基于混沌理论和蚁群算法的多水源供水系统优化调度研究
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摘要
城市供水系统已逐步发展为广地域分布的联网多水源系统。虽然每个水源都有就近供水性质,但由于泵站所属用户用水特征不同,对泵站各时段供水要求存在明显差异。对系统水量的优化预测协调调度的目的是优化资源的合理利用,减少能量损耗又可以较好解决供水边缘地带供水质量,获取良好的社会和经济效益。城市供水系统表现为供水环境复杂、用户多样化,特别是受城市发展布局变化影响用水需求多变,对多水源供水系统的优化调度学术上可归为动态不确定环境下受多条件约束的多目标优化控制问题,该问题具有高度非线性和耦合混合变量的供水系统模型,要实现并满足实时调度需要找出足够精度的用水量预测方法和先进的优化调度策略。
论文在寻求取得城市时用水量的时间序列基础上,通过推演算得延迟时间和嵌入维数,探索并应用相空间重构技术,借助混沌理论研究时用水量的混沌特性,证明了一般城市的时用水量具有典型的混沌特性,因而多水源供水系统属典型的混沌系统。通过现代先进理论工具,系统分析研究了某城市给定对象的沿程各大用户用水量观测序列的分形和链级混沌关联,并依据系统相图和最大Lyapunov指数变化研究比较漏损故障发生时的漏水时序的不同混沌特性。仿真结果表明,通过跟踪各混沌特征参数的演化趋势可识别与检测某些漏损故障,该结果可作实际检测验证参考,为及时查找及维护供水系统提供依据,有助于防止资源损耗。
通过对不同长度历史训练数据下的各混沌方法预测效果作分析比较后,找出了适用于多水源供水系统时用水量短期预测的混沌预测工具。提出一种混沌横向分时段预测方法,以模式识别获得高关联度的横向时序为研究样本,重构横向分时段相空间并分析典型时段流量数据的混沌特性,通过在线最小二乘支持向量机做混沌预测工具求得各时段用水流量。为了能动态跟踪用水突变,提出纵向残差修正预测方法,实时采集纵向数据序列作残差计算,进而用灰色模型进行残差预测修正以提高实时预测精度。依据杭州市萧山某大用户时用水量实例,对一段时间的正常用水和突变用水做连续24小时以上时间的短期混沌预测,全面比较了相关类型方法的预测效果表明,混沌横向分时段预测方法能很好反映被调控对象沿程用户的用水特点,较好地达到了系统短期预测精度；在此基础上作纵向残差修正能很好跟踪实时用水变化情况,更易满足供水系统实时优化调度的需求。
针对多水源供水系统用户用水的特征,借助日益成熟的计算机控制技术寻求现代理论调度控制算法,发现蚁群算法有其可取之处,但常规蚁群算法存在易陷入局部最优、易早熟和分散搜优收敛慢的缺点。采用聚度控制蚁群算法求取离散问题,引入黄金分割法则设置参数,根据蚂蚁聚集的信息权重调整决策概率,能较好克服上述缺点,获取了好的求解效果。并针对求解连续变量全局优化的难题,提出改进聚度控制的蚁群算法,在连续变量域采用实数编码,决策概率中引入区间聚度信息权重,并利用灵活转移步长和动态挥发系数对蚁群分布寻优进行控制,使其迭代前期保持解值多样性与后期又具有快速收敛的双重特性。仿真结果表明,该方法能较好平衡广范围搜索和信息素正反馈能力,有效降低了陷入局部最优的风险,在求解多维多极值连续函数的全局优化问题时具有明显优势。将这两种聚度控制蚁群算法应用于多水源供水系统常规优化调度,仿真论证了其有获得期望效果的潜力。
文章最后针对给定的多水源供水系统约束条件众多耗时长且压力波动较大等问题做了更进一步的研究,提出一种基于增量模型控制压力恒定的优化调度新策略。由用户流量参数预测建立了增量模型,以分界监控点压力参数恒定为目标函数,并给出该策略：将机泵出口压力、机泵状态及变频机泵转速为优化决策变量,并采用混合聚度控制蚁群算法同时优化连续和离散变量做实时优化计算。算例仿真表明,在上述给定模型下,新算法可快速找到优化调度的最优解,能较好跟踪用水流量变化和保持监测控制点的实时压力恒定,提高了多水源的实时协调调度能力,有效降低了能耗。
The urban supply system develops into a vast distributed large-scale system. For the significant different demands at different time due to the different characteristic of consumers, the multi-source water system needs to be scheduled properly. The rational forecast and scheduling of water demands can bring social and economic benefits by reducing energy consumption and providing high quality of marginal consumers. There are complex environments and different kinds of water consumers. Because the water demands are changed as the development of the city, it is a dynamic constrained multi-objective optimization problem. Since it is a mixed integer nonlinear programming problem, it is necessary to bring up a paccurate forecast method and an advanced scheduling strategy.
By computing the delay time and embedded dimension, the phase space of urban hourly water consumption time series is reconstructed. Chaos theory is used to study the chaotic characters, and the hourly water consumption is turning out to be a typical chaotic system. The water time series of successive users are proved to be fractal and chaotic chaining relevant by advanced tools. On this basis, the different chaotic characters of booster and leakage are compared by phase diagram and the maximum lyapunov exponent variation. Test results show that the chaotic characters are changed immediately when the booster occurs, and slow leakage can be discovered after two hours. Thus this method supplies new judgments to effectively amend water system in time and decrease the loss of water resource.
After the comparison of different chaos prediction methods by training different length history data, a new prediction method is proposed named chaotic horizontal period clustering, aiming at the high short-term prediction accuracy of hourly water consumption. The horizontal time series are determined as research samples by pattern recognition with high relevancy. After reconstructing the phase space of horizontal period clustering and analyzing chaotic characteristics of typical period data, chaotic prediction model is established. On line least square support vector machine (LS-SVM) is used to forecaste the period flows. Furthermore, to track water consumptions dynamically, vertical residuals are modified by grey model prediction (GMP) after collecting real-time data. The period historical data from Xiao Shan are supplied in the normal and abnormal case study to forecast the day-ahead hourly water consumption, and prediction accuracy with different methods are compared.
A Cohesion Control Ant Colony algorithm (CCAC) is used to optimize the discrete problem, by using the golden section method to set parameter, and using gathered information weights to tuning decision policy. Then the CCAC is improved (ICCAC) with continuous coding to solve global optimization problem of continuous function. Section cohesion weight is brought into the decision policy to control ant distributions; flexible search steps are used to encourage local search after ICCAC locating the most promising direction to transfer; and dynamic evaporation factor is incorporated in pheromone updating. Experimental results show that ICCAC can keep good balance between wide exploration and pheromone exploitation, is an effective method to solve continuous global optimization problems. The algorithm mentioned above has shown an execellent performance in the short time scheduling problem of multi-source water system.
This paper deals with the real-time scheduling problem of numerous constraints, long time-consuming, the highly variable nodal pressure and an optimal scheduling strategy based on increment model controlling the pressure constant is proposed. Firstly, the flow parameter increment model is established by predicting the nodal real-time water demands, and the variations of nodal pressures are obtained. Then the scheduling strategy is deduced from controlling the constant monitoring pressure parameters. At last, the parameters of pumps output pressures, pumps operation status and speed changes are regarded as decision variables to be regulated, and ICCAC is used to optimize the continuous and discrete variables at a time. The test results show that the new strategy can find the optimal schedule solution quickly, and well track the nodal stream variations to keep the constant monitoring nodal pressure, thus it strengthens the real-time regulation ability of multi-source water supply system, and can reduce the energy cost effectively.
