基于蚁群算法的给水管网改扩建研究
|
摘要
给水管网在保障经济建设和人民生活中发挥着重要的作用。随着经济的持续发展、城市规模的不断扩大,各发展中的城市面临着给水管网系统改扩建问题。由于给水管网投资大、费用高,合理进行管网优化改扩建能够节省大量投资,实现良好的经济效益和社会效益。本文结合某市的给水管网改扩建实际工程进行了研究。
较为准确的探讨管网分析模型是管网改扩建优化的必要基础。本文结合实际工程,建立了城市的管网微观模型,并进行了模型校核和现状评价,为管网系统改扩建优化设计奠定了坚实的基础。针对目前采用最大时流量进行的单工况管网设计中,管径都取值较大的情况,建立了基于多工况考虑的给水管网改扩建优化设计模型。
针对改扩建优化设计问题为复杂非线性规划问题、其决策变量为离散变量及其目标函数为多峰值函数的特点,本文结合某小区管网优化算例,分别采用遗传算法、蚁群算法及蚁群改进算法进行计算分析。结果表明:蚁群改进算法更容易实现全局最优解,且优化效率较高。
应用蚁群改进算法与传统设计方法在某市给水管网改扩建实际工程的应用表明:优化设计方案要比传统设计方案节省管网造价,多工况模型优于单工况模型。
Urban water network is an important part of the water-supply systems. According with the development of economic,expanding of city,the developing cities are facing the problem of upgrading and expansion of water distribution system.Because of the huge investment and management cost,optimal upgrading and expansion can save much money and actualize good ecnomic and social situation.The accomplishment of this paper is concerned with the practical water networks uprading and expansion engineering.Hydraulic modeling is the important foundation of the upgrading and expansion of water distribution system.Combining with real project . the preferable network mode) is obtained.It settled base of the upgrading and expansion of water distribution system. Because the simple loads optimal design for water supply is unreasonable, the multiple loads optimal design for water supply network systems is applied .Owing to the discrete character of the pipe diameter, with the object fuction being a multimodel function, and optimal upgrading and expansion being complex non-linear matter, genetic algorithm, simple ant colony optimization algorithm and improved ant colony optimization algorithm are seperataedly applied to a simple network optimization problem and the results obtained from improved ant colony optimization algorithm were better than those from the simple ACAAs and GA.Comparison of the optimal solution and the traditional solution of distribution system upgrading and expansion engineering in some city illustrates the optimal plan which applies improved ant colony Optimization algorithm saves the cost of water networks . furthermore,multiple loads optimal design for water supply network systems is better than simple load optimal design.
较为准确的探讨管网分析模型是管网改扩建优化的必要基础。本文结合实际工程,建立了城市的管网微观模型,并进行了模型校核和现状评价,为管网系统改扩建优化设计奠定了坚实的基础。针对目前采用最大时流量进行的单工况管网设计中,管径都取值较大的情况,建立了基于多工况考虑的给水管网改扩建优化设计模型。
针对改扩建优化设计问题为复杂非线性规划问题、其决策变量为离散变量及其目标函数为多峰值函数的特点,本文结合某小区管网优化算例,分别采用遗传算法、蚁群算法及蚁群改进算法进行计算分析。结果表明:蚁群改进算法更容易实现全局最优解,且优化效率较高。
应用蚁群改进算法与传统设计方法在某市给水管网改扩建实际工程的应用表明:优化设计方案要比传统设计方案节省管网造价,多工况模型优于单工况模型。
Urban water network is an important part of the water-supply systems. According with the development of economic,expanding of city,the developing cities are facing the problem of upgrading and expansion of water distribution system.Because of the huge investment and management cost,optimal upgrading and expansion can save much money and actualize good ecnomic and social situation.The accomplishment of this paper is concerned with the practical water networks uprading and expansion engineering.Hydraulic modeling is the important foundation of the upgrading and expansion of water distribution system.Combining with real project . the preferable network mode) is obtained.It settled base of the upgrading and expansion of water distribution system. Because the simple loads optimal design for water supply is unreasonable, the multiple loads optimal design for water supply network systems is applied .Owing to the discrete character of the pipe diameter, with the object fuction being a multimodel function, and optimal upgrading and expansion being complex non-linear matter, genetic algorithm, simple ant colony optimization algorithm and improved ant colony optimization algorithm are seperataedly applied to a simple network optimization problem and the results obtained from improved ant colony optimization algorithm were better than those from the simple ACAAs and GA.Comparison of the optimal solution and the traditional solution of distribution system upgrading and expansion engineering in some city illustrates the optimal plan which applies improved ant colony Optimization algorithm saves the cost of water networks . furthermore,multiple loads optimal design for water supply network systems is better than simple load optimal design.
