年保山、昭通、丽江、临沧、红河、文山、怒江两种方法的分配结果相差最小,在0.02亿~0.41亿m³之间;昆明、玉溪和德宏两种方法的分配结果相差最大,分别为5.89亿、5.66亿和3.54亿m³;其余州市两种方法的分配结果在1.89亿~2.85亿m³之间。3）论文提出的初始水权分配模型及方法具有一定的可操作性和有效性,可为区域初始水权分配提供新的思路和方法。

Initial Water Rights Allocation in Yunnan Based on Whale Optimization Algorithm-Projection Pursuit Model

Based on the principles of equity, efficiency and sustainability, the water resources allocation index system of Yunnan Province was established based on 17 water allocation indexes, such as the initial water right of each city in Yunnan Province, using the Projection Pursuit (PP) allocation of water. Since the optimal projection direction of PP is difficult to be determined, a new swarm intelligence algorithm—Whale Optimization Algorithm (WOA) was used to optimize the projection direction of PP model, and an initial water rights allocation model of WOA-PP coupling was constructed. Culture algorithm (CA), Differential Evolution (DE) algorithm, Shuffled Frog Leaping Algorithm (SFLA), Cuckoo Search (CS) algorithm, Particle Swarm Optimization (PSO) algorithm and Artificial Bee colony (ABC) were used to simulate WOA by six typical test functions. The results show that WOA is able to explore different search spaces, whether it is a unimodal or a multimodal function, and it has good development and exploration ability. The searching accuracies of sphere and other six functions are all higher than those of CA, DE, SFLA, CS, PSO and ABC algorithm, showing better precision, convergence speed, global optimization ability and convergence stability. 2) By comparing the results of initial water rights allocation of WOA-PP model and current water allocation of comprehensive method, the allocation results of Zhaotong, Lijiang, Lincang, Honghe, Wenshan and Nujiang in 2015 had the least difference, the difference of allocation results of Yuxi, Pu'er, Dali, Dehong and Diqing were between 2.06×10⁸-4.38×10⁸ m³, and the allocation difference of other cities were between 1.12×10⁸-1.61×10⁸ m³. For the year of 2020, the allocation results of Baoshan, Zhaotong, Lijiang, Lincang, Honghe, Wenshan and Nujiang have the least difference, which are between 0.02×10⁸-0.41×10⁸ m³. The allocation results of Kunming, Yuxi and Dehong have the most difference, which are 5.89×10⁸, 5.66×10⁸ and 3.54×10⁸ m³, respectively. The difference of distribution in other cities and counties is between 1.89×10⁸ and 2.85×10⁸ m³. The initial water rights allocation model and optimization method proposed in this paper are feasible and effective, which can provide new ideas and methods for regional initial water rights allocation.