论文在寻求取得城市时用水量的时间序列基础上,通过推演算得延迟时间和嵌入维数,探索并应用相空间重构技术,借助混沌理论研究时用水量的混沌特性,证明了一般城市的时用水量具有典型的混沌特性,因而多水源供水系统属典型的混沌系统。通过现代先进理论工具,系统分析研究了某城市给定对象的沿程各大用户用水量观测序列的分形和链级混沌关联,并依据系统相图和最大Lyapunov指数变化研究比较漏损故障发生时的漏水时序的不同混沌特性。仿真结果表明,通过跟踪各混沌特征参数的演化趋势可识别与检测某些漏损故障,该结果可作实际检测验证参考,为及时查找及维护供水系统提供依据,有助于防止资源损耗。
通过对不同长度历史训练数据下的各混沌方法预测效果作分析比较后,找出了适用于多水源供水系统时用水量短期预测的混沌预测工具。提出一种混沌横向分时段预测方法,以模式识别获得高关联度的横向时序为研究样本,重构横向分时段相空间并分析典型时段流量数据的混沌特性,通过在线最小二乘支持向量机做混沌预测工具求得各时段用水流量。为了能动态跟踪用水突变,提出纵向残差修正预测方法,实时采集纵向数据序列作残差计算,进而用灰色模型进行残差预测修正以提高实时预测精度。依据杭州市萧山某大用户时用水量实例,对一段时间的正常用水和突变用水做连续24小时以上时间的短期混沌预测,全面比较了相关类型方法的预测效果表明,混沌横向分时段预测方法能很好反映被调控对象沿程用户的用水特点,较好地达到了系统短期预测精度；在此基础上作纵向残差修正能很好跟踪实时用水变化情况,更易满足供水系统实时优化调度的需求。
针对多水源供水系统用户用水的特征,借助日益成熟的计算机控制技术寻求现代理论调度控制算法,发现蚁群算法有其可取之处,但常规蚁群算法存在易陷入局部最优、易早熟和分散搜优收敛慢的缺点。采用聚度控制蚁群算法求取离散问题,引入黄金分割法则设置参数,根据蚂蚁聚集的信息权重调整决策概率,能较好克服上述缺点,获取了好的求解效果。并针对求解连续变量全局优化的难题,提出改进聚度控制的蚁群算法,在连续变量域采用实数编码,决策概率中引入区间聚度信息权重,并利用灵活转移步长和动态挥发系数对蚁群分布寻优进行控制,使其迭代前期保持解值多样性与后期又具有快速收敛的双重特性。仿真结果表明,该方法能较好平衡广范围搜索和信息素正反馈能力,有效降低了陷入局部最优的风险,在求解多维多极值连续函数的全局优化问题时具有明显优势。将这两种聚度控制蚁群算法应用于多水源供水系统常规优化调度,仿真论证了其有获得期望效果的潜力。
文章最后针对给定的多水源供水系统约束条件众多耗时长且压力波动较大等问题做了更进一步的研究,提出一种基于增量模型控制压力恒定的优化调度新策略。由用户流量参数预测建立了增量模型,以分界监控点压力参数恒定为目标函数,并给出该策略：将机泵出口压力、机泵状态及变频机泵转速为优化决策变量,并采用混合聚度控制蚁群算法同时优化连续和离散变量做实时优化计算。算例仿真表明,在上述给定模型下,新算法可快速找到优化调度的最优解,能较好跟踪用水流量变化和保持监测控制点的实时压力恒定,提高了多水源的实时协调调度能力,有效降低了能耗。
The urban supply system develops into a vast distributed large-scale system. For the significant different demands at different time due to the different characteristic of consumers, the multi-source water system needs to be scheduled properly. The rational forecast and scheduling of water demands can bring social and economic benefits by reducing energy consumption and providing high quality of marginal consumers. There are complex environments and different kinds of water consumers. Because the water demands are changed as the development of the city, it is a dynamic constrained multi-objective optimization problem. Since it is a mixed integer nonlinear programming problem, it is necessary to bring up a paccurate forecast method and an advanced scheduling strategy.
By computing the delay time and embedded dimension, the phase space of urban hourly water consumption time series is reconstructed. Chaos theory is used to study the chaotic characters, and the hourly water consumption is turning out to be a typical chaotic system. The water time series of successive users are proved to be fractal and chaotic chaining relevant by advanced tools. On this basis, the different chaotic characters of booster and leakage are compared by phase diagram and the maximum lyapunov exponent variation. Test results show that the chaotic characters are changed immediately when the booster occurs, and slow leakage can be discovered after two hours. Thus this method supplies new judgments to effectively amend water system in time and decrease the loss of water resource.
After the comparison of different chaos prediction methods by training different length history data, a new prediction method is proposed named chaotic horizontal period clustering, aiming at the high short-term prediction accuracy of hourly water consumption. The horizontal time series are determined as research samples by pattern recognition with high relevancy. After reconstructing the phase space of horizontal period clustering and analyzing chaotic characteristics of typical period data, chaotic prediction model is established. On line least square support vector machine (LS-SVM) is used to forecaste the period flows. Furthermore, to track water consumptions dynamically, vertical residuals are modified by grey model prediction (GMP) after collecting real-time data. The period historical data from Xiao Shan are supplied in the normal and abnormal case study to forecast the day-ahead hourly water consumption, and prediction accuracy with different methods are compared.
A Cohesion Control Ant Colony algorithm (CCAC) is used to optimize the discrete problem, by using the golden section method to set parameter, and using gathered information weights to tuning decision policy. Then the CCAC is improved (ICCAC) with continuous coding to solve global optimization problem of continuous function. Section cohesion weight is brought into the decision policy to control ant distributions; flexible search steps are used to encourage local search after ICCAC locating the most promising direction to transfer; and dynamic evaporation factor is incorporated in pheromone updating. Experimental results show that ICCAC can keep good balance between wide exploration and pheromone exploitation, is an effective method to solve continuous global optimization problems. The algorithm mentioned above has shown an execellent performance in the short time scheduling problem of multi-source water system.
This paper deals with the real-time scheduling problem of numerous constraints, long time-consuming, the highly variable nodal pressure and an optimal scheduling strategy based on increment model controlling the pressure constant is proposed. Firstly, the flow parameter increment model is established by predicting the nodal real-time water demands, and the variations of nodal pressures are obtained. Then the scheduling strategy is deduced from controlling the constant monitoring pressure parameters. At last, the parameters of pumps output pressures, pumps operation status and speed changes are regarded as decision variables to be regulated, and ICCAC is used to optimize the continuous and discrete variables at a time. The test results show that the new strategy can find the optimal schedule solution quickly, and well track the nodal stream variations to keep the constant monitoring nodal pressure, thus it strengthens the real-time regulation ability of multi-source water supply system, and can reduce the energy cost effectively.
引文
[1]Robert D J, Lawrence B H. Macroscopic distribution system modeling[J].AWWA,1975,7:377-380.
[2]Pezeshk S, Helweg O J.Adaptive search optimization in reducing pump operming costs, Journal of Water Resources Planning and Management,ASCE,1996,122(1),57-63.
[3]郑爽英.城市供水系统两级优化调度的宏观模型研究[J].四川联合大学学报(工程科学版),1997,1(2)：60-68.
[4]Shvartser L, Shamir U, Feldman M. Forecasting hourly water demands by pattern recognition approach[J]. Journals of Water Resources Planning and anagement,ASCE,1993,119(6):611-627.
[5]Homwongs C, Sastri T, Foster J W. A daptive forecasting of hourly municipal water consumption[J]. Journals of Water Resources Planning and Management, ASCE,1994,120(6):888-905.
[6]Liu H B, Zhang H W. Comparison of the City water consumption Shot-Term Forecasting Methods[J]. Transactions of Tianjin University,2002,8(3):211-215.
[7]柳景青.调度时用水量预测的分时段混沌建模方法[J].浙江大学学报(工学版),2005,39(1)：11-15.
[8]赵鹏,张宏伟.城市用水量的混沌特性与预测[J].中国给水排水,2008,24(5)：90-93.
[9]Efallside F, Perry P F.Optimization of a water supply network[C]. Proceeding institute of electricity engineering,1975,122(2):202-208.
[10]Nitivattananon V, Sadowski E C, et al.Optimization of water supply system operation[J]. Journal of Water Resources Planning and Management,ASCE,1996,122(5):374-384.
