混合量子进化算法及其在变电站规划中的应用
|
摘要
量子进化算法(Quantum-inspired Evolutionary Algorithm, QIEA)是一种以量子计算和进化算法结合的概率搜索方法,是进化算法家族中的后起之秀。与传统进化算法相比,量子进化算法在“勘探”和“开采”之间更容易取得平衡,具有全局搜索能力强、收敛速度快和种群规模小等优点,但QIEA在解决一些复杂优化问题时容易过快收敛,从而出现早熟现象得不到最优解,仍需要进一步提高搜索能力。目前国内外对量子进化算法的研究有许多改进策略,其中一个重要研究方向正是通过与其他优化算法相结合,形成新的进化搜索算法,这是基于各种优化算法都有各自的优缺点,不同优化算法的合理结合能很大程度上增强优势,弥补劣势的研究理念。本文将量子进化算法与擅长局部搜索的贪婪随机自适应搜索算法相结合,提出一种新的混合量子进化算法并将其应用到城市配电网规划优化中。
变电站规划是城市配电网规划工作中的重要部分,变电站规划结果直接影响到电力网络投资,供电可靠性和运行经济性。本文将HQIEA应用到某地区110kV变电站规划工作中,实验结果表明该方法很好的完成了对该地区变电站选址定容的规划优化,符合该地区电力需求和未来电网建设趋势,对该地区电网规划建设有重要参考意义。
论文主要工作及研究成果如下：
1、对量子进化算法的基本理论进行概述,指出要解决的问题并给出量子进化算法的算法流程图和实现过程。以0/1背包问题为测试函数,将传统进化算法——遗传算法作为对比算法,在实验中对这两种算法进行测试。实验结果表明,量子进化算法有着更好的“勘探”能力,相比遗传算法在求解组合优化问题方面有着更优越性能,有着重要的研究价值,为后面内容打下基础。
2、为提高量子进化算法的搜索性能,加强其“开采”能力,探讨了五种当前文献中有代表性的局部搜索方法。对这几种局部搜索方法进行了性能比较,概述了它们的优缺点,并用0/1背包问题对它们进行测试。将搜索性能最好的贪婪随机自适应搜索与量子进化算法结合,提出一种新混合量子进化算法。通过0/1背包问题测试验证该算法性能,实验中与当前文献中的几种方法进行了比较,得出该混合量子进化算法具有比较满意的全局搜索能力和局部搜索能力,在求解组合优化问题上有着优越的性能。
3、将混合量子进化算法应用到变电站规划优化中,以某地区110kV变电站优化为实际案例进行试验,并以现有文献中的方法作对比分析,实验结果表明混合量子进化算法能很好的求解变电站规划优化问题,得到的优化方案合理可行,且能达到投资最省,运行经济及供电可靠的规划优化目标。从而拓展了量子进化算法及其改进算法的应用范围。
本文工作得到教育部新世纪优秀人才支持计划项目(NCET-11-0715),中央高校基本科研业务费专项资金(SWJTY11ZT07)和国家自然科学基金(61170016)的共同资助。
The quantum-inspired evolutionary algorithm (QIEA) is a kind of probability search method, which is combined the quantum computing and evolutionary algorithm. It is a rising star in the evolutionary algorithm family. Compared with traditional evolutionary algorithm, the quantum-inspired evolutionary algorithm are more likely to achieve a balance between exploitation and exploration. It has advantages of small population size, fast convergence speed and strong global search capability. However, the QIEA is easy to rapid convergence and result in precocious phenomena when it solves some complex optimization problems. So it can't get the optimal solution. So the QIEA still need to further improve the search ability. There are many improvement strategies about the research of the QIEA. One of the QIEA's important research directions is by combining with other optimization algorithm and then it can form a new evolution search algorithm. Because all kinds of optimization algorithm have its own advantages and disadvantages, so different optimization algorithm can largely enhance advantages and make up for disadvantages by reasonable combination. This paper combines with the quantum evolutionary algorithm (QIEA) and greed random adaptive search algorithm (GRASP) and puts forward a new hybrid quantum evolutionary algorithm (HQIEA). The GRASP is good at the local search. The HQIEA has the advantage both QIEA and GRASP and abandons theirs shortage. The HQIEA is applied to the urban distribution network planning optimization.
Substation planning is the most important part urban distribution network planning and substation planning results directly affect the investment of the power network、power distribution reliability and operational efficiency. The paper applies the HQIEA to the110kV substations planning work of an area. The experimental results show that method is very good to complete the capacity and the site of the substations in the region. The results comply with current power demand and substations construction trend of the county, it has important reference value to the current power grid planning construction planning.
