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基于划分的多尺度量子谐振子算法多峰优化

陆志君 安俊秀 王鹏

陆志君, 安俊秀, 王鹏. 基于划分的多尺度量子谐振子算法多峰优化. 自动化学报, 2016, 42(2): 235-245. doi: 10.16383/j.aas.2016.c150429
引用本文: 陆志君, 安俊秀, 王鹏. 基于划分的多尺度量子谐振子算法多峰优化. 自动化学报, 2016, 42(2): 235-245. doi: 10.16383/j.aas.2016.c150429
LU Zhi-Jun, AN Jun-Xiu, WANG Peng. Partition-based MQHOA for Multimodal Optimization. ACTA AUTOMATICA SINICA, 2016, 42(2): 235-245. doi: 10.16383/j.aas.2016.c150429
Citation: LU Zhi-Jun, AN Jun-Xiu, WANG Peng. Partition-based MQHOA for Multimodal Optimization. ACTA AUTOMATICA SINICA, 2016, 42(2): 235-245. doi: 10.16383/j.aas.2016.c150429

基于划分的多尺度量子谐振子算法多峰优化

doi: 10.16383/j.aas.2016.c150429
基金项目: 

国家社会科学基金 12XSH019

国家自然科学基金 60702075

详细信息
    作者简介:

    陆志君 成都信息工程大学软件工程学院硕士研究生.2013年获得南京信息工程大学软件工程学院学士学位.主要研究方向为分布式计算, 智能算法.E-mail:bingjungg@126.com

    安俊秀 成都信息工程大学软件工程学院教授.2004年获得西安交通大学工学硕士学位.主要研究方向为社会计算, 智能搜索, 分布式计算.E-mail:anjunxiu@cuit.edu.cn

    通讯作者:

    王鹏 成都信息工程大学软件工程学院教授.2004年获得中国科学院成都计算机应用研究所博士学位.主要研究方向为分布式计算, 智能算法.本文通信作者.E-mail:wp002005@163.com

Partition-based MQHOA for Multimodal Optimization

Funds: 

National Social Science Foundation of China 12XSH019

Supported by National Natural Science Foundation of China 60702075

More Information
    Author Bio:

    Master student at the College of Software, Chengdu University of Information Technology. He received his bachelor degree from the College of Software, Nanjing University of Information Technology in 2013. His research interest covers distributed computing and intelligent algorithm

    Professor at the College of Software, Chengdu University of Information Technology. She received her master degree from Xi0an Jiaotong University in 2004. Her research interest covers social computing, intelligent searching, and distributed computing

    Corresponding author: WANG Peng Professor at the College of Software, Chengdu University of Information Technology. He received his Ph. D. degree from Chengdu Institute of Computer Application, Chinese Academy of Sciences in 2004. His research interest covers distributed computing and intelligent algorithm. Corresponding author of this paper
  • 摘要: 针对多峰优化问题, 本文结合多尺度量子谐振子算法的全局优化特性提出了基于划分的多尺度量子谐振子算法.对定义域进行合理均匀划分, 根据划分区域长度构建初始基态高斯曲线, 随着标准差衰减高斯曲线逐渐收敛, 从而在各个区域内快速搜索到极值点.对于实际函数的维度和极值数不同, 本文提出固定分辨率策略和多级分辨率策略来解决实际问题, 通过寻优精确性、全极值点寻优和全局多峰优化三个角度进行实验, 对比蚁群算法、差分进化算法等主流群智能算法, 可以表明该算法参数设置简单, 具有很好的寻优准确性、快速收敛性和记忆性.
  • 图  1  k个高斯分布函数均匀叠加概率密度图

    Fig.  1  Probability density map of the uniform superpositionwith k Gauss distribution functions