[11]Tarquin A J, Dowdy J.Optimal Pump Operation in Water Distribution[J]. Journal of Hydraulic Engineering, ASCE,1989,115(2):158-168.
[12]仲伟俊,徐南荣,陈森发.城市供水系统调度的分解—协调优化方法[J].自动化学报,1990,16(3)：217-225.
[13]Ormsbee L E. Implicit network calibration[J].Water Resour.Plng.and Mgmt.,ASCE,1989,115(2):243-257.
[14]Jowitt Paul W, Germanopoulos G.Optimal Pump Scheduling in Water-Supply Networks[J]. Journal of Water Resources Planning and Management,1992,118(4):406-420.
[15]Chase DV,OrmsbeeLE.Optimal pump operation of water distribution system with multiple storage tanks[C].Proceeding conference on water resources planning and management, ASCE, New York, 1989:733-736.
[16]Brion L M, Mays LW.Methodology for Optimal Operation of Pumping Stations in Water Distribution Systems[J].Journal of Hydraulic Engineering ASCE,1991,117(11):1551-1569.
[17]Ormsbee L E, Reddy S L. Nonlinear heuristic for pump operation[J]. Journal of Water Resources Planning and Management, ASCE,1995,121(4:302-309.
[18]王增义,张宏伟.送水泵站的优化调度[J].中国给水排水,1991,7(1)：55-57
[19]Simpson A R, Dandy G C, Murphy L J. Genetic algorithms compared to other techniques for pipe optimization[J]. Water Resour. Ping, and Mgmt, ASCE,1994,120(4:423-443.
[20]Carlos E,Victor H,Eduardo F.Multi-objective optimization of water-using systems[J].European Journal of Operational Research,2007,181:1691-1707.
[21]张承慧,廖莉,李洪斌.水工业系统的优化调度及其遗传算法求解[J].计算机集成制造系统—CIMS,2003,9(8)：645-651.
[22]Reis L F R,Bessler F T,Waiters G A, et al. Water supply reservoir operation by combined genetic algorithmlinear programming(GA-LP)approach[J]. Water Resources Management,2006, (20):227-255.
[23]Haghighi A, Samani H M V, Samani Z M V. GA-ILP Method for Optimization of Water Distribution Networks[J].Water Resour Manage,2011,25:1791-1808.
[24]俞亭超,张土乔.供水系统直接优化调度遗传算法求解模型研究[J].浙江大学学报(工学版),2006,(5)：74-79
[25]Maier H R, Simpson A R, Zecchin A C, Foong WK, et al.Ant colony optimization for design of water distribution systems[J]. J Water Resour Plan Manage,2003,129(3):200-209.
[26]Lopez-Ibanez M, Prasad T D, Paechter B. Ant Colony Optimization for Optimal Control of Pumps in Water Distribution Netwoiks[J]. JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT,2008,134(4):337-347.
[27]Eric Bonabeau,Marco Dorigo,and Guy Theraulaz.Swarm intelligence:from natural to artificial systems[M], New York:Oxford University Press,1999.
[28]Kennedy J, Eberhart R C, Shi Y H.Swarm Intelligence[M].San Francisco:Morgan Kaufmann,2001.
[29]Colomi A, Dorigo M, Maffioli F, et al.Trubian.Heuristics from nature for hard combinational problems[J]. International Transactions in Opernational Research,1996,3(1):1-21.
[30]Dorigo M, Maniezzo V, Colorni A. Positive feedback as a search strategy[R].Technical Report 91-106,Dipartimento di Elettronica,Politecnico di Milano,IT,1991.
[31]Dorigo M.Optimization Learning and Natural Algorithma[D]. Ph.D.thesis, Dipartimento di Elettronica, Politecnico di Milano,IT,1992.
[32]Colorni A, Dorigo M, Maniezzo V. Distributed optimization by ant colonies[C]. European Conference on Artificial Life,134-142 Elsevier,1992.
[33]Bullnheimer B, Hartl R F, Stranss C. A New Rank Based Version of the Ant System:A Computational Study[J].Central European Journal for Operations Research and Eeonomies,1999,7(l):25-38.
[34]Stutzle T, Hoos H H. Max-Min ant system[J]. Future Generation computer Systems,2000,16:889-914.
[35]Dorigo M, Stutzle T. Ant colony Optimization[M].MIT Press,2004.
[36]Dorigo M, Bonabeau E, Theraulaz G. Ant algorithms and stigmergy[J]. Future Generation computer systems, 2000,16:851-871.
[37]Dorigo M, Maniezzo V, Colomi A. The Ant System:An autocatalytic optimizing Process[R]. Technical Report 91-016 Revised, DiPartimento di Elettroniea, Politecnieo di Milano, Milan, Italy,1991.
[38]Dorigo M, ManiezzoV, Colorni A.The Ant System:Optimization by a colony of cooperating agents[J]. IEEE Transactions on Systems, Man, and Cybemeties-Part B,1996,26(1):29-41.
[39]Gambardella L M, Dorigo M. Ant-Q:A reinforcement learning approach to the traveling salesman problem[C].In A.Prieditis and S.Russell,editors,Proceedings of the Twelfth International Conference on Machine Leaming(ML-95),pages 252-260.Morgan Kaufmann Publishers,Palo Alto,CA,1995.
[40]Dorigo M, Gambardella L M. A study of some Properties of ANT-Q[C]. Proceedings of PPSNIV-Fourth International Conference on Parallel Problem Solving From Nature, SPringer-Verlag, Berlin,1996:656-665.
[41]Dorigo M, Gambardella L M. Ant Colony System:A cooperative learning approach to the traveling salesman Problem[J].IEEE Transaetions on Evolutionary Computation,1997, 1(1):53-66.
[42]Dorigo M, Maniezzo V, Colorni A. The ant system:Optimization by a colony of cooperating agents[J]. IEEE Transactions on System, Man, and Cybernetics-Part B.1996,26(1):29-41.
[43]Gutjahr W J. A graph based ant system and its convergence[J]. Future Gener.Comput System, 2000,16(8):873-888.
[44]Blum C, Roli A, Dorigo M. HC-ACO:The hyper-cube framework for Ant colony Optimization[C]. In proeeedings of MIC'2001-Metaheuristies International Conferenee,2001:399-403, Porto, Portugal.
[45]Kong M, Tian P, Kao YC. A new ant colony optimization algorithm for the multidimensional knapsack problem[J]. Computers and Operations Research,2008,35:2672-2683.
[46]覃刚力,杨家本.自适应调整信息素的蚁群算法[J].信.息与控制,2002,31(3)：198-201.
[47]谢剑英,王颖.一种自适应蚁群算法及其仿真研究[J].系统仿真学报,2002,14(1)：31-33.
[48]吴斌,史忠植.一种基于蚁群算法的TSP问题分段求解算法[J].计算机学报2002.24(12)：1328-1333.
[49]Gambardella L M, Dorigo M. Solving symmetric and asymmetrie TSPs by ant colonies[C]. in:Proeeedings of the IEEE International Conference on Evolutionary Computation (ICEC'96), IEEEPress, Piseataway, USA,1996:622-27.
[50]张纪会,高齐圣,徐心和.自适应蚁群算法[J].控制理论与应用,2000,17(1)：1-3.
[51]Stutzle T, Dorigo M. ACO algorithms for the quadratie assignment Problem.In Come,D., Dorigo M and Glover F, editors, New Ideas in Optimization,1999:33-50. MeGrawHill, London, UK.
[52]ManiezzoV, Colorni A.The Ant System applied to the quadratie assignment Problem[J]. IEEE Trans.Knowledge Data Eng,1999,11(5):769-778.
[53]Dicaro G, Dorigo M. Ant Net:Distributed stigmergetice on control communications networks[J]. Journal of Artificial Intelligence Researeh,1998,9:317-365.