引文
[1] 严煦世,赵洪宾.给水管网理论与计算[M],北京:中国建筑工业出版社,1986
[2] 赵洪宾,严煦世.给水管网系统理论与分析[M].北京:中国建筑工业出版社,2003
[3] I.C.Goulter.Systems Analysis in Water-Distribution Network Design:From Theory to Practice[J].Water.Res.Plan.Magmt, 1990,vol. 118(3):P.238～248
[4] Alperovits E.,Shamir U.Design of Optimal Water DistributionSystems[J].Water. Resoures. Research, 1977.vol. 13(6):P.885～889
[5] Gerald E.,Quindry etc.Optimization of Looped Water Distribution Systems[J], ASCE, 1981, vol. 107(4):P.665～679
[6] 俞国平.给水管网优化设计的新方法—广义简约梯度法[J].给水排水,1988,No.5:P12-15
[7] Okitsugu Fujiwara,Do Ba Khang.A Two Phase Decomposition Method for Optimal Design of Looped Water Distribution Networks[J].Water. Resources.Research, 1990,vol.26(4):R539～549
[8] IanC.Goulter, Francois Bouchart. Reliability-Constrained Pipe Network Model[J]. Hyr.Eng.ASCE, 1990,vol. 116(2):R211～229
[9] Kofi Awumah,lan Goulter,Suresh K Bhah.Entrophy-BasedRedundancy Measures in Water-Distribution Networks[J].Hyr.Eng.ASCE, 1991,vol. 117(5):R595～613
[10] Okitsugu Fujiwara,Amal U. Silva.Algorithm for Reliability-Based Optimal Design of Water Network[J].Env.Eng.ASCE, 1990,vol. 116(3):R575～587
[11] Heekyung Park,Jon C. Liebman. Redundancy-Constrained Minimum-cost designofwater-distributionnets[J]Water.Res.Plan.Magmt.ASCE, 1993,vol. 119(1):E83-99
[12] Kevin E.Laney,Larry W.Mays.Optimization Model for WaterDistribution System Design[J]. Hyr.Eng., 1989,vol.115(10):R.1401～1419
[13] Joong Hoon Kim,Larry W. Mays.Optimal Rehabiliatation Model For Water-Distribution Systems[J].Water.Res.Plan.Magmt., 1994,vo1.120(5):P.239～252
[14] M.JohnCullinane,KevinE.Lansey,LarryW.Mays.Optimization-Availability-Base d Design of Water Distribution Networks[J].Hyr.Engr., 1992, vol23(12):P22～25
[15] Yuchun Su,Larry W. Mays,Ning Duan,Kevin E. Lansey.Reliability-Based OptimizationModelforWater-DistributionSystems[J].Hyr.Eng., 1988,vol.114(2):P.1539-1555
[16] Ning Duan,Larry W. Mays,Kevin E. Lansey.Optimal Reliability-BasedDesign of Pumping and Distribution Systems[J].Hyr.Eng., 1990,vol.116(2):R249～268