    图  2  不同函数的极小值搜索

    Fig.  2  Search minimum values of different functions

    图  3  P-MQHOA收敛过程示意图

    Fig.  3  Schematic diagram of P-MQHOA convergence process

    图  4  3级分辨率策略下对 $f (x, y)$ 求极值

    Fig.  4  3-level resolution strategy for the extreme value of $f (x, y)$

    图  5  不等值极值点函数搜索准确性随a变化图

    Fig.  5  Searching accuracy of unequal-value-extremum functionvaring with a

    图  6  等值极值点函数搜索准确性随a变化图

    Fig.  6  Searching accuracy of equal-value-extremum functionvaring with a

    图  7  一维震荡函数曲线

    Fig.  7  One-dimensional shock function curve

    图  8  二维Griewank函数

    Fig.  8  Two-dimensional Griewank function

    图  9  算法全局寻优比较热力图

    Fig.  9  Comparison of global optimization algorithms thermodynamic diagram

    表  1  一维震荡函数两种策略寻优性能比较

    Table  1  Comparison of two strategies for one dimensional shock function

    K0 λ0 K1 CN1 TC1 K2 CN2 TC2
    2 0.1 3.9 10 0.0030 4.0 4 0.0038
    12 0.01 13.9 100 0.0180 11.9 10 0.0084
    46 0.001 47.7 1 000 0.1499 41.6 31 0.0348
    156 0.0001 157.0 10 000 1.312 144.2 100 0.167
    500 0.00001 493.2 100 000 10.374 461.0 316 0.767
    1592 0.000001 1515.0 1 000 000 95.614 1 419.6 1 000 3.067
    下载: 导出CSV

    表  2  二维Griewank函数两种策略寻优性能比较

    Table  2  Comparison of two strategies for two dimensional Griewank function

    K0 λ0 K1 CN1 TC1 K2 CN2 TC2
    1 369 20 75.7 10 0.051 40.3 4 0.036
    1 369 10 307.8 400 0.183 231.2 10 0.291
    1 369 5 1 049.2 1 600 0.726 617.5 31 1.472
    1 369 2 1 333.4 10 000 4.078 670.2 100 1.657
    1 369 1 1 340.5 40 000 15.312 783.0 316 9.64
    1 369 0.5 1 353.10 160 000 57.272 1 924.1 1 000 21.04
    下载: 导出CSV

    表  3  P-MQHOA与蚁群算法全极值搜索比较

    Table  3  Comparison of total-extremum-searching of P-MQHOA and ant colony algorithm

    NO. P-MQHOA
    (x1, x2, f/(x1, x2))
    ANT
    1 (-0.878093608, -0.878093599, 3.53255484) (-0.8781, -0.8781, 3.5326)
    2 (-0.878093550, -0.526852857, 3.042136418) -0.8737, -0.5310, 3.0362
    3 (-0.878093617, -0.17561706, 2.796928371) (-0.8725, -0.1810, 2.7873)
    4 (-0.878093568, 0.175617049, 2.796928371) (-0.8725, -0.5310, 3.0362)
    5 (-0.878093628, 0.526852825, 3.042136418) (-0.8700, 0.5175, 3.0176)
    6 (-0.878093611, 0.878093569, 3.53255484) (-0.8675, 0.8675, 3.4966)
    7 (-0.52685281, -0.878093573, 3.042136418) (-0.5310, -0.8737, 3.0362)
    8 (-0.526852791, -0.526852812, 2.551717996) (-0.5268, -0.5268, 2.5517)
    9 (-0.526852794, -0.175617069, 2.306509949) (-0.5352, -0.1773, 2.3056)
    10 (-0.526852803, 0.17561705, 2.306509949) (-0.5215, 0.1700, 2.2969)
    11 (-0.526852866, 0.526852858, 2.551717996) (-0.5200, 0.5200, 2.5367)
    12 (-0.526852827, 0.878093628, 3.042136418) (-0.5175, 0.8700, 3.0176)
    13 (-0.175617027, -0.878093592, 2.796928371) (-0.1810, -0.8725, 2.7873)
    14 (-0.175617075, -0.526852805, 2.306509949) (-0.1773, -0.5252, 2.3056)
    15 (-0.175617028, -0.175617046, 2.061301903) (-0.1756, -0.1756, 2.0613)
    16 (-0.175617006, 0.175617028, 2.061301903) (-0.1756, 0.1756, 2.0559)
    17 (-0.175617067, 0.526852847, 2.306509949) (-0.1700, 0.5215, 2.2969)
    18 (-0.175617056, 0.878093620, 2.796928371) (-0.1675, 0.8700, 2.7759)
    19 (0.175617041, -0.878093592, 2.796928371) (0.1675, -0.8700, 2.7759)
    20 (0.175617068, -0.526852815, 2.306509949) (0.1700, -0.5215, 2.2969)
    21 (0.175617061, -0.175617041, 2.061301903) (0.1715, -0.1715, 2.0559)
    22 (0.175617051, 0.175617057, 2.061301903) (0.1756, 0.1756, 2.0613)
    23 (0.175617054, 0.526852783, 2.306509949) (0.1773, 0.5252, 2.3056)
    24 (0.175617039, 0.878093590, 2.796928371) (0.1810, 0.8725, 2.7873)
    25 (0.526852762, -0.878093542, 3.042136418) (0.5175, -0.8700, 3.0176)
    26 (0.526852876, -0.526852885, 2.551717996) (0.5200, -0.5200, 2.5367)
    27 (0.526852785, -0.175617064, 2.306509949) (0.5215, -0.1700, 2.2969)
    28 (0.526852823, 0.175617064, 2.306509949) (0.5252, 0.1773, 2.3056)
    29 (0.52685278, 0.52685282, 2.551717996) (0.5268, 0.5268, 2.5517)
    30 (0.526852781, 0.878093598, 3.042136418) (0.5310, 0.8737, 3.0362)
    31 (0.878093552, -0.878093598, 3.53255484) (0.8675, -0.8675, 3.4966)
    32 (0.87809359, -0.526852814, 3.042136418) (0.8700, -0.5175, 3.0176)
    33 (0.878093528, -0.175617038, 2.796928371) (0.8700, -0.1675, 2.7759)
    34 (0.878093604, 0.175617041, 2.796928371) (0.8725, 0.1810, 2.7873)
    35 (0.878093617, 0.526852807, 3.042136418) (0.8737, 0.5310, 3.0362)
    36 (0.878093597, 0.878093581, 3.53255484) (0.8781, 0.8781, 3.5326)
    下载: 导出CSV