The main work and research results are as follows:
1. The basic theory and related concepts of QIEA are introduced. The problems need to be solved are also pointed out. The algorithm process of QIEA also has been described. Genetic algorithm (GA) is one of the traditional evolutionary algorithms and as the comparative method in the knapsack problem experiments. By the comparative analysis, the experimental results show that QIEA has very good ability to exploration and strong global search ability. The QIEA has better performance in solving combinatorial optimization problems that compared with the GA. It has very important research value.
2. To improve the search performance and enhance the exploitation ability of QIEA. This paper discusses five kinds of typical local methods in current literature. Their performance is compared with each other, the advantages and disadvantages are summarized. GRASP is elected to best performance of them, and puts forward a new hybrid quantum evolutionary algorithm (HQIEA). The HQIEA has better performance in solving knapsack problems that compared with several methods in current literature. It has the convergence speed, ideal global search ability and local search ability. The HQIEA has superior performance in solving combinatorial optimization problems.
3. The HQIEA is applied to the substation planning optimization. The method of the current literature is as the comparative method in the110kV substations planning experiments of one area. The experimental results show that the HQIEA can well solve the substation planning optimization work. The optimization scheme is feasible and it gets the optimal object of investment in the least, running in the most economic, reliability of power supply. The results comply with current power demand and substations construction trend of the county, it has important reference value to the current power grid planning construction planning. It shows the effectiveness of the method. So as to the application range of the QIEA and its improved algorithm is expanded.
This paper work is supported by the program for New Century Excellent Talents in university (NCET-11-0715), the project sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and the National Natural Science Foundation of China (61170016).
变电站规划是城市配电网规划工作中的重要部分,变电站规划结果直接影响到电力网络投资,供电可靠性和运行经济性。本文将HQIEA应用到某地区110kV变电站规划工作中,实验结果表明该方法很好的完成了对该地区变电站选址定容的规划优化,符合该地区电力需求和未来电网建设趋势,对该地区电网规划建设有重要参考意义。
论文主要工作及研究成果如下：
1、对量子进化算法的基本理论进行概述,指出要解决的问题并给出量子进化算法的算法流程图和实现过程。以0/1背包问题为测试函数,将传统进化算法——遗传算法作为对比算法,在实验中对这两种算法进行测试。实验结果表明,量子进化算法有着更好的“勘探”能力,相比遗传算法在求解组合优化问题方面有着更优越性能,有着重要的研究价值,为后面内容打下基础。
2、为提高量子进化算法的搜索性能,加强其“开采”能力,探讨了五种当前文献中有代表性的局部搜索方法。对这几种局部搜索方法进行了性能比较,概述了它们的优缺点,并用0/1背包问题对它们进行测试。将搜索性能最好的贪婪随机自适应搜索与量子进化算法结合,提出一种新混合量子进化算法。通过0/1背包问题测试验证该算法性能,实验中与当前文献中的几种方法进行了比较,得出该混合量子进化算法具有比较满意的全局搜索能力和局部搜索能力,在求解组合优化问题上有着优越的性能。
3、将混合量子进化算法应用到变电站规划优化中,以某地区110kV变电站优化为实际案例进行试验,并以现有文献中的方法作对比分析,实验结果表明混合量子进化算法能很好的求解变电站规划优化问题,得到的优化方案合理可行,且能达到投资最省,运行经济及供电可靠的规划优化目标。从而拓展了量子进化算法及其改进算法的应用范围。
本文工作得到教育部新世纪优秀人才支持计划项目(NCET-11-0715),中央高校基本科研业务费专项资金(SWJTY11ZT07)和国家自然科学基金(61170016)的共同资助。
The quantum-inspired evolutionary algorithm (QIEA) is a kind of probability search method, which is combined the quantum computing and evolutionary algorithm. It is a rising star in the evolutionary algorithm family. Compared with traditional evolutionary algorithm, the quantum-inspired evolutionary algorithm are more likely to achieve a balance between exploitation and exploration. It has advantages of small population size, fast convergence speed and strong global search capability. However, the QIEA is easy to rapid convergence and result in precocious phenomena when it solves some complex optimization problems. So it can't get the optimal solution. So the QIEA still need to further improve the search ability. There are many improvement strategies about the research of the QIEA. One of the QIEA's important research directions is by combining with other optimization algorithm and then it can form a new evolution search algorithm. Because all kinds of optimization algorithm have its own advantages and disadvantages, so different optimization algorithm can largely enhance advantages and make up for disadvantages by reasonable combination. This paper combines with the quantum evolutionary algorithm (QIEA) and greed random adaptive search algorithm (GRASP) and puts forward a new hybrid quantum evolutionary algorithm (HQIEA). The GRASP is good at the local search. The HQIEA has the advantage both QIEA and GRASP and abandons theirs shortage. The HQIEA is applied to the urban distribution network planning optimization.