[54]Roli A, Blum C, Dorigo M. ACO for maximal constraint satisfaction problems[C]. In Proeeedings of MIC'2001,2001,1:187-191, Porto-Portugal.
[55]Solnon C. Ants can solve constraint satisfaction Problems[J]. IEEE Transactionson Evolutionary Computation,2002,6(4):347-357.
[56]Merkle D, Middendorf M, Sehmeek H. Ant colony optimization for resource constrained Project scheduling[J]. IEEE Transaetions on Evolutionary Computation,2002,6(4):333-346.
[57]Bullnheimer B, Hartal R F, Strauss C. Applying the ant system to the vehicle problem[J].IN I.H. Osman S.Vo.S.Martello and C.Roucairol,editors,Meta-Heuris-tics:Advances and Trends in Local Search Paradigms for Optimization,pages 109-120.Kluwer Academics,1998.
[58]Bullnheimer B, Hartal R F, Strauss C. An improved ant system algorithm for the vehicle routing problem[A]. Annals of Operations Research,89:319-328,1999.
[59]侯云鹤,熊信艮,吴耀武等.基于广义蚁群算法的电力系统经济负荷分配[J].中国电机工程学报,2003,23(3)：56-64.
[60]Dorigo M, Dicaro G, Gambardella L M. Ant algorithms for discrete optimization[J].Artificial Life,1999, 5(2):137-172.
[61]郝晋,石立宝,周家启.求解复杂TSP问题的随机扰动蚁群算法[J].系统工程理论与实践,2002,(9)：88-91.
[62]Gambardella L M, Taillard E D, Dorigo M. Ant colonies for the QAP[J]. Journal of the Operational Research Society(JORS),1999,50(2):167-176.
[63]Maniezzo V, Colorni A.The Ant System Applied to the quadratic assignment problem[J]. IEEE Transactions on Data a nd Knowledge Engineering,1999,11(5):769-778.
[64]Colorni A, Dorigo M, Maniezzo V, et al.Ant System for job-shop scheduling[J].Belgian Journal of Operations Researchm,Statistics and Computer Science (JORBEL),1994,34:39-53.
[65]李艳君,吴铁军.求解混杂生产调度问题的嵌套混合蚁群算法[J].自动化学报.2003,29(1)：95-101.
[66]Merkle D, Middendorf M, Schmeck H.Ant colony optimization for resource constrained project scheduling[C]. In Proceedings of the Genetic and Evlutionary Computation Conference (GECCO-2000), 2000:893-900. Mogan Kaufinann Publishers, San Francisco,CA.
[67]Costa D, Hertz A. Ants can color graphs[J]. Journal of the Operational Research Society,1997,48:295-305.
[68]Gambardella L M, Taillard E D, Agazzi G. MACS-VRPTW:A multiple ant colony system for vehicle routing problems with time windows[M].In D.Corne, M.Dorigo, and F.Glover, editors, New Ideas in Optimizations,pages 63-76.McGraw Hill,London,UK,1999.
[69]林锦,朱文兴.凸整数规划问题的混合蚁群算法[J].福州大学学报(自然科学版).1999,27(6)：5-9.
[70]汪镭,吴启迪.蚁群算法在系统辨识中的应用[J].自动化学报.2003,29(1)：102-109.
[71]金飞虎,洪炳熔,高庆吉.基于蚁群算法的自由飞行空间机器人路径规划[J].机器人,2002,24(6)：526-529.
[72]Parpinelli R S, Lopes H S, Freitas A A. Data Mining With an Ant Colony Optimization Algorithm[J]. IEEE Transactions on Evolutionary Computing,2002,6(4):321-332.
[73]Dicaro G, Dorigo M. AntNet:Distributed Stigmergetic Control for Communications Networks[J]. Journal of Artificial Intelligence Research,1998,9:317-365.
[74]Heusse M, Guerin S, Syners D, Kuntz P. Adaptive agent-driven routing and load Balancing in communication networks[R]. Technical Report RR-98001-IASC,D'e-partment Intelligengce Artificielle et Sciences Cognitives,ENST Bretagne,1998.
[75]Subramanian D, Druschel P, Chen J. Ants and reinforcement learning:A case study in routing in dynamic networks[C].In Proceedings of IJCAI-97, International Joint Conference on Artificial lntelligence,pages 832-838.Morgan Kaufmann,1997.
[76]Lu G Y, Liu Z M. QoS Multicast Routing Based on Ant Algorithm in Internet[J].The Jounal of China Universities of Posts and Telecommunication,2000,7(4):12-17.
[77]吕国英,刘泽民,周正.基于蚂蚁算法的分布式QoS路由选择算法[J].通信学报,2001,22(9)：35-42.
[78]张素兵,刘泽民.基于蚂蚁算法的分级QoS路由调度方法[J].北京邮电大学学报,2000,23(4)：12-15.
[79]王颖,谢剑英.一种基于蚁群算法的多媒体网络多播路由算法[J].上海交通大学学报.2002,36(4)：526-531.
[80]Stiitzle T. An ant approach to the flowshop problem[C]. in:proceedings of European Congress on Intelligent Techniques and Soft ComPuting(EUFIT,98), Aachen, Germany,1998:1560-1564.
[81]Zwaan S, Pais A R, Marques C.Ant colony optimisation for jobshop scheduling In proceedings of the Third Workshovon Genetie Algorithms and ArtifieialLife(GAAL99),1999.
[82]Bauer B, Bullnheimer R F, Haitl C. An Ant Colony Optimization approach for the single machine to taltardiness Problem[C]. in:Proceedings of the 1999 Congresson Evolutionary ComPultion, IEEEpress, Piseatawas,NJ,1999:1445-1450.
[83]Merkle D, Middendorf M.An ant algorithm with a new Pheromone evaluation rule for totaltardiness Problems[C].In Proeeeding of the Evowork shops 2000, number1803 in Lecture Notesin Computer Seienee, 2000:287-296. SPringerVerlag.
[84]Merkle D, Middendof M. Ant colony Optimization with global Pheromone evaluation for scheduling a single maehine[J]. Applied Intelligenee,2003,18(1):105-111.
[85]Jayaraman V K, Kulkarni B D, Karale S, et al. Ant colony framework for optimal design and scheduling of batch plants. Computers and chemical engineering,2000,24:1901-1912.
[86]Packard N H,Crutchfield J P, Farmer J D, et al. Geometry from a time series[J]. Physical Review Letters,1980,45(9):712-716.
[87]赵玉成,肖忠会,许庆余.差别混沌与噪声的局部可变神经网络方法[J].西安交通大学学报,1999,33(10)：72-76.
[88]王凌,郑大钟.一种基于退火策略的混沌神经网络优化算法[J].控制理论与应用,2000,17(1)：69-92.
[89]Hagan M T, Behr S M. The time series approach to short term load forecasting[J],IEEE Trans. On Power System,PWRRS-2,3,1987.
[90]Bakirtzis A G, Theocharis J B, Kiartzis S J, et al. Short Term Load Forecasting Using Fuzzy Neural Networks[J].IEEE Trans. On Power System.August,1995,10(3):1518-1524.
[91]吕金虎,占勇,陆君安.电力系统短期负荷预测的非线性混沌改进模型[J].中国电机工程学报,2000,20(12)：80-83.
[92]Hesieh D. Testing for nonlinear deendence in daily foreign exchange rates[J]. Journal business,1989,62(3): 339-359.
[93]Liu J Q, Zhang T Q, Yu S K. Chaotic pheromone and the maximum predictable time scale of observation series of urban hourly water consumption[J]. journal of zhejiang university science.2004,5(9):1053-1059.
[94]于国荣,夏自强.混沌时间序列支持向量机模型及其在径流预测中应用[J].水科学进展,2008,19(1)：116-122.
[95]Farmer J D, Sidorowich J J.predicting chaotic time series[J]. phys.rev.lett.,1987,59(8):845-848.
[96]Cao L, Hong Y, Fang H, et al. Predicting chaotic time series using wavelet network[J]. Physica D,1995, 85(1):225-238
[97]崔万照,朱长纯,保文星,刘君华.基于模糊模型支持向量机的混沌时间序列预测[J].物理学报,2005,54(7)：3009-3017.