    表  4  二维Griewank函数极值分布拟合结果

    Table  4  Fitting results of extremum values0 distribution of Griewank function

    Func. No. ε P-MQHOA MOBi-DE CDE SDE S-CMA CMA SPSO PER-PSO r2pso r3pso Niching-based BNPGA
    NSGA-Ⅱ
    f1 1 0.05 1(4) 1(4) 1(4) 1(4) 1(4) 1(4) 0.44(12) 0.82(10) 0.76(11) 0.84(9) 1(4) 1(4)
    f2 1 0.05 1(5) 1(5) 1(5) 1(5) 1(5) 1(5) 0.40(12) 1(5) 0.88(11) 0.96(10) 1(5) 1(5)
    f3 2 1E-6 2(2.5) 2(2.5) 2(2.5) 1.96(5) 1.92(7) 1.95(6) 1.38(9) 0.8(10) 0.48(12) 0.6(11) 2(2.5) 1.5(8)
    f4 5 1E-6 5(1.5) 5(1.5) 3.84(10) 4.70(6) 0.04(12) 0.6(11) 4.88(3) 4.84(4) 4.68(7) 4.74(5) 4.37(9) 4.64(8)
    f5 1 1E-6 1(6) 1(6) 0.72(12) 1(6) 1(6) 1(6) 1(6) 1(6) 1(6) 1(6) 1(6) 1(6)
    f6 5 1E-6 5(1.5) 5(1.5) 3.96(9) 4.6(7) 0(12) 0.64(11) 4.92(4) 4.96(3) 4.88(5) 4.72(6) 4.52(8) 3.56(10)
    f7 1 1E-6 1(5.5) 1(5.5) 0.8(11) 1(5.5) 1(5.5) 1(5.5) 1(5.5) 1(5.5) 1(5.5) 1(5.5) 0.6(12) 1(5.5)
    f8 4 5E-4 4(1.5) 4(1.5) 0.32(12) 3.72(4.5) 3.72(4.5) 3.43(7) 0.84(11) 3.68(6) 2.92(9) 2.76(10) 3.74(3) 3.34(8)
    f9 2 1E-6 2(3) 2(3) 0.04(12) 2(3) 1.6(7) 2(3) 0.08(11) 1.96(6) 1.44(9) 1.56(8) 2(3) 1.24(10)
    f10 1 1E-6 1(2) 1(2) 0.52(9) 0.32(10) 0.06(12) 0.18(11) 0.56(8) 1(2) 0.88(6) 0.76(7) 0.94(5) 0.96(4)
    f11 18 5 E-2 17.5(1) 17.4(2) 11.39(12) 12.78(9) 12.04(10) 12(11) 14.36(7) 15.61(6) 15.95(5) 16.45(4) 16.94(3) 13.72(8)
    f12 6 0.05 6(1.5) 6(1.5) 5.56(6.5) 4.88(12) 5.56(6.5) 5.81(3) 5.6(5) 5.28(10) 5.52(8) 5.16(11) 5.36(9) 5.71(4)
    f13 36 1E-3 35.6(1) 35.4(2) 33.8(3) 23.8(7) 24.6(6) 23.6(8) 25.72(5) 21.8(12) 22.4(9) 22.2(10) 22.05(11) 31.76(4)
    f14 218 1E-3 163.56(2) 175.88(1) 152(3) 50.6(8) 0.6(12) 32.5(11) 70.12(6) 68.6(7) 40.6(10) 45.4(9) 92.76(5) 121.54(4)
    Total ranks 38 39 111 92 109.5 102.5 104.5 92.5 113.5 111.5 85.5 88.5
    下载: 导出CSV