Substation planning is the most important part urban distribution network planning and substation planning results directly affect the investment of the power network、power distribution reliability and operational efficiency. The paper applies the HQIEA to the110kV substations planning work of an area. The experimental results show that method is very good to complete the capacity and the site of the substations in the region. The results comply with current power demand and substations construction trend of the county, it has important reference value to the current power grid planning construction planning.
The main work and research results are as follows:
1. The basic theory and related concepts of QIEA are introduced. The problems need to be solved are also pointed out. The algorithm process of QIEA also has been described. Genetic algorithm (GA) is one of the traditional evolutionary algorithms and as the comparative method in the knapsack problem experiments. By the comparative analysis, the experimental results show that QIEA has very good ability to exploration and strong global search ability. The QIEA has better performance in solving combinatorial optimization problems that compared with the GA. It has very important research value.
2. To improve the search performance and enhance the exploitation ability of QIEA. This paper discusses five kinds of typical local methods in current literature. Their performance is compared with each other, the advantages and disadvantages are summarized. GRASP is elected to best performance of them, and puts forward a new hybrid quantum evolutionary algorithm (HQIEA). The HQIEA has better performance in solving knapsack problems that compared with several methods in current literature. It has the convergence speed, ideal global search ability and local search ability. The HQIEA has superior performance in solving combinatorial optimization problems.
3. The HQIEA is applied to the substation planning optimization. The method of the current literature is as the comparative method in the110kV substations planning experiments of one area. The experimental results show that the HQIEA can well solve the substation planning optimization work. The optimization scheme is feasible and it gets the optimal object of investment in the least, running in the most economic, reliability of power supply. The results comply with current power demand and substations construction trend of the county, it has important reference value to the current power grid planning construction planning. It shows the effectiveness of the method. So as to the application range of the QIEA and its improved algorithm is expanded.
This paper work is supported by the program for New Century Excellent Talents in university (NCET-11-0715), the project sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and the National Natural Science Foundation of China (61170016).
引文
[1]钱洁,郑建国,张超群,王翔,阎瑞霞.量子进化算法研究现状综述.控制与决策,2011,26(3)：321-326.
[2]张华.量子进化算法及其在图像稀疏分解中的应用.西南交通大学硕士学位论文,2011.
[3]Hey T. Quantum computing:an introduction. Computing and Control Engineering Journal,1999,10(3):105-112.
[4]Narayanan A. Quantum computing for beginners. Proceedings of the 1999 Congress on Evolutionary Computation,1999:2231-2238.
[5]Han K H, Kim J H. Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Transactions on Evolutionary Computation,2002, 6(6):580-593.
[6]Narayanan A, Moore M. Quantum-inspired genetic algorithm. Proceedings of IEEE International Conference on Evolutionary Computation,1996:61-66.
[7]Han K H, Kim J H. Genetic quantum algorithm and its application to combinatorial optimization problem.Proceedings of the 2000 Congress on Evolutionary Computiation, July,2000:1354-1360.
[8]Zhang G X. Quantum-inspired evolutionary algorithms:a survey and empirical study. Journal of Heuristics,2011,17(3):303-351.
[9]Zhang G X, Jin W D, Li N. An improved quantum genetic algorithm and its application. Lecture Notes in Computer Science,2003,2639:449-452.
[10]Zhang G X, Li N, Jin W D.Novel quantum genetic algorithm and its applications. Frontiers of Electrical and Electronic Engineering in China,2006,1(1):31-36.
[11]梁锦照.城市电网规划方法研究.北京：中国电力出版社,2010.
[12]程吉祥.基于时频原子方法的雷达辐射源信号识别.西南交通大学硕士论文,2011.
[13]Najaran T, Akbarzadeh M. Improvement of quantum evolutionary algorithms for financial data analysis.Proceedings of the Conference on Evolutionary Computation, 2008:133-143.
[14]Alba E, Dorron B. The exploration exploitation tradeoff in dynamic cellular genetic algorithms. IEEE Transactions on Evolutionary Computation,2005,9(2):126-142.
[15]Nodehi A, Tayarani M, Mahmoudi F. A novel functional sized population quantum evolutionary algorithm for fractal image compression. Proceedings of the 14th International CSI Computer Conference,2009:564-568.
[16]Guo J, Sun L, Wang R. An improved quantum genetic algorithm. Proceedings of the 2009 Third International Conference on Genetic and Evolutionary Computing,2009, 10(1):14-18.