[17] L.Gyergyek,S.Persen.Simulation and Optimal Control of Large Water Distribution Systems[J]. Mathematics and Computers in Simulation, 1982, vol.96(2):R214～216
[18] 王雪梅,王义合.模拟退火算法与遗传算法的结合[J].计算机学报,1997,v01.20(4):P.381～383
[19] 阮刚石.城市供水管网改扩建优化方法的研究[J].湖南城市学院学报(自然科学版),2004,vol.13(3):p.29～30
[19] David E Goldberg,Chie Hsiung Kuo.Genetic Algorithms in Pipe Optimization[J].Comp.Civ.Eng., 1987,vol.l(2):P.120～141
[21] Lansey Kevin,Mays Larry W.Optmization model for water distribution system design[J]. Journal of Hydraulic Enginering, 1989, vol.115(10):P.1401～1418
[22] L in C Y, Hajela P. Genetic algorithms in optimization problems with discrete and integerdesign variables[J]. Engineering Optimization, 1992, vo1.19(4):P.309～327
[23] Simpson,Dandy,Murphy.Genetic Algorithms Compared To Other Techniques for PipOptimization[J].Water.Res.Plan.Magmt., 1995,vol.120(4),P:423-441
[24] Savic D A,Walter G A .Genetic algorithms for lease-cost design of water distribution networks[J].Water Resource Plngand Mgmt. ASCE, 1997, vo1.123(2): P.69～76
[25] D.A.Savic,G.A.Walters.Evolving Sustainable Water Networks[J].Hydrological Sciences, 1997,vol.42(4). P:403～411
[26] Halbal D,Walter G A,Ouazar D,Savic D A.Water networks rehabilitation with structure messy genetic algorithm[J]. Water Resource Plng and Mgmt.ASCE, 1997, vol.123(3):p.137～145
[27] 邹林,马光文,丁晶.给水管网管径优化设计的遗传算法[J].四川联合大学学报(工程科学版),1998,vol.2(1):P.16～19
[28] 王雪峰.遗传算法在给水管网优化设计中的应用[D].同济大学硕士学位论文,1999
[29] 浙江造价信息,2004年第11期
[30] 信昆仑.遗传算法应用于给水管网管径组合优化[D].青岛:青岛建筑工程学院硕士学位论文,2000
[31] 吕鉴,贾燕兵.遗传算法在水分配系统优化设计内的应用研究[J].给水排水,2001,vol.27(3):P.36～39
[32] 刘小静,何元春,贺国定等.管网改扩建中管线布局和离散管径的遗传解法[J].管道技术与设备,2001.vol.18(3):P.12～14
[33] 222周荣敏,林性粹.用基于整数编码的改进遗传算法进行环状管网优化砹计[J].灌溉排水,2001,vol.20(3):P.49～52
[34] 贾燕兵,吕鑑.应用遗传算法进行给水管网优化设计[J].北京工业大学学报.2001,vo1.27(1):P.91～95
[35] 杜锐.遗传算法在给水管网优化设计中的应用[D].合肥:合肥工业大学硕士学位论文,2002
[36] 江志贤.改进遗传算法在城市给水管网优化中的应用[D].重庆:重庆大学硕士学位论文,2002
[37] 信昆仑,刘遂庆.混合编码遗传算法基于面向对象方法的实现及心用[J].计算机工程与应用.2003,vol.12(21):P.36～38
[38] 卜义惠,赵洪宾,周建华.用遗传算法求解给水管网系统优化改扩建模型[J].给水排水,2003,vol.29(12):P.89～92.