[98]邬莉娜,汪雄海.基于自适应遗传算法的机泵群效率优化控制[J].浙江大学学报(工学版),2008,42(11)：1910-1914.
[99]柳景青.用水量时间观测序列中的分形和混沌特性[J].浙江大学学报(理学版),2004,31(2)：236-40.
[100]秦奕青,蔡卫东,杨炳儒.非线性时间序列的相空间重构技术研究[J].系统仿真学报,2008,20(11)：2969-2973.
[101]Takens F. Detecting strange attractors in turbulence[M].In:Dynamical Systems and Turbulence, Warwick 1980, Lecture Notes in Mathematics,898 (eds. D. Rand and L.-S.Young),1980:366-381, Springer, Berlin.
[102]张筑生.微分动力系统原理[M].北京：科学出版社,1988.
[103]Grassberger P, Procaccia I. Measureing the strangeness of strange attractors [J]. Physica D:Nonlinear Phenomona,9(1-2):189-208.
[104]Kleiner Y, Rajani B. Comprehensive review of structural deterioration of water mains:statistical models[J]. Urban Water,2001,3(3):131-150.
[105]Covas D, Ramos H, Graham N,et.al. Application of hydraulic transients for leak detection in water supply systems[J]. Water Science and Technology:Water Supply,2004,4(5):365-374.
[106]Rajani B, Kielner Y. Comprehensive review of structural deterioration of water mains:physically based models[J]. Urban Water,2001,(3):177-190.
[107]Wang J, Ling Z B. Design of new type intelligent correlation detector for leakage of water supply pipe[J]. Journal of Electronic Measurement and Instrument,2004,2:1779-1782.
[108]Tafurl A N. Locating Leaks with Acoustic Technology [J].American Water Works Association,2000, 92,(7):57-66.
[109]朱东海,城市给水管网爆管点动态定位的神经网络模型研究[J].水利学报.2000,(10)：1-5.
[110]Yuan Y X, Zhang J, Xu H F, et al. Study on medium and long-term forecasting model of urban water consumption[J].Water and Waste Water,2004,30(6:102-104.
[111]Marcellon, Govannim S. Mixed Optimization Technique for Large-Scale Water Resources systems[J]. Journal water Resources Planning and Management,1996,6:387-393
[112]Zhou S L, Mcmahon T A, Wai T A, et al. Forecasting operational demand for an urban water supply zone [J].Journal of Hydrology,2002,259:189-202.
[113]Towler E, Rajagopalan B, Summers R S, et al. An approach for probabilistic forecasting of seasonal turbidity threshold exceedance[J]. Water Resources Research,2010,46(6:W06511.
[114]Kisil O. Streamflow Forecasting using different artificial neural network algorithms [J]. Journal of Hydrologic Engineering,2007,532-539.
[115]席剑辉,韩敏,殷福亮.基于卡尔曼滤波的混沌系统辨识[J].大连理工大学学报,2003,43(4)：516-521.
[116]Vapnik V N. The Nature of Statistical Learning Theory[M].New York:Springer-Verlag,1995.
[117]丁涛,周惠成.混沌时间序列局域预测方法[J].系统工程与电子技术,2004,3(26)：338-340.
[118]赵鹏,张宏伟.基于最大Lyapunov指数的改进预测模型及其在用水量短期预测中的应用[J].天津大学学报,2007,40(12)：1500-1506.
[119]Hippert H S, Pefreira C E and Souza R C., Neural network for short-term load forecasting:A review and evaluation[J]. IEEE Trans. Power System,2001,16(2):44-54.
[120]Li T L, He L M, Li H P. Prediction and analysis of chaotic time series on the basis of support vector[J]. Journal of Systems Engineering and Electronics,2008,19(4):806-811.
[121]崔万照,朱长纯,保文星等.混沌时间序列的支持向量机预测[J].物理学报,2004,53(10)：3303-3310.
[122]Suykens J A K, Gestel T V, Brabanter J D, et al. Least Squares Support Vector Machines[J]. World Scientific, Singapore Pub Co,2002:308.
[123]侯越先.可丕廉,王雷.适应于高必要嵌入维的混沌时间序列预测算法[J].天津大学学报,1999,32(5)：594-598.
[124]Liu H B, Zhang H W, Tian L. Study on artificial neural network forecasting method of water consumption per hour[J]. Transactions of Tianjin University,2001,7(4):233-237
[125]邓聚龙.灰色系统基本方法[M].武汉：华中科技大学出版社,2005.
[126]崔杰,党耀国,刘思峰.一种新的灰色预测模型及其建模机理[J].控制与决策,2009,24(11)：1702-1706.
[127]陈崚,沈洁,秦玲等.基于分布均匀度的自适应蚁群算法[J].软件学报,2003,14(8)：1379-1387.
[128]Stutzle T, Dorigo M. A Short Convergence Proof for a class of Ant Colony Optimization Algorithms[J]. IEEE Transaction on Evolutionary Computation,2002,6(4):358-365.
[129]Gutjahr W J. ACO algorithm with guaranteed convergence to the optimal solution[J]. Information Processing Letters,2002,82:145-153.
[130]Socha K, Dorigo M. Ant colony optimization for continuous domains[J]. European Journal of Operational research,2008,185(3):1155-1173.
[131]Monmarche N, Venturini G, Slimane M. On how Pachycondyla apicalisants suggest a new search algorithm[J]. Future Generation Computer Systems,2000,16(8):937-946.
[132]Dreo J, Siarry P. Continuous interacting ant colony algorithm based on dense hierarchy[J]. Future Generation Computer Systems,2004,20(5:841-856.
[133]Chelouah R, Siarry P. A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions[J]. Journal of Heuristics,2000,6:191-213.
[134]Chelouah R, Siarry P. Enhanced continuous Tabu search:An algorithm for the global optimization of multi-minima functions. In:Voss S., Martello S. and Osman I.H. et al. Meta-Heuristics Advances and Trends in Local Search Paradigms for Optimization[M]. Kluwer Academic Publishers, Boston, MA, 1999:49-61 (Chapter 4).
[135]Siarry P, Berthiau G, Durbin F, et al. Enhanced simulated annealing for globally minimizing functions of many continuous variables[J]. ACM Transactions on Mathematical Software,1997,23(2):209-228.
[136]Bosman P A N, Thierens D. Continuous iterated density estimation evolutionary algorithms within the IDEA framework[C]. Proceedings of OBUPM Workshop at GECCO-2000. Mor-gan-Kaufmann Publishers, San Francisco, CA,2002:197-200.
[137]Zecchin A C, Simpson A R, Maier H R, et al. Application of two ant colony optimization algorithms to water distribution system optimization. Mathematical and Computer Modelling,2006,44:451-468.
[138]Tu M Y, Tsai F T C, Yeh W W G. Optimization of water distribution and water quality by hybrid genetic algorithm[J].Journal of Water Reso-urces Planning and Management,2005,131(6):431-440.
[139]Ostfeld A, Tubaltzev A. Ant colony Optimization for Least-Cost Design and Operation of Pumping Water Distribution Systems[J]. Water Resour. Plan. Manage.,2008,134(2):107-118.
[2]Pezeshk S, Helweg O J.Adaptive search optimization in reducing pump operming costs, Journal of Water Resources Planning and Management,ASCE,1996,122(1),57-63.
[3]郑爽英.城市供水系统两级优化调度的宏观模型研究[J].四川联合大学学报(工程科学版),1997,1(2)：60-68.
[4]Shvartser L, Shamir U, Feldman M. Forecasting hourly water demands by pattern recognition approach[J]. Journals of Water Resources Planning and anagement,ASCE,1993,119(6):611-627.
[5]Homwongs C, Sastri T, Foster J W. A daptive forecasting of hourly municipal water consumption[J]. Journals of Water Resources Planning and Management, ASCE,1994,120(6):888-905.