[17]Tayarani N Akbarzadeh. A sinusoid size ring structure quantum evolutionary algorithm. Proceedings of IEEE Conference on Cybernetics and Intelligent Systems.Chengdu, 2008:1165-1169.
[18]Imabeppu T, Nakayama S, Ono S. A study on a quantum-inspired evolutionary algorithm based on pair swap. Artificial Life and Robotics,2008,12(1):148-152.
[19]Andre V, Marley M. Quantum evolutionary algorithm for numerical optimization. Studies in Computational Intelligence,2008,121(7):115-132.
[20]覃朝勇,郑建国.一种实数编码量子进化算法及其收敛性.控制与决策,2009,24(6)：56-60.
[21]高辉,徐光辉,张锐等.实数编码量子进化算法.控制与决策,2008,23(1)：87-90.
[22]Li P, Li S. Quantum-inspired evolutionary algorithm for continuous space optimization based on Bloch coordinates of qubits. Neurocomputing,2008,72(1/2/3):581-591.
[23]Zhao S, Xu G, Tao T. Real-coded chaotic quantum-inspired genetic algorithm for training of fuzzy neural networks. Computers Mathematics with Applications,2009,57 (11/12):2009-2015.
[24]申抒含,金炜东.多进制概率角复合位编码量子进化算法.模式识别与人工智能,2005,18(6)：657-663.
[25]Wang Y, Feng X Y, Huang Y X. A novel quantum swarm evolutionary algorithm and its applications. Neurocomputing,2007,70(4/5/6):633-640.
[26]周殊,潘炜.一种基于粒子群优化方法的改进量子遗传算法及应用.电子学报,2006,34(5)：897-901.
[27]Qu H J, Zhou F Z, Zhang X. An application of new quantum inspired immune evolutionary algorithm.2009 1st International Workshop on Database Technology and Applications. Bruges,2009:468-471.
[28]Teng H, Yang B, Zhao B. A new mutative scale chaos optimization quantum genetic algorithm. Chinese control and Decision conf. Yantai,2008:1547-1549.
[29]焦嵩鸣,韩璞,黄宇.模糊量子遗传算法及其在热工程模型辨识中的应用.中国电机工程学报,2007,27(5)：87-92.
[30]Da C A, Pacheco M, Vellasco M. Cultural operators for a quantum-inspired evolutionary algorithm applied to numerical optimizetion problems. Articial Intelligence and Knowledge Engeering Applications,2005,356(2):1-10.
[31]Zhang G X, Gheorghe M, Wu C Z. A quantum-inspired evolutionary algorithm based on P systems for knapsack problem. Fundamenta Informaticae,2008,87(1):93-116.
[32]王利锋,白瑞林.求解约束优化问题的一种新方法——基于量子粒子群优化算法.计算机工程与应用,2005,33：124-146.
[33]解平,李斌,庄镇泉.一种新的混合量子进化算法.计算机科学,2008,35(2)：166-170.
[34]Wang L, Li L. An effective hybrid quantum-inspired evolutionary algorithm for parameter estimation of chaotic systems. Expert Systems with Applications,2010, 37(2):1279-1285.
[35]Hossain M, Hashem M. Hybrid real coded quantum evolutionary algorithm based on particle swarm. Proceedings of 12th International Conference on Computers and Information Technology,2009:13-17.
[36]李盼池,李士勇.求解连续空间优化问题的量子蚁群算法.控制理论与应用，2008,25(2)：237-241.
[37]Zhang G X, Rong H N. Quantum-inspired genetic algorithm based time-frequency atom decomposition. Lecture Notes in Computer Science,2007,4490:243-250.
[38]Zhang G X, Rong H N. Improved quantum-inspired genetic algorithm based time-frequency analysis of radar emitter signals. Lecture Notes in Artifical Intelligence, 2006,4481:484-491.
[39]Zhang G X. Time-frequency atom decomposition with quantum-inspired evolutionary algorithms. Circuit System Signal Process,2010,29:209-233.
[40]Han K H, Park K H, Lee C H and Kim J H. Parallel quantum-inspired genetic algorithm for combinatorial optimization problem. Proceedings of 2001 Congress on Evolutionary Computation,2001,2:1422-1329.
[41]Zhang G X, Rong H N. Real-observation quantum-inspired evolutionary algorithm for a class of numerical optimizatiom problems. Lecture Notes in Computer Science,2007, 4490:989-996.
[42]Zhang G X, Jin W D, Hu L Z. Quantum evolutionary algorithm for multi-objective optimization problems. Proceedings of 2003 IEEE International Symposium on Intelligent Control,2003:703-708.
[43]娄素华,李研,吴耀武,熊信银.多目标电网无功优化的量子遗传算法.高电压技术,2005,31(9)：69-71.