[39] 朱家松,龚健雅,郑皓.遗传算法在管网优化设计中的应用[J].武汉大学学报(自然科学版).2003,vol.28(3):P.254～256
[40] 工圃,龙腾锐,江志贤.改进遗传算法在给水管网改扩建工程中的应用[J].给水排水,2004,vol.30(7):P.102～106
[41] 葛琳、许仕荣.基于遗传算法的给水管网优化设计[J].湖南大学学报(自然科学版),2003,vol.30(3):P.167-170
[42] 况青松.改进的遗传算法在给水管网优化设计中的应用[D].合肥:合肥工业大学硕士学位论文,2003
[43] 潘玲.并行遗传算法在一种新的给水管网优化设计中的应用[D].合肥:合肥工业大学硕士学位论文,2004
[44] Colorni A,Dorigo M and Maniezzo V.Distributed optimization by ant colonies[A], proc,of lst European confArtificalLife.France,EIsevier,1991, P.134～142
[45] Colorni A,Dorigo M, ManiezzoV.An investigation of some properties of ant alogrithm[A]. Proc PPSN,london,1992, P.509～520
[46] Colorni A,Dorigo M ,Maniezzo V.Trubian N.Ant syetem for job-shop scheduling[A] .Belgian Jounal of Operation Reasearh and Statistic Computing Science,1995, P.105～128
[47] Dorigo,M.,Stutzle,T. Ant Colony opitimation[M].2004
[48] Luca M,Gambardella a, Dorigo M.Ant-Q:an reinforcement learning approach to the traveling salesmen problem[C].conf,France:Morgan Kaufmann 1995,P.252～260
[49] Fallside,P.perry.Hierarchical Optimization of a Water-Supply network[J]. Institute of Electrical Engineers,1975, vol.122(2):P.202～208
[50] P.Beaujean,H.Lecocq,G.Hutsemekers,P.Hermesse,L.Kenens.A new Design Approach for the the Terminal Units and Supervisory Systems Usedin Remote Control-lntergration of St and Products from the PC and lnternet World Proceedings of the International Conference on Cumputing and Control for the Water Industry,Leicester,2001:P.321～332
[51] 刘春兰.城市给水管网系统实用优化改扩建研究[D].哈尔滨:哈尔滨工业大学硕士学位论文,2000
[52] 王砚波.给水管网辅助优化改扩建研究[D].哈尔滨:哈尔滨工业大学硕士学位论文,2001
[53] 刘德钊.哈尔滨市给水管网系统优化改扩建研究[D].哈尔滨:哈尔滨工业大学学硕士学位论文,2003
[54] 王峪飞,俞国平,彭丽娜.关于给水管道技术经济计算模型的讨论[J].给水排水,vol.27(3),2001:.P.46～47
[55] Nlperovits,E.and.Shamir.U. Design of Optimal Water Distribution System[J],Water Res,1997,vol.13(6):P.885～900
[56] 新华,陈春芳,郑毅.给水管网可靠度得计算,中国给水排水[J],2000,vol.16(1):P.57～60
[57] 解可新,韩立兴,林皮联.最优化方法[M].天津大学出版社 第一版.1997.
[58] 施光燕,董加礼.最优化方法[M].高等教育出版社第一版.1999.
[59] Rossman,L.A,EPANET 2 Users Manual.2000,Washington,D.C
[60] Thomas stilizle and Holger Hoos.Max-Min ant system and local search for combinationalopitimationProblems[A], prof2~ndlnt .confMetaheurisic[C].Wien,spring-Verlag,1997
[61] 许刚,吕谋,张士乔,俞亭超.蚁群改进算法优化给水管刚神经网络宏观模型[A].控制与决策年会,2005,哈尔滨
[62] 许刚,张士乔,吕谋,俞亭超.蚁群改进算法用于供水系统直接优化调度[J].计算机集成制造系统
[63] 邱模杰,若干优化问题的蚂蚁算法及其实验研究[D].上海:上海理工大学硕士学位论文,2000
[64] 张纪会,徐心和.带遗忘因子的蚁群算法[J].系统仿真学报,2000,vol.17(1):P1～3
[65] 张纪会.徐心和.具有变异特征的蚁群算法[J].计算机研究与发展,1999,vol.36(10) :P.1240～1245
[66] 张纪会.自适应蚁群算法[J].控制理论与应用,2000,vol.17(2):P.1～4
[67] Water Authorities Associates/WRC.Network Analysis-A Code of Practice ,1989,vol.13(4):P.685～700