[6]Liu H B, Zhang H W. Comparison of the City water consumption Shot-Term Forecasting Methods[J]. Transactions of Tianjin University,2002,8(3):211-215.
[7]柳景青.调度时用水量预测的分时段混沌建模方法[J].浙江大学学报(工学版),2005,39(1)：11-15.
[8]赵鹏,张宏伟.城市用水量的混沌特性与预测[J].中国给水排水,2008,24(5)：90-93.
[9]Efallside F, Perry P F.Optimization of a water supply network[C]. Proceeding institute of electricity engineering,1975,122(2):202-208.
[10]Nitivattananon V, Sadowski E C, et al.Optimization of water supply system operation[J]. Journal of Water Resources Planning and Management,ASCE,1996,122(5):374-384.
[11]Tarquin A J, Dowdy J.Optimal Pump Operation in Water Distribution[J]. Journal of Hydraulic Engineering, ASCE,1989,115(2):158-168.
[12]仲伟俊,徐南荣,陈森发.城市供水系统调度的分解—协调优化方法[J].自动化学报,1990,16(3)：217-225.
[13]Ormsbee L E. Implicit network calibration[J].Water Resour.Plng.and Mgmt.,ASCE,1989,115(2):243-257.
[14]Jowitt Paul W, Germanopoulos G.Optimal Pump Scheduling in Water-Supply Networks[J]. Journal of Water Resources Planning and Management,1992,118(4):406-420.
[15]Chase DV,OrmsbeeLE.Optimal pump operation of water distribution system with multiple storage tanks[C].Proceeding conference on water resources planning and management, ASCE, New York, 1989:733-736.
[16]Brion L M, Mays LW.Methodology for Optimal Operation of Pumping Stations in Water Distribution Systems[J].Journal of Hydraulic Engineering ASCE,1991,117(11):1551-1569.
[17]Ormsbee L E, Reddy S L. Nonlinear heuristic for pump operation[J]. Journal of Water Resources Planning and Management, ASCE,1995,121(4:302-309.
[18]王增义,张宏伟.送水泵站的优化调度[J].中国给水排水,1991,7(1)：55-57
[19]Simpson A R, Dandy G C, Murphy L J. Genetic algorithms compared to other techniques for pipe optimization[J]. Water Resour. Ping, and Mgmt, ASCE,1994,120(4:423-443.
[20]Carlos E,Victor H,Eduardo F.Multi-objective optimization of water-using systems[J].European Journal of Operational Research,2007,181:1691-1707.
[21]张承慧,廖莉,李洪斌.水工业系统的优化调度及其遗传算法求解[J].计算机集成制造系统—CIMS,2003,9(8)：645-651.
[22]Reis L F R,Bessler F T,Waiters G A, et al. Water supply reservoir operation by combined genetic algorithmlinear programming(GA-LP)approach[J]. Water Resources Management,2006, (20):227-255.
[23]Haghighi A, Samani H M V, Samani Z M V. GA-ILP Method for Optimization of Water Distribution Networks[J].Water Resour Manage,2011,25:1791-1808.
[24]俞亭超,张土乔.供水系统直接优化调度遗传算法求解模型研究[J].浙江大学学报(工学版),2006,(5)：74-79
[25]Maier H R, Simpson A R, Zecchin A C, Foong WK, et al.Ant colony optimization for design of water distribution systems[J]. J Water Resour Plan Manage,2003,129(3):200-209.
[26]Lopez-Ibanez M, Prasad T D, Paechter B. Ant Colony Optimization for Optimal Control of Pumps in Water Distribution Netwoiks[J]. JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT,2008,134(4):337-347.
[27]Eric Bonabeau,Marco Dorigo,and Guy Theraulaz.Swarm intelligence:from natural to artificial systems[M], New York:Oxford University Press,1999.
[28]Kennedy J, Eberhart R C, Shi Y H.Swarm Intelligence[M].San Francisco:Morgan Kaufmann,2001.
[29]Colomi A, Dorigo M, Maffioli F, et al.Trubian.Heuristics from nature for hard combinational problems[J]. International Transactions in Opernational Research,1996,3(1):1-21.
[30]Dorigo M, Maniezzo V, Colorni A. Positive feedback as a search strategy[R].Technical Report 91-106,Dipartimento di Elettronica,Politecnico di Milano,IT,1991.
[31]Dorigo M.Optimization Learning and Natural Algorithma[D]. Ph.D.thesis, Dipartimento di Elettronica, Politecnico di Milano,IT,1992.
[32]Colorni A, Dorigo M, Maniezzo V. Distributed optimization by ant colonies[C]. European Conference on Artificial Life,134-142 Elsevier,1992.
[33]Bullnheimer B, Hartl R F, Stranss C. A New Rank Based Version of the Ant System:A Computational Study[J].Central European Journal for Operations Research and Eeonomies,1999,7(l):25-38.
[34]Stutzle T, Hoos H H. Max-Min ant system[J]. Future Generation computer Systems,2000,16:889-914.
[35]Dorigo M, Stutzle T. Ant colony Optimization[M].MIT Press,2004.
[36]Dorigo M, Bonabeau E, Theraulaz G. Ant algorithms and stigmergy[J]. Future Generation computer systems, 2000,16:851-871.
[37]Dorigo M, Maniezzo V, Colomi A. The Ant System:An autocatalytic optimizing Process[R]. Technical Report 91-016 Revised, DiPartimento di Elettroniea, Politecnieo di Milano, Milan, Italy,1991.
[38]Dorigo M, ManiezzoV, Colorni A.The Ant System:Optimization by a colony of cooperating agents[J]. IEEE Transactions on Systems, Man, and Cybemeties-Part B,1996,26(1):29-41.
[39]Gambardella L M, Dorigo M. Ant-Q:A reinforcement learning approach to the traveling salesman problem[C].In A.Prieditis and S.Russell,editors,Proceedings of the Twelfth International Conference on Machine Leaming(ML-95),pages 252-260.Morgan Kaufmann Publishers,Palo Alto,CA,1995.
[40]Dorigo M, Gambardella L M. A study of some Properties of ANT-Q[C]. Proceedings of PPSNIV-Fourth International Conference on Parallel Problem Solving From Nature, SPringer-Verlag, Berlin,1996:656-665.
[41]Dorigo M, Gambardella L M. Ant Colony System:A cooperative learning approach to the traveling salesman Problem[J].IEEE Transaetions on Evolutionary Computation,1997, 1(1):53-66.
[42]Dorigo M, Maniezzo V, Colorni A. The ant system:Optimization by a colony of cooperating agents[J]. IEEE Transactions on System, Man, and Cybernetics-Part B.1996,26(1):29-41.
[43]Gutjahr W J. A graph based ant system and its convergence[J]. Future Gener.Comput System, 2000,16(8):873-888.
[44]Blum C, Roli A, Dorigo M. HC-ACO:The hyper-cube framework for Ant colony Optimization[C]. In proeeedings of MIC'2001-Metaheuristies International Conferenee,2001:399-403, Porto, Portugal.
[45]Kong M, Tian P, Kao YC. A new ant colony optimization algorithm for the multidimensional knapsack problem[J]. Computers and Operations Research,2008,35:2672-2683.
[46]覃刚力,杨家本.自适应调整信息素的蚁群算法[J].信.息与控制,2002,31(3)：198-201.
[47]谢剑英,王颖.一种自适应蚁群算法及其仿真研究[J].系统仿真学报,2002,14(1)：31-33.
[48]吴斌,史忠植.一种基于蚁群算法的TSP问题分段求解算法[J].计算机学报2002.24(12)：1328-1333.
[49]Gambardella L M, Dorigo M. Solving symmetric and asymmetrie TSPs by ant colonies[C]. in:Proeeedings of the IEEE International Conference on Evolutionary Computation (ICEC'96), IEEEPress, Piseataway, USA,1996:622-27.
[50]张纪会,高齐圣,徐心和.自适应蚁群算法[J].控制理论与应用,2000,17(1)：1-3.