[44]Vlachogiannis J G, Lee K Y. Quantum-inspired evolutionary algorithm for real and reactive power dispatch. IEEE Transactions on Power Systems,2008,23(4): 1627-1636.
[45]Wang L, Tang F, Wu H. Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation. Applied mathematics and Computa-tion,2005,171(2):1143-1158.
[46]李恒建,尹忠科,王建英.基于量子遗传优化算法的图像稀疏分解.西南交通大学学报,2007,42(1)：19-23.
[47]封晓强,何铁军.基于量子进化算法的交通图像稀疏分解.南京理工大学学报(自然科学版),2010,34(1)：40-44.
[48]Li Y, Jiao L C. An effective method of image edge detection based on parallel quantum evolutionary algorithm. Signal Processing,2003,19(1):69-74.
[49]Khorsand A R, AkbarzadehT M, Moin H. Genetic quantum algorithm for Voltage and pattern design of piezoelectric actuator. Proceedings of 2006 IEEE Congess on Evolutionary Computation,2006:2593-2600.
[50]王成山,刘涛,谢莹华.基于混合遗传算法的变电站选址定容.电力系统自动化,2006,30(6)：30-34.
[51]Enver M. An interactive procedure for sizing and timing distribution substations using optimization techniques. IEEE Transactions on Power Apparatus and Systems,1974, 93(5):1281-1286.
[52]Crawford D M, Holt S B. A mathematical optimization technique for locating and sizing distribution substations and deriving their optimal service areas. IEEE Transactions on Power Apparatus and Systems,1975,94(2):30-234.
[53]Thompson G L, Wall D L. A branch and bound model for choosing optimal substation locations. IEEE Transactions on Power Apparatus and Systems,1981,100(5): 2683-2687.
[54]路志英,葛少云,王成山.基于粒子群优化的加权伏罗诺伊图变电站规划.中国电机工程学报,2009,29(16)：35-41.
[55]王玉瑾,王主丁,张宗益等.基于初始站址冗余网格动态减少的变电站规划.电力系统自动化,2010,34(12)：39-43.
[56]王艳松,解飞.油田配电网临时变电站规划的研究.电力系统保护与控制,2010,38(4)：84-87.
[57]高付良,张鹏,赛雪等.考虑负荷不确定性变电站站址定容.电力系统保护与控制,2010,38(15)：75-80.
[58]邱富东,汤红卫.基于GIS空间查询和遗传算法的变电站规划.华东电力,2010,38(3)：341-344.
[59]高炜欣,罗先觉,朱颖.贪心算法结合Hopfield神经网络优化配电变电站规划.电网技术,2004,28(7)：73-76.
[60]刘志发,张建华.基于改进多组织粒子群算法优化计算的配电网络变电站选址定容.中国电机工程学报,2007,27(1)：105-111.
[61]张葛祥,李娜,金炜东,胡来招.一种新量子遗传算法及其应用.电子学报,2004,32(3)：476-479.
[62]Qin Y H, Zhang G X, Li Y Q. A comprehensive learning quantum-inspired evolutionary algorithm. Communications in Computer and Information Science,2011, 268:151-157.
[63]栾丽君,谭立静,牛奔.一种基于粒子群优化算法和差分进化算法的新型混合全局优化算法.信息与控制,2007,36(6)：708-714.
[64]Christian B, Andrea R. Metaheuristics in combinatorial optimization:overview and conceptual comparison. ACM Computer Surveys,2003,35(3):268-308.
[65]张忆.基于遗传退火的生物信息学多序列比对算法研究.电子科技大学硕士论文,2009.
[66]李静.基于JIT供应的集货车辆路线问题研究.长安大学硕士论文,2007.
[67]孙丰荣,李艳玲,曲怀敬,刘泽,张梅.基于活动轮廓模型和边缘对比度特征量的血管内超声图像边缘提取.中国生物医学工程学报,2006,25(4)：385-389.
[68]朱颢东,钟勇.一种改进的模拟退火算法.计算机技术与发展,2009,19(6)：32-35.
[69]王明兴.连续禁忌搜索算法改进及应用研究.浙江大学硕士学位论文,2005.
[70]陈铁梅.精密电子表面贴装生产优化问题研究.华南理工大学博士论文,2012.
[71]吴爽.共享性Flow shop调度算法设计及应用研究.四川大学硕士论文,2007.
[72]李雪梅,张素琴.基于仿生理论的几种优化算法综述.计算机应用研究,2009,26(6)：2032-2034.
[73]金华征,程浩忠,奚殉,夏夷,奚增辉,沈晓岚.贪婪随机自适应搜索法在电网规划中的应用.上海大学学报,2006,40(4)：563-567.