[68] 陶建科,刘遂庆.建立给水管网微观动态水力模型标准方法研究[J].给水排水,2000,vol.26(5):P.4～8
[69] 张洪国,袁一星,赵洪宾.给水管网动态模型中管道15阻力系数的组合灰色推定方法[J].哈尔滨建筑大学学报,1998,vol.31(5):P.58～63
[70] 袁一星,曲世琳,伍悦滨.城市给水管网水力模型准确度的阻力变化规律研究[J].中国给水排水,2003,vol.19(10):P.52～54
[71] 王荣和,刘遂庆.给水管网系统多工况优化设计及拟稳定状态水力模拟研究.同济大学博士学位论文[D],1998,上海
[72] Maier, H. R., Simpson, A. R., Zecchin, A. C. Ant colony optimization for design of water distribution systems[J]. Journal of Water Resources Planning and Management, 2003, vol. 129(3):P. 200～209
[73] 杭州市城市规划设计研究院,临海市域给水工程专业规划(送审稿),2004.12
[2] 赵洪宾,严煦世.给水管网系统理论与分析[M].北京:中国建筑工业出版社,2003
[3] I.C.Goulter.Systems Analysis in Water-Distribution Network Design:From Theory to Practice[J].Water.Res.Plan.Magmt, 1990,vol. 118(3):P.238～248
[4] Alperovits E.,Shamir U.Design of Optimal Water DistributionSystems[J].Water. Resoures. Research, 1977.vol. 13(6):P.885～889
[5] Gerald E.,Quindry etc.Optimization of Looped Water Distribution Systems[J], ASCE, 1981, vol. 107(4):P.665～679
[6] 俞国平.给水管网优化设计的新方法—广义简约梯度法[J].给水排水,1988,No.5:P12-15
[7] Okitsugu Fujiwara,Do Ba Khang.A Two Phase Decomposition Method for Optimal Design of Looped Water Distribution Networks[J].Water. Resources.Research, 1990,vol.26(4):R539～549
[8] IanC.Goulter, Francois Bouchart. Reliability-Constrained Pipe Network Model[J]. Hyr.Eng.ASCE, 1990,vol. 116(2):R211～229
[9] Kofi Awumah,lan Goulter,Suresh K Bhah.Entrophy-BasedRedundancy Measures in Water-Distribution Networks[J].Hyr.Eng.ASCE, 1991,vol. 117(5):R595～613
[10] Okitsugu Fujiwara,Amal U. Silva.Algorithm for Reliability-Based Optimal Design of Water Network[J].Env.Eng.ASCE, 1990,vol. 116(3):R575～587
[11] Heekyung Park,Jon C. Liebman. Redundancy-Constrained Minimum-cost designofwater-distributionnets[J]Water.Res.Plan.Magmt.ASCE, 1993,vol. 119(1):E83-99
[12] Kevin E.Laney,Larry W.Mays.Optimization Model for WaterDistribution System Design[J]. Hyr.Eng., 1989,vol.115(10):R.1401～1419
[13] Joong Hoon Kim,Larry W. Mays.Optimal Rehabiliatation Model For Water-Distribution Systems[J].Water.Res.Plan.Magmt., 1994,vo1.120(5):P.239～252
[14] M.JohnCullinane,KevinE.Lansey,LarryW.Mays.Optimization-Availability-Base d Design of Water Distribution Networks[J].Hyr.Engr., 1992, vol23(12):P22～25
[15] Yuchun Su,Larry W. Mays,Ning Duan,Kevin E. Lansey.Reliability-Based OptimizationModelforWater-DistributionSystems[J].Hyr.Eng., 1988,vol.114(2):P.1539-1555
[16] Ning Duan,Larry W. Mays,Kevin E. Lansey.Optimal Reliability-BasedDesign of Pumping and Distribution Systems[J].Hyr.Eng., 1990,vol.116(2):R249～268
