改进飞蛾火焰算法在多目标水资源优化配置中的应用
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摘要
水资源紧缺局面愈演愈烈,迫切需要进行水资源优化配置,以此提高水资源利用效率。基于自然元启发的优化算法越来越多的应用于求解多目标水资源优化配置问题。飞蛾火焰算法全局收敛性能较差且容易陷入局部最优解,针对以上问题,结合帕累托最优解概念,引入快速非支配排序策略,利用拥挤度及拥挤度比较算子对飞蛾火焰算法进行改进,继而采用改进的飞蛾火焰算法对ZTD1、ZTD2及ZDT3等3个多目标函数进行仿真实验,结果表明计算得到的帕累托最优前沿接近于理想帕累托前沿,收敛性能及精度优于本文所列举大部分多目标优化算法。最后将改进飞蛾火焰算法应用于三亚市水资源优化配置中,得到了23组帕累托最优解。选择了对缺水量最小有特殊偏好的方案作为最终决策方案,结果显示三亚市不同用水户总需水量39 015万m~3,各用水户总分配水量为39 015万m~3,缺水量为0,产生的经济效益为203.91亿元。改进的飞蛾火焰算法为多目标水资源优化配置问题提供了新的求解方法。
The shortage of water resources is intensifying,and there is an urgent need for the optimal allocation of water resources to improve the utilization efficiency of water resources. Nature-inspired meta-heuristic optimization algorithms are increasingly applied to solve multiobjective optimal allocation of water resources. Considering that the moth flame algorithm( MFO) has poor global convergence performance and is easy to fall into the local optimal solution,we adopt the concept of Pareto optimal solution,introduce a fast non-dominated sorting strategy,the crowding distance and the crowded-comparison operator on the MFO. Then the improved moth flame algorithm is used to simulate three multi-objective functions such as ZTD1,ZTD2 and ZDT3. The results show that the obtained Pareto optimal front is close to the true Pareto optimal front,and the convergence performance and accuracy are better than most of the multi-objective optimization algorithms listed in this paper. Finally,the improved moth flame algorithm is applied to the optimal allocation of water resources in Sanya City,and 23 Pareto optimal solutions have been obtained. The scheme with the special preference for the minimum water shortage is chosen as the final decision-making scheme. The results show that the total water demand of different water users in Sanya City is 39 015×10~4 m~3,the total water allocation of each water user is 39 015×10~4 m~3,the water shortage is 0,and the economic benefit is 203.91×10~8 RMB. The improved moth flame algorithm provides a new method for multi-objective water resources optimization configuration problem.
The shortage of water resources is intensifying,and there is an urgent need for the optimal allocation of water resources to improve the utilization efficiency of water resources. Nature-inspired meta-heuristic optimization algorithms are increasingly applied to solve multiobjective optimal allocation of water resources. Considering that the moth flame algorithm( MFO) has poor global convergence performance and is easy to fall into the local optimal solution,we adopt the concept of Pareto optimal solution,introduce a fast non-dominated sorting strategy,the crowding distance and the crowded-comparison operator on the MFO. Then the improved moth flame algorithm is used to simulate three multi-objective functions such as ZTD1,ZTD2 and ZDT3. The results show that the obtained Pareto optimal front is close to the true Pareto optimal front,and the convergence performance and accuracy are better than most of the multi-objective optimization algorithms listed in this paper. Finally,the improved moth flame algorithm is applied to the optimal allocation of water resources in Sanya City,and 23 Pareto optimal solutions have been obtained. The scheme with the special preference for the minimum water shortage is chosen as the final decision-making scheme. The results show that the total water demand of different water users in Sanya City is 39 015×10~4 m~3,the total water allocation of each water user is 39 015×10~4 m~3,the water shortage is 0,and the economic benefit is 203.91×10~8 RMB. The improved moth flame algorithm provides a new method for multi-objective water resources optimization configuration problem.
引文
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[19]YAN Zhi Hong,SHA Jin Xia,LIU Bin,et al.An Ameliorative Whale Optimization Algorithm for Multi-Objective Optimal Allocation of Water Resources in Handan,China[J].Water,2018,10(1):87.
[20]MIRJALILI S.Moth-flame optimization algorithm:a novel natureinspired heuristic paradigm[J].Knowledge-Based Systems,2015,89(7):228-249.
[21]杨德友,刘世宇.求解电力系统多目标环境经济调度的帕累托最优MFO算法[J].电工电能新技术,2018,37(2):30-37.