[74]董红宇,黄敏,王兴伟.变邻域搜索算法综述.控制工程,2009,16(1)：1-5.
[75]陈萍.启发式算法及其在车辆路径问题中的应用.北京交通大学博士学位论文,2009.
[76]Han K H, Kim J H. Quantum-inspired evolutionary algorithm with a new termination criterion,Hε gate and two-phase scheme. IEEE Trans on Evolutionary Computation, 2004,8(2):156-169.
[77]Zhang R, Gao H. Improved quantum evolutionary algorithm for combinatorial optimization problem. Proceedings of the Six International Conference on Machine Learning and Cybernetics,2007,3501-3505.
[78]Zhou M, Huang M, Yin J. Optimal 110/10kV substations planning.Proceedings of 2010 China International Conference on Electricity Distribution (CICED),2010:1-6.
[79]王林梅,黄民翔.变电站站址两阶段优化规划的实用改进方法.浙江电力,2006,2006(5)：1-5.
[80]中华人民共和国住房和城乡建设部.城市电力规划规范,1999.
[81]刘振亚.国家电网公司输变电工程通用造价.北京：中国电力出版社,2010.
[2]张华.量子进化算法及其在图像稀疏分解中的应用.西南交通大学硕士学位论文,2011.
[3]Hey T. Quantum computing:an introduction. Computing and Control Engineering Journal,1999,10(3):105-112.
[4]Narayanan A. Quantum computing for beginners. Proceedings of the 1999 Congress on Evolutionary Computation,1999:2231-2238.
[5]Han K H, Kim J H. Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Transactions on Evolutionary Computation,2002, 6(6):580-593.
[6]Narayanan A, Moore M. Quantum-inspired genetic algorithm. Proceedings of IEEE International Conference on Evolutionary Computation,1996:61-66.
[7]Han K H, Kim J H. Genetic quantum algorithm and its application to combinatorial optimization problem.Proceedings of the 2000 Congress on Evolutionary Computiation, July,2000:1354-1360.
[8]Zhang G X. Quantum-inspired evolutionary algorithms:a survey and empirical study. Journal of Heuristics,2011,17(3):303-351.
[9]Zhang G X, Jin W D, Li N. An improved quantum genetic algorithm and its application. Lecture Notes in Computer Science,2003,2639:449-452.
[10]Zhang G X, Li N, Jin W D.Novel quantum genetic algorithm and its applications. Frontiers of Electrical and Electronic Engineering in China,2006,1(1):31-36.
[11]梁锦照.城市电网规划方法研究.北京：中国电力出版社,2010.
[12]程吉祥.基于时频原子方法的雷达辐射源信号识别.西南交通大学硕士论文,2011.
[13]Najaran T, Akbarzadeh M. Improvement of quantum evolutionary algorithms for financial data analysis.Proceedings of the Conference on Evolutionary Computation, 2008:133-143.
[14]Alba E, Dorron B. The exploration exploitation tradeoff in dynamic cellular genetic algorithms. IEEE Transactions on Evolutionary Computation,2005,9(2):126-142.
[15]Nodehi A, Tayarani M, Mahmoudi F. A novel functional sized population quantum evolutionary algorithm for fractal image compression. Proceedings of the 14th International CSI Computer Conference,2009:564-568.
[16]Guo J, Sun L, Wang R. An improved quantum genetic algorithm. Proceedings of the 2009 Third International Conference on Genetic and Evolutionary Computing,2009, 10(1):14-18.
[17]Tayarani N Akbarzadeh. A sinusoid size ring structure quantum evolutionary algorithm. Proceedings of IEEE Conference on Cybernetics and Intelligent Systems.Chengdu, 2008:1165-1169.
[18]Imabeppu T, Nakayama S, Ono S. A study on a quantum-inspired evolutionary algorithm based on pair swap. Artificial Life and Robotics,2008,12(1):148-152.
[19]Andre V, Marley M. Quantum evolutionary algorithm for numerical optimization. Studies in Computational Intelligence,2008,121(7):115-132.
[20]覃朝勇,郑建国.一种实数编码量子进化算法及其收敛性.控制与决策,2009,24(6)：56-60.
[21]高辉,徐光辉,张锐等.实数编码量子进化算法.控制与决策,2008,23(1)：87-90.
[22]Li P, Li S. Quantum-inspired evolutionary algorithm for continuous space optimization based on Bloch coordinates of qubits. Neurocomputing,2008,72(1/2/3):581-591.
[23]Zhao S, Xu G, Tao T. Real-coded chaotic quantum-inspired genetic algorithm for training of fuzzy neural networks. Computers Mathematics with Applications,2009,57 (11/12):2009-2015.