[17] L.Gyergyek,S.Persen.Simulation and Optimal Control of Large Water Distribution Systems[J]. Mathematics and Computers in Simulation, 1982, vol.96(2):R214～216
[18] 王雪梅,王义合.模拟退火算法与遗传算法的结合[J].计算机学报,1997,v01.20(4):P.381～383
[19] 阮刚石.城市供水管网改扩建优化方法的研究[J].湖南城市学院学报(自然科学版),2004,vol.13(3):p.29～30
[19] David E Goldberg,Chie Hsiung Kuo.Genetic Algorithms in Pipe Optimization[J].Comp.Civ.Eng., 1987,vol.l(2):P.120～141
[21] Lansey Kevin,Mays Larry W.Optmization model for water distribution system design[J]. Journal of Hydraulic Enginering, 1989, vol.115(10):P.1401～1418
[22] L in C Y, Hajela P. Genetic algorithms in optimization problems with discrete and integerdesign variables[J]. Engineering Optimization, 1992, vo1.19(4):P.309～327
[23] Simpson,Dandy,Murphy.Genetic Algorithms Compared To Other Techniques for PipOptimization[J].Water.Res.Plan.Magmt., 1995,vol.120(4),P:423-441
[24] Savic D A,Walter G A .Genetic algorithms for lease-cost design of water distribution networks[J].Water Resource Plngand Mgmt. ASCE, 1997, vo1.123(2): P.69～76
[25] D.A.Savic,G.A.Walters.Evolving Sustainable Water Networks[J].Hydrological Sciences, 1997,vol.42(4). P:403～411
[26] Halbal D,Walter G A,Ouazar D,Savic D A.Water networks rehabilitation with structure messy genetic algorithm[J]. Water Resource Plng and Mgmt.ASCE, 1997, vol.123(3):p.137～145
[27] 邹林,马光文,丁晶.给水管网管径优化设计的遗传算法[J].四川联合大学学报(工程科学版),1998,vol.2(1):P.16～19
[28] 王雪峰.遗传算法在给水管网优化设计中的应用[D].同济大学硕士学位论文,1999
[29] 浙江造价信息,2004年第11期
[30] 信昆仑.遗传算法应用于给水管网管径组合优化[D].青岛:青岛建筑工程学院硕士学位论文,2000
[31] 吕鉴,贾燕兵.遗传算法在水分配系统优化设计内的应用研究[J].给水排水,2001,vol.27(3):P.36～39
[32] 刘小静,何元春,贺国定等.管网改扩建中管线布局和离散管径的遗传解法[J].管道技术与设备,2001.vol.18(3):P.12～14
[33] 222周荣敏,林性粹.用基于整数编码的改进遗传算法进行环状管网优化砹计[J].灌溉排水,2001,vol.20(3):P.49～52
[34] 贾燕兵,吕鑑.应用遗传算法进行给水管网优化设计[J].北京工业大学学报.2001,vo1.27(1):P.91～95
[35] 杜锐.遗传算法在给水管网优化设计中的应用[D].合肥:合肥工业大学硕士学位论文,2002
[36] 江志贤.改进遗传算法在城市给水管网优化中的应用[D].重庆:重庆大学硕士学位论文,2002
[37] 信昆仑,刘遂庆.混合编码遗传算法基于面向对象方法的实现及心用[J].计算机工程与应用.2003,vol.12(21):P.36～38
[38] 卜义惠,赵洪宾,周建华.用遗传算法求解给水管网系统优化改扩建模型[J].给水排水,2003,vol.29(12):P.89～92.
[39] 朱家松,龚健雅,郑皓.遗传算法在管网优化设计中的应用[J].武汉大学学报(自然科学版).2003,vol.28(3):P.254～256
[40] 工圃,龙腾锐,江志贤.改进遗传算法在给水管网改扩建工程中的应用[J].给水排水,2004,vol.30(7):P.102～106
[41] 葛琳、许仕荣.基于遗传算法的给水管网优化设计[J].湖南大学学报(自然科学版),2003,vol.30(3):P.167-170
[42] 况青松.改进的遗传算法在给水管网优化设计中的应用[D].合肥:合肥工业大学硕士学位论文,2003
[43] 潘玲.并行遗传算法在一种新的给水管网优化设计中的应用[D].合肥:合肥工业大学硕士学位论文,2004
[44] Colorni A,Dorigo M and Maniezzo V.Distributed optimization by ant colonies[A], proc,of lst European confArtificalLife.France,EIsevier,1991, P.134～142
[45] Colorni A,Dorigo M, ManiezzoV.An investigation of some properties of ant alogrithm[A]. Proc PPSN,london,1992, P.509～520