[22]ANBARASAN P,JAYABARATHI T.Optimal reactive power dispatch using moth-flame optimization algorithm[J].International Journal of Applied Engineering Research,2017,12(13):3 690-3 701.
[23]王子琪,陈金富,张国芳,等.基于飞蛾扑火优化算法的电力系统最优潮流计算[J].电网技术,2017,41(11):3 641-3 647.
[24]张强.基于MFO算法与PCNN的图像分割研究[D].兰州:兰州大学,2018.
[25]Aziz Mohamed Abd Ei,Ewees Ahmed A.,Hassanien Aboul Ella.Whale Optimization Algorithm and Moth-Flame Optimization for multilevel thresholding image segmentation[J].Expert Systems with Applications,2017,83:242-256.
[26]徐慧,方策,刘翔,等.改进的飞蛾扑火优化算法在网络入侵检测系统中的应用[J].计算机应用,2018,38(11):3 231-3 235,3 240.
[27]DEB K,AGRAWAL S,PRATAP A,et al.A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization:NSGA-Ⅱ[C]∥International Conference on Parallel Problem Solving from Nature.Berlin:Springer-Verlag,2000:849-858.
[28]SAVSANI V,TAWHID M A.Non-dominated sorting moth flame optimization(NS-MFO)for multi-objective problems[J].Engineering Applications of Artificial Intelligence,2017,63:20-32.
[29]ZITZLER E,DEB K,THIELE L.Comparison of Multi-objective Evolutionary Algorithms:Empirical Results[J].Evolutionary Computation,2000,8(2):173-195.
[30]DEB K.Multi-objective optimization using evolutionary algorithms[J].Mathematical Gazette,2008,87(509):487-410.
[31]FONSECA C M,FLEMING P J.On the performance assessment and comparison of stochastic multi-objective optimizers[C]∥International Conference on Evolutionary Computation the International Conference on Parallel Problem Solving from Nature-ppsn IV.Springer Berlin Heidelberg,1996:584-593.
[32]ZITZLER E.Evolutionary algorithms for multi-objective optimization:methods and applications[D].Zurich:Swiss Federal Institute of Technology Zurich,1999.
[33]YANG X S,DEB S.Multi-objective cuckoo search for design optimization[J].Computers&Operations Research,2013,40(6):1616-1 624.
[34]张亭亭,王树谦,刘彬,等.基于规则的水资源配置模型在三亚市的应用[J].河北工程大学学报(自然科学版),2014,31(3):68-70,85.
[2]公茂果,焦李成,杨咚咚,等.进化多目标优化算法研究[J].软件学报,2009,20(2):271-289.
[3]Rosenberg Richard Stuart.Simulation of genetic populations with biochemical properties[D].Michigan:University of Michigan,1967.
[4]Holland John Henry.Adaption in Natural and Artificial Systems[M].Michigan:The university of Michigan Press,1975.
[5]Schaffer J.David.Multiple Objective Optimization with Vector Evaluated Genetic Algorithms[C]∥Genetic algorithms and their applications:Proceedings of the First International Conference on Genetic Algorithms.Hillsdale:Lawrence Erlbaum Associates Publishers,1985:93-100.
[6]FONSECA C M,FLEMING P J.Genetic Algorithms for Multi-objective Optimization:Formulation Discussion and Generalization[C]∥Proceedings of the Fifth International Conference On Genetic Algorithms.Morgan Kaufmann Publishers Inc,1993:416-423.
[7]SRINIVAS N,Deb Kalyanmoy.Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms[J].Evolutionary Computation,1994,2(3):221-248.
[8]Zitzler Eckart,Thiele Lothar.Multiobjective evolutionary algorithms:a comparative case study and the strength Pareto approach.[J].IEEETransactions on Evolutionary Computation,1999,3(4):257-271.
[9]Zitzler Eckart,Laumanns Marco,Thiele L.SPEA2:Improving the Strength Pareto Evolutionary Algorithm[C]∥Evolutionary Methods for Design,Optimization and Control with Applications To Industrial Problems.Berlin:Springer-Verlag,2002,95-100.
[10]COELLO C A C C,PULIDO G T.A Micro-Genetic Algorithm for Multiobjective Optimization[C]∥International Conference on Evolutionary Multi-Criterion Optimization.Berlin:Springer-Verlag,2001:126-140.