[51]Stutzle T, Dorigo M. ACO algorithms for the quadratie assignment Problem.In Come,D., Dorigo M and Glover F, editors, New Ideas in Optimization,1999:33-50. MeGrawHill, London, UK.
[52]ManiezzoV, Colorni A.The Ant System applied to the quadratie assignment Problem[J]. IEEE Trans.Knowledge Data Eng,1999,11(5):769-778.
[53]Dicaro G, Dorigo M. Ant Net:Distributed stigmergetice on control communications networks[J]. Journal of Artificial Intelligence Researeh,1998,9:317-365.
[54]Roli A, Blum C, Dorigo M. ACO for maximal constraint satisfaction problems[C]. In Proeeedings of MIC'2001,2001,1:187-191, Porto-Portugal.
[55]Solnon C. Ants can solve constraint satisfaction Problems[J]. IEEE Transactionson Evolutionary Computation,2002,6(4):347-357.
[56]Merkle D, Middendorf M, Sehmeek H. Ant colony optimization for resource constrained Project scheduling[J]. IEEE Transaetions on Evolutionary Computation,2002,6(4):333-346.
[57]Bullnheimer B, Hartal R F, Strauss C. Applying the ant system to the vehicle problem[J].IN I.H. Osman S.Vo.S.Martello and C.Roucairol,editors,Meta-Heuris-tics:Advances and Trends in Local Search Paradigms for Optimization,pages 109-120.Kluwer Academics,1998.
[58]Bullnheimer B, Hartal R F, Strauss C. An improved ant system algorithm for the vehicle routing problem[A]. Annals of Operations Research,89:319-328,1999.
[59]侯云鹤,熊信艮,吴耀武等.基于广义蚁群算法的电力系统经济负荷分配[J].中国电机工程学报,2003,23(3)：56-64.
[60]Dorigo M, Dicaro G, Gambardella L M. Ant algorithms for discrete optimization[J].Artificial Life,1999, 5(2):137-172.
[61]郝晋,石立宝,周家启.求解复杂TSP问题的随机扰动蚁群算法[J].系统工程理论与实践,2002,(9)：88-91.
[62]Gambardella L M, Taillard E D, Dorigo M. Ant colonies for the QAP[J]. Journal of the Operational Research Society(JORS),1999,50(2):167-176.
[63]Maniezzo V, Colorni A.The Ant System Applied to the quadratic assignment problem[J]. IEEE Transactions on Data a nd Knowledge Engineering,1999,11(5):769-778.
[64]Colorni A, Dorigo M, Maniezzo V, et al.Ant System for job-shop scheduling[J].Belgian Journal of Operations Researchm,Statistics and Computer Science (JORBEL),1994,34:39-53.
[65]李艳君,吴铁军.求解混杂生产调度问题的嵌套混合蚁群算法[J].自动化学报.2003,29(1)：95-101.
[66]Merkle D, Middendorf M, Schmeck H.Ant colony optimization for resource constrained project scheduling[C]. In Proceedings of the Genetic and Evlutionary Computation Conference (GECCO-2000), 2000:893-900. Mogan Kaufinann Publishers, San Francisco,CA.
[67]Costa D, Hertz A. Ants can color graphs[J]. Journal of the Operational Research Society,1997,48:295-305.
[68]Gambardella L M, Taillard E D, Agazzi G. MACS-VRPTW:A multiple ant colony system for vehicle routing problems with time windows[M].In D.Corne, M.Dorigo, and F.Glover, editors, New Ideas in Optimizations,pages 63-76.McGraw Hill,London,UK,1999.
[69]林锦,朱文兴.凸整数规划问题的混合蚁群算法[J].福州大学学报(自然科学版).1999,27(6)：5-9.
[70]汪镭,吴启迪.蚁群算法在系统辨识中的应用[J].自动化学报.2003,29(1)：102-109.
[71]金飞虎,洪炳熔,高庆吉.基于蚁群算法的自由飞行空间机器人路径规划[J].机器人,2002,24(6)：526-529.
[72]Parpinelli R S, Lopes H S, Freitas A A. Data Mining With an Ant Colony Optimization Algorithm[J]. IEEE Transactions on Evolutionary Computing,2002,6(4):321-332.
[73]Dicaro G, Dorigo M. AntNet:Distributed Stigmergetic Control for Communications Networks[J]. Journal of Artificial Intelligence Research,1998,9:317-365.
[74]Heusse M, Guerin S, Syners D, Kuntz P. Adaptive agent-driven routing and load Balancing in communication networks[R]. Technical Report RR-98001-IASC,D'e-partment Intelligengce Artificielle et Sciences Cognitives,ENST Bretagne,1998.
[75]Subramanian D, Druschel P, Chen J. Ants and reinforcement learning:A case study in routing in dynamic networks[C].In Proceedings of IJCAI-97, International Joint Conference on Artificial lntelligence,pages 832-838.Morgan Kaufmann,1997.
[76]Lu G Y, Liu Z M. QoS Multicast Routing Based on Ant Algorithm in Internet[J].The Jounal of China Universities of Posts and Telecommunication,2000,7(4):12-17.
[77]吕国英,刘泽民,周正.基于蚂蚁算法的分布式QoS路由选择算法[J].通信学报,2001,22(9)：35-42.
[78]张素兵,刘泽民.基于蚂蚁算法的分级QoS路由调度方法[J].北京邮电大学学报,2000,23(4)：12-15.
[79]王颖,谢剑英.一种基于蚁群算法的多媒体网络多播路由算法[J].上海交通大学学报.2002,36(4)：526-531.
[80]Stiitzle T. An ant approach to the flowshop problem[C]. in:proceedings of European Congress on Intelligent Techniques and Soft ComPuting(EUFIT,98), Aachen, Germany,1998:1560-1564.
[81]Zwaan S, Pais A R, Marques C.Ant colony optimisation for jobshop scheduling In proceedings of the Third Workshovon Genetie Algorithms and ArtifieialLife(GAAL99),1999.
[82]Bauer B, Bullnheimer R F, Haitl C. An Ant Colony Optimization approach for the single machine to taltardiness Problem[C]. in:Proceedings of the 1999 Congresson Evolutionary ComPultion, IEEEpress, Piseatawas,NJ,1999:1445-1450.
[83]Merkle D, Middendorf M.An ant algorithm with a new Pheromone evaluation rule for totaltardiness Problems[C].In Proeeeding of the Evowork shops 2000, number1803 in Lecture Notesin Computer Seienee, 2000:287-296. SPringerVerlag.
[84]Merkle D, Middendof M. Ant colony Optimization with global Pheromone evaluation for scheduling a single maehine[J]. Applied Intelligenee,2003,18(1):105-111.
[85]Jayaraman V K, Kulkarni B D, Karale S, et al. Ant colony framework for optimal design and scheduling of batch plants. Computers and chemical engineering,2000,24:1901-1912.
[86]Packard N H,Crutchfield J P, Farmer J D, et al. Geometry from a time series[J]. Physical Review Letters,1980,45(9):712-716.
[87]赵玉成,肖忠会,许庆余.差别混沌与噪声的局部可变神经网络方法[J].西安交通大学学报,1999,33(10)：72-76.
[88]王凌,郑大钟.一种基于退火策略的混沌神经网络优化算法[J].控制理论与应用,2000,17(1)：69-92.
[89]Hagan M T, Behr S M. The time series approach to short term load forecasting[J],IEEE Trans. On Power System,PWRRS-2,3,1987.
[90]Bakirtzis A G, Theocharis J B, Kiartzis S J, et al. Short Term Load Forecasting Using Fuzzy Neural Networks[J].IEEE Trans. On Power System.August,1995,10(3):1518-1524.
[91]吕金虎,占勇,陆君安.电力系统短期负荷预测的非线性混沌改进模型[J].中国电机工程学报,2000,20(12)：80-83.
[92]Hesieh D. Testing for nonlinear deendence in daily foreign exchange rates[J]. Journal business,1989,62(3): 339-359.