[46] Colorni A,Dorigo M ,Maniezzo V.Trubian N.Ant syetem for job-shop scheduling[A] .Belgian Jounal of Operation Reasearh and Statistic Computing Science,1995, P.105～128
[47] Dorigo,M.,Stutzle,T. Ant Colony opitimation[M].2004
[48] Luca M,Gambardella a, Dorigo M.Ant-Q:an reinforcement learning approach to the traveling salesmen problem[C].conf,France:Morgan Kaufmann 1995,P.252～260
[49] Fallside,P.perry.Hierarchical Optimization of a Water-Supply network[J]. Institute of Electrical Engineers,1975, vol.122(2):P.202～208
[50] P.Beaujean,H.Lecocq,G.Hutsemekers,P.Hermesse,L.Kenens.A new Design Approach for the the Terminal Units and Supervisory Systems Usedin Remote Control-lntergration of St and Products from the PC and lnternet World Proceedings of the International Conference on Cumputing and Control for the Water Industry,Leicester,2001:P.321～332
[51] 刘春兰.城市给水管网系统实用优化改扩建研究[D].哈尔滨:哈尔滨工业大学硕士学位论文,2000
[52] 王砚波.给水管网辅助优化改扩建研究[D].哈尔滨:哈尔滨工业大学硕士学位论文,2001
[53] 刘德钊.哈尔滨市给水管网系统优化改扩建研究[D].哈尔滨:哈尔滨工业大学学硕士学位论文,2003
[54] 王峪飞,俞国平,彭丽娜.关于给水管道技术经济计算模型的讨论[J].给水排水,vol.27(3),2001:.P.46～47
[55] Nlperovits,E.and.Shamir.U. Design of Optimal Water Distribution System[J],Water Res,1997,vol.13(6):P.885～900
[56] 新华,陈春芳,郑毅.给水管网可靠度得计算,中国给水排水[J],2000,vol.16(1):P.57～60
[57] 解可新,韩立兴,林皮联.最优化方法[M].天津大学出版社 第一版.1997.
[58] 施光燕,董加礼.最优化方法[M].高等教育出版社第一版.1999.
[59] Rossman,L.A,EPANET 2 Users Manual.2000,Washington,D.C
[60] Thomas stilizle and Holger Hoos.Max-Min ant system and local search for combinationalopitimationProblems[A], prof2~ndlnt .confMetaheurisic[C].Wien,spring-Verlag,1997
[61] 许刚,吕谋,张士乔,俞亭超.蚁群改进算法优化给水管刚神经网络宏观模型[A].控制与决策年会,2005,哈尔滨
[62] 许刚,张士乔,吕谋,俞亭超.蚁群改进算法用于供水系统直接优化调度[J].计算机集成制造系统
[63] 邱模杰,若干优化问题的蚂蚁算法及其实验研究[D].上海:上海理工大学硕士学位论文,2000
[64] 张纪会,徐心和.带遗忘因子的蚁群算法[J].系统仿真学报,2000,vol.17(1):P1～3
[65] 张纪会.徐心和.具有变异特征的蚁群算法[J].计算机研究与发展,1999,vol.36(10) :P.1240～1245
[66] 张纪会.自适应蚁群算法[J].控制理论与应用,2000,vol.17(2):P.1～4
[67] Water Authorities Associates/WRC.Network Analysis-A Code of Practice ,1989,vol.13(4):P.685～700
[68] 陶建科,刘遂庆.建立给水管网微观动态水力模型标准方法研究[J].给水排水,2000,vol.26(5):P.4～8
[69] 张洪国,袁一星,赵洪宾.给水管网动态模型中管道15阻力系数的组合灰色推定方法[J].哈尔滨建筑大学学报,1998,vol.31(5):P.58～63
[70] 袁一星,曲世琳,伍悦滨.城市给水管网水力模型准确度的阻力变化规律研究[J].中国给水排水,2003,vol.19(10):P.52～54
[71] 王荣和,刘遂庆.给水管网系统多工况优化设计及拟稳定状态水力模拟研究.同济大学博士学位论文[D],1998,上海
[72] Maier, H. R., Simpson, A. R., Zecchin, A. C. Ant colony optimization for design of water distribution systems[J]. Journal of Water Resources Planning and Management, 2003, vol. 129(3):P. 200～209
[73] 杭州市城市规划设计研究院,临海市域给水工程专业规划(送审稿),2004.12