[11]KENNEDY J,EBERHART R.Particle swarm optimization[C]∥In Proceedings of the 1995 IEEE international conference on neural networks,Australia,1995,4:1 942-1 948.
[12]李晓磊,邵之江,钱积新.一种基于动物自治体的寻优模式:鱼群算法[J].系统工程理论与实践,2002,22(11):32-38.
[13]DORIGO M,BIRATTARI M,Stutzle T.Ant colony optimization[J].IEEE Comput.Intell.,2006,1:28-39.
[14]Pinto Pedro C,Runkler Thomas A,Sousa Jo2o M C.Wasp Swarm Algorithm for Dynamic MAX-SAT Problems[C]∥International Conference on Adaptive&Natural Computing Algorithms.Berlin:Springer-Verlag,2007:350-357.
[15]MIRJALILI S,LEWIS A.The whale optimization algorithm[J].Advances in Engineering Software,2016,95:51-67.
[16]郭慧芳,马海波,董增川,等.改进的多目标粒子群算法在鄱阳湖水资源优化配置中的应用[J].中国农村水利水电,2012(10):61-64.
[17]伍爱华.多目标蚁群遗传算法在区域水资源优化配置中的应用研究[J].电脑知识与技术(学术交流),2007,(23):1 392-1 393,1398.
[18]刘彬,沙金霞.改进人工鱼群算法在水资源优化配置中的应用[J].人民黄河,2017,39(8):58-62.
[19]YAN Zhi Hong,SHA Jin Xia,LIU Bin,et al.An Ameliorative Whale Optimization Algorithm for Multi-Objective Optimal Allocation of Water Resources in Handan,China[J].Water,2018,10(1):87.
[20]MIRJALILI S.Moth-flame optimization algorithm:a novel natureinspired heuristic paradigm[J].Knowledge-Based Systems,2015,89(7):228-249.
[21]杨德友,刘世宇.求解电力系统多目标环境经济调度的帕累托最优MFO算法[J].电工电能新技术,2018,37(2):30-37.
[22]ANBARASAN P,JAYABARATHI T.Optimal reactive power dispatch using moth-flame optimization algorithm[J].International Journal of Applied Engineering Research,2017,12(13):3 690-3 701.
[23]王子琪,陈金富,张国芳,等.基于飞蛾扑火优化算法的电力系统最优潮流计算[J].电网技术,2017,41(11):3 641-3 647.
[24]张强.基于MFO算法与PCNN的图像分割研究[D].兰州:兰州大学,2018.
[25]Aziz Mohamed Abd Ei,Ewees Ahmed A.,Hassanien Aboul Ella.Whale Optimization Algorithm and Moth-Flame Optimization for multilevel thresholding image segmentation[J].Expert Systems with Applications,2017,83:242-256.
[26]徐慧,方策,刘翔,等.改进的飞蛾扑火优化算法在网络入侵检测系统中的应用[J].计算机应用,2018,38(11):3 231-3 235,3 240.
[27]DEB K,AGRAWAL S,PRATAP A,et al.A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization:NSGA-Ⅱ[C]∥International Conference on Parallel Problem Solving from Nature.Berlin:Springer-Verlag,2000:849-858.
[28]SAVSANI V,TAWHID M A.Non-dominated sorting moth flame optimization(NS-MFO)for multi-objective problems[J].Engineering Applications of Artificial Intelligence,2017,63:20-32.
[29]ZITZLER E,DEB K,THIELE L.Comparison of Multi-objective Evolutionary Algorithms:Empirical Results[J].Evolutionary Computation,2000,8(2):173-195.
[30]DEB K.Multi-objective optimization using evolutionary algorithms[J].Mathematical Gazette,2008,87(509):487-410.
[31]FONSECA C M,FLEMING P J.On the performance assessment and comparison of stochastic multi-objective optimizers[C]∥International Conference on Evolutionary Computation the International Conference on Parallel Problem Solving from Nature-ppsn IV.Springer Berlin Heidelberg,1996:584-593.
[32]ZITZLER E.Evolutionary algorithms for multi-objective optimization:methods and applications[D].Zurich:Swiss Federal Institute of Technology Zurich,1999.
[33]YANG X S,DEB S.Multi-objective cuckoo search for design optimization[J].Computers&Operations Research,2013,40(6):1616-1 624.
[34]张亭亭,王树谦,刘彬,等.基于规则的水资源配置模型在三亚市的应用[J].河北工程大学学报(自然科学版),2014,31(3):68-70,85.