[24]申抒含,金炜东.多进制概率角复合位编码量子进化算法.模式识别与人工智能,2005,18(6)：657-663.
[25]Wang Y, Feng X Y, Huang Y X. A novel quantum swarm evolutionary algorithm and its applications. Neurocomputing,2007,70(4/5/6):633-640.
[26]周殊,潘炜.一种基于粒子群优化方法的改进量子遗传算法及应用.电子学报,2006,34(5)：897-901.
[27]Qu H J, Zhou F Z, Zhang X. An application of new quantum inspired immune evolutionary algorithm.2009 1st International Workshop on Database Technology and Applications. Bruges,2009:468-471.
[28]Teng H, Yang B, Zhao B. A new mutative scale chaos optimization quantum genetic algorithm. Chinese control and Decision conf. Yantai,2008:1547-1549.
[29]焦嵩鸣,韩璞,黄宇.模糊量子遗传算法及其在热工程模型辨识中的应用.中国电机工程学报,2007,27(5)：87-92.
[30]Da C A, Pacheco M, Vellasco M. Cultural operators for a quantum-inspired evolutionary algorithm applied to numerical optimizetion problems. Articial Intelligence and Knowledge Engeering Applications,2005,356(2):1-10.
[31]Zhang G X, Gheorghe M, Wu C Z. A quantum-inspired evolutionary algorithm based on P systems for knapsack problem. Fundamenta Informaticae,2008,87(1):93-116.
[32]王利锋,白瑞林.求解约束优化问题的一种新方法——基于量子粒子群优化算法.计算机工程与应用,2005,33：124-146.
[33]解平,李斌,庄镇泉.一种新的混合量子进化算法.计算机科学,2008,35(2)：166-170.
[34]Wang L, Li L. An effective hybrid quantum-inspired evolutionary algorithm for parameter estimation of chaotic systems. Expert Systems with Applications,2010, 37(2):1279-1285.
[35]Hossain M, Hashem M. Hybrid real coded quantum evolutionary algorithm based on particle swarm. Proceedings of 12th International Conference on Computers and Information Technology,2009:13-17.
[36]李盼池,李士勇.求解连续空间优化问题的量子蚁群算法.控制理论与应用，2008,25(2)：237-241.
[37]Zhang G X, Rong H N. Quantum-inspired genetic algorithm based time-frequency atom decomposition. Lecture Notes in Computer Science,2007,4490:243-250.
[38]Zhang G X, Rong H N. Improved quantum-inspired genetic algorithm based time-frequency analysis of radar emitter signals. Lecture Notes in Artifical Intelligence, 2006,4481:484-491.
[39]Zhang G X. Time-frequency atom decomposition with quantum-inspired evolutionary algorithms. Circuit System Signal Process,2010,29:209-233.
[40]Han K H, Park K H, Lee C H and Kim J H. Parallel quantum-inspired genetic algorithm for combinatorial optimization problem. Proceedings of 2001 Congress on Evolutionary Computation,2001,2:1422-1329.
[41]Zhang G X, Rong H N. Real-observation quantum-inspired evolutionary algorithm for a class of numerical optimizatiom problems. Lecture Notes in Computer Science,2007, 4490:989-996.
[42]Zhang G X, Jin W D, Hu L Z. Quantum evolutionary algorithm for multi-objective optimization problems. Proceedings of 2003 IEEE International Symposium on Intelligent Control,2003:703-708.
[43]娄素华,李研,吴耀武,熊信银.多目标电网无功优化的量子遗传算法.高电压技术,2005,31(9)：69-71.
[44]Vlachogiannis J G, Lee K Y. Quantum-inspired evolutionary algorithm for real and reactive power dispatch. IEEE Transactions on Power Systems,2008,23(4): 1627-1636.
[45]Wang L, Tang F, Wu H. Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation. Applied mathematics and Computa-tion,2005,171(2):1143-1158.
[46]李恒建,尹忠科,王建英.基于量子遗传优化算法的图像稀疏分解.西南交通大学学报,2007,42(1)：19-23.
[47]封晓强,何铁军.基于量子进化算法的交通图像稀疏分解.南京理工大学学报(自然科学版),2010,34(1)：40-44.
[48]Li Y, Jiao L C. An effective method of image edge detection based on parallel quantum evolutionary algorithm. Signal Processing,2003,19(1):69-74.
[49]Khorsand A R, AkbarzadehT M, Moin H. Genetic quantum algorithm for Voltage and pattern design of piezoelectric actuator. Proceedings of 2006 IEEE Congess on Evolutionary Computation,2006:2593-2600.
[50]王成山,刘涛,谢莹华.基于混合遗传算法的变电站选址定容.电力系统自动化,2006,30(6)：30-34.