[93]Liu J Q, Zhang T Q, Yu S K. Chaotic pheromone and the maximum predictable time scale of observation series of urban hourly water consumption[J]. journal of zhejiang university science.2004,5(9):1053-1059.
[94]于国荣,夏自强.混沌时间序列支持向量机模型及其在径流预测中应用[J].水科学进展,2008,19(1)：116-122.
[95]Farmer J D, Sidorowich J J.predicting chaotic time series[J]. phys.rev.lett.,1987,59(8):845-848.
[96]Cao L, Hong Y, Fang H, et al. Predicting chaotic time series using wavelet network[J]. Physica D,1995, 85(1):225-238
[97]崔万照,朱长纯,保文星,刘君华.基于模糊模型支持向量机的混沌时间序列预测[J].物理学报,2005,54(7)：3009-3017.
[98]邬莉娜,汪雄海.基于自适应遗传算法的机泵群效率优化控制[J].浙江大学学报(工学版),2008,42(11)：1910-1914.
[99]柳景青.用水量时间观测序列中的分形和混沌特性[J].浙江大学学报(理学版),2004,31(2)：236-40.
[100]秦奕青,蔡卫东,杨炳儒.非线性时间序列的相空间重构技术研究[J].系统仿真学报,2008,20(11)：2969-2973.
[101]Takens F. Detecting strange attractors in turbulence[M].In:Dynamical Systems and Turbulence, Warwick 1980, Lecture Notes in Mathematics,898 (eds. D. Rand and L.-S.Young),1980:366-381, Springer, Berlin.
[102]张筑生.微分动力系统原理[M].北京：科学出版社,1988.
[103]Grassberger P, Procaccia I. Measureing the strangeness of strange attractors [J]. Physica D:Nonlinear Phenomona,9(1-2):189-208.
[104]Kleiner Y, Rajani B. Comprehensive review of structural deterioration of water mains:statistical models[J]. Urban Water,2001,3(3):131-150.
[105]Covas D, Ramos H, Graham N,et.al. Application of hydraulic transients for leak detection in water supply systems[J]. Water Science and Technology:Water Supply,2004,4(5):365-374.
[106]Rajani B, Kielner Y. Comprehensive review of structural deterioration of water mains:physically based models[J]. Urban Water,2001,(3):177-190.
[107]Wang J, Ling Z B. Design of new type intelligent correlation detector for leakage of water supply pipe[J]. Journal of Electronic Measurement and Instrument,2004,2:1779-1782.
[108]Tafurl A N. Locating Leaks with Acoustic Technology [J].American Water Works Association,2000, 92,(7):57-66.
[109]朱东海,城市给水管网爆管点动态定位的神经网络模型研究[J].水利学报.2000,(10)：1-5.
[110]Yuan Y X, Zhang J, Xu H F, et al. Study on medium and long-term forecasting model of urban water consumption[J].Water and Waste Water,2004,30(6:102-104.
[111]Marcellon, Govannim S. Mixed Optimization Technique for Large-Scale Water Resources systems[J]. Journal water Resources Planning and Management,1996,6:387-393
[112]Zhou S L, Mcmahon T A, Wai T A, et al. Forecasting operational demand for an urban water supply zone [J].Journal of Hydrology,2002,259:189-202.
[113]Towler E, Rajagopalan B, Summers R S, et al. An approach for probabilistic forecasting of seasonal turbidity threshold exceedance[J]. Water Resources Research,2010,46(6:W06511.
[114]Kisil O. Streamflow Forecasting using different artificial neural network algorithms [J]. Journal of Hydrologic Engineering,2007,532-539.
[115]席剑辉,韩敏,殷福亮.基于卡尔曼滤波的混沌系统辨识[J].大连理工大学学报,2003,43(4)：516-521.
[116]Vapnik V N. The Nature of Statistical Learning Theory[M].New York:Springer-Verlag,1995.
[117]丁涛,周惠成.混沌时间序列局域预测方法[J].系统工程与电子技术,2004,3(26)：338-340.
[118]赵鹏,张宏伟.基于最大Lyapunov指数的改进预测模型及其在用水量短期预测中的应用[J].天津大学学报,2007,40(12)：1500-1506.
[119]Hippert H S, Pefreira C E and Souza R C., Neural network for short-term load forecasting:A review and evaluation[J]. IEEE Trans. Power System,2001,16(2):44-54.
[120]Li T L, He L M, Li H P. Prediction and analysis of chaotic time series on the basis of support vector[J]. Journal of Systems Engineering and Electronics,2008,19(4):806-811.
[121]崔万照,朱长纯,保文星等.混沌时间序列的支持向量机预测[J].物理学报,2004,53(10)：3303-3310.
[122]Suykens J A K, Gestel T V, Brabanter J D, et al. Least Squares Support Vector Machines[J]. World Scientific, Singapore Pub Co,2002:308.
[123]侯越先.可丕廉,王雷.适应于高必要嵌入维的混沌时间序列预测算法[J].天津大学学报,1999,32(5)：594-598.
[124]Liu H B, Zhang H W, Tian L. Study on artificial neural network forecasting method of water consumption per hour[J]. Transactions of Tianjin University,2001,7(4):233-237
[125]邓聚龙.灰色系统基本方法[M].武汉：华中科技大学出版社,2005.
[126]崔杰,党耀国,刘思峰.一种新的灰色预测模型及其建模机理[J].控制与决策,2009,24(11)：1702-1706.
[127]陈崚,沈洁,秦玲等.基于分布均匀度的自适应蚁群算法[J].软件学报,2003,14(8)：1379-1387.
[128]Stutzle T, Dorigo M. A Short Convergence Proof for a class of Ant Colony Optimization Algorithms[J]. IEEE Transaction on Evolutionary Computation,2002,6(4):358-365.
[129]Gutjahr W J. ACO algorithm with guaranteed convergence to the optimal solution[J]. Information Processing Letters,2002,82:145-153.
[130]Socha K, Dorigo M. Ant colony optimization for continuous domains[J]. European Journal of Operational research,2008,185(3):1155-1173.
[131]Monmarche N, Venturini G, Slimane M. On how Pachycondyla apicalisants suggest a new search algorithm[J]. Future Generation Computer Systems,2000,16(8):937-946.
[132]Dreo J, Siarry P. Continuous interacting ant colony algorithm based on dense hierarchy[J]. Future Generation Computer Systems,2004,20(5:841-856.
[133]Chelouah R, Siarry P. A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions[J]. Journal of Heuristics,2000,6:191-213.
[134]Chelouah R, Siarry P. Enhanced continuous Tabu search:An algorithm for the global optimization of multi-minima functions. In:Voss S., Martello S. and Osman I.H. et al. Meta-Heuristics Advances and Trends in Local Search Paradigms for Optimization[M]. Kluwer Academic Publishers, Boston, MA, 1999:49-61 (Chapter 4).
[135]Siarry P, Berthiau G, Durbin F, et al. Enhanced simulated annealing for globally minimizing functions of many continuous variables[J]. ACM Transactions on Mathematical Software,1997,23(2):209-228.
[136]Bosman P A N, Thierens D. Continuous iterated density estimation evolutionary algorithms within the IDEA framework[C]. Proceedings of OBUPM Workshop at GECCO-2000. Mor-gan-Kaufmann Publishers, San Francisco, CA,2002:197-200.
[137]Zecchin A C, Simpson A R, Maier H R, et al. Application of two ant colony optimization algorithms to water distribution system optimization. Mathematical and Computer Modelling,2006,44:451-468.
[138]Tu M Y, Tsai F T C, Yeh W W G. Optimization of water distribution and water quality by hybrid genetic algorithm[J].Journal of Water Reso-urces Planning and Management,2005,131(6):431-440.
[139]Ostfeld A, Tubaltzev A. Ant colony Optimization for Least-Cost Design and Operation of Pumping Water Distribution Systems[J]. Water Resour. Plan. Manage.,2008,134(2):107-118.