[51]Enver M. An interactive procedure for sizing and timing distribution substations using optimization techniques. IEEE Transactions on Power Apparatus and Systems,1974, 93(5):1281-1286.
[52]Crawford D M, Holt S B. A mathematical optimization technique for locating and sizing distribution substations and deriving their optimal service areas. IEEE Transactions on Power Apparatus and Systems,1975,94(2):30-234.
[53]Thompson G L, Wall D L. A branch and bound model for choosing optimal substation locations. IEEE Transactions on Power Apparatus and Systems,1981,100(5): 2683-2687.
[54]路志英,葛少云,王成山.基于粒子群优化的加权伏罗诺伊图变电站规划.中国电机工程学报,2009,29(16)：35-41.
[55]王玉瑾,王主丁,张宗益等.基于初始站址冗余网格动态减少的变电站规划.电力系统自动化,2010,34(12)：39-43.
[56]王艳松,解飞.油田配电网临时变电站规划的研究.电力系统保护与控制,2010,38(4)：84-87.
[57]高付良,张鹏,赛雪等.考虑负荷不确定性变电站站址定容.电力系统保护与控制,2010,38(15)：75-80.
[58]邱富东,汤红卫.基于GIS空间查询和遗传算法的变电站规划.华东电力,2010,38(3)：341-344.
[59]高炜欣,罗先觉,朱颖.贪心算法结合Hopfield神经网络优化配电变电站规划.电网技术,2004,28(7)：73-76.
[60]刘志发,张建华.基于改进多组织粒子群算法优化计算的配电网络变电站选址定容.中国电机工程学报,2007,27(1)：105-111.
[61]张葛祥,李娜,金炜东,胡来招.一种新量子遗传算法及其应用.电子学报,2004,32(3)：476-479.
[62]Qin Y H, Zhang G X, Li Y Q. A comprehensive learning quantum-inspired evolutionary algorithm. Communications in Computer and Information Science,2011, 268:151-157.
[63]栾丽君,谭立静,牛奔.一种基于粒子群优化算法和差分进化算法的新型混合全局优化算法.信息与控制,2007,36(6)：708-714.
[64]Christian B, Andrea R. Metaheuristics in combinatorial optimization:overview and conceptual comparison. ACM Computer Surveys,2003,35(3):268-308.
[65]张忆.基于遗传退火的生物信息学多序列比对算法研究.电子科技大学硕士论文,2009.
[66]李静.基于JIT供应的集货车辆路线问题研究.长安大学硕士论文,2007.
[67]孙丰荣,李艳玲,曲怀敬,刘泽,张梅.基于活动轮廓模型和边缘对比度特征量的血管内超声图像边缘提取.中国生物医学工程学报,2006,25(4)：385-389.
[68]朱颢东,钟勇.一种改进的模拟退火算法.计算机技术与发展,2009,19(6)：32-35.
[69]王明兴.连续禁忌搜索算法改进及应用研究.浙江大学硕士学位论文,2005.
[70]陈铁梅.精密电子表面贴装生产优化问题研究.华南理工大学博士论文,2012.
[71]吴爽.共享性Flow shop调度算法设计及应用研究.四川大学硕士论文,2007.
[72]李雪梅,张素琴.基于仿生理论的几种优化算法综述.计算机应用研究,2009,26(6)：2032-2034.
[73]金华征,程浩忠,奚殉,夏夷,奚增辉,沈晓岚.贪婪随机自适应搜索法在电网规划中的应用.上海大学学报,2006,40(4)：563-567.
[74]董红宇,黄敏,王兴伟.变邻域搜索算法综述.控制工程,2009,16(1)：1-5.
[75]陈萍.启发式算法及其在车辆路径问题中的应用.北京交通大学博士学位论文,2009.
[76]Han K H, Kim J H. Quantum-inspired evolutionary algorithm with a new termination criterion,Hε gate and two-phase scheme. IEEE Trans on Evolutionary Computation, 2004,8(2):156-169.
[77]Zhang R, Gao H. Improved quantum evolutionary algorithm for combinatorial optimization problem. Proceedings of the Six International Conference on Machine Learning and Cybernetics,2007,3501-3505.
[78]Zhou M, Huang M, Yin J. Optimal 110/10kV substations planning.Proceedings of 2010 China International Conference on Electricity Distribution (CICED),2010:1-6.
[79]王林梅,黄民翔.变电站站址两阶段优化规划的实用改进方法.浙江电力,2006,2006(5)：1-5.
[80]中华人民共和国住房和城乡建设部.城市电力规划规范,1999.
[81]刘振亚.国家电网公司输变电工程通用造价.北京：中国电力出版社,2010.