    表  5  P-MQHOA算法与MOBi-DE算法时间消耗 (s)

    Table  5  Time consumption of P-MQHOA algorithm and MOBi-DE algorithm (s)

    Func. f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14
    P-MQHOA 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.1 0.1 0.1 1.76 0.28 4.32 12.14
    MOBi-DE 1.56 1.46 2.82 2.64 1.54 2.04 1.68 18.34 15.28 41.24 46.28 36.49 51.74 72.36
    下载: 导出CSV
  • [1] Chang Y W, Yu G F. Multi-Sub-Swarm PSO algorithm for multimodal function optimization. In:Proceedings of the 2014 International Conference on Computer Science and Information Technology. India:Springer, 2014. 687-695
    [2] Qu B Y, Suganthan P N, Das S. A distance-based locally informed particle swarm model for multimodal optimization. IEEE Transactions on Evolutionary Computation, 2013, 17(3):387-402 doi: 10.1109/TEVC.2012.2203138
    [3] Shih C J, Teng T L, Chen S K. A niche-related particle swarm meta-heuristic algorithm for multimodal optimization. In:Proceedings of the 2nd International Conference on Intelligent Technologies and Engineering Systems. Switzerland, Germany:Springer, 2014. 313-321
    [4] Agrawal S, Sanjay S. FRPSO:fletcher-reeves based particle swarm optimization for multimodal function optimization. Soft Computing, 2014, 18(11):2227-2243 doi: 10.1007/s00500-013-1196-2
    [5] Qu B Y, Suganthan P N, Liang J J. Differential evolution with neighborhood mutation for multimodal optimization. IEEE Transactions on Evolutionary Computation, 2012, 16(5):601-614 doi: 10.1109/TEVC.2011.2161873
    [6] Basak A, Das S, Tan K C. Multimodal optimization using a biobjective differential evolution algorithm enhanced with mean distance-based selection. IEEE Transactions on Evolutionary Computation, 2013, 17(5):666-685 doi: 10.1109/TEVC.2012.2231685
    [7] Pang C Y, Li X, Liu H, Wang Y F, Hu B Q. Applying ant colony optimization to search all extreme points of function. In:Proceedings of the 5th IEEE Conference on Industrial Electronics and Applications. Taichung, China:IEEE, 2010. 1517-1521
    [8] Dasgupta B, Divya K, Mehta V K, Deb K. RePAMO:recursive perturbation approach for multimodal optimization. Engineering Optimization, 2013, 45(9):1073-1090 doi: 10.1080/0305215X.2012.725050
    [9] Vidya R C, Phaneendra H D, Shivakumar M S. Quantum algorithms and hard problems. In:Proceedings of 5th IEEE International Conference on Cognitive Informatics. Washington, DC, USA:IEEE, 2006. 783-787
    [10] 王鹏.云计算的关键技术与应用实例.北京:人民邮电出版社, 2010. 168-194

    Wang Peng. The Key Technology and Application Examples of Cloud Computing. Beijing:People's Posts and Telecommunications Press, 2010. 168-194
    [11] 王鹏, 黄焱, 任超, 郭又铭.多尺度量子谐振子高维函数全局优化算法.电子学报, 2013, 41(12):2468-2473 http://www.cnki.com.cn/Article/CJFDTOTAL-DZXU201312023.htm

    Wang Peng, Huang Yan, Ren Chao, Guo You-Ming. Multi-Scale quantum harmonic oscillator for high-dimensional function global optimization algorithm. Acta Electronica Sinica, 2013, 41(12):2468-2473 http://www.cnki.com.cn/Article/CJFDTOTAL-DZXU201312023.htm
    [12] 王鹏, 黄焱.多尺度量子谐振子优化算法物理模型.计算机科学与探索, 2015, 9(10):1271-1280 http://www.cnki.com.cn/Article/CJFDTOTAL-KXTS201510014.htm

    Wang Peng, Huang Yan. Physical model of multi-scale quantum harmonic oscillator optimization algorithm. Journal of Frontiers of Computer Science and Technology, 2015, 9(10):1271-1280 http://www.cnki.com.cn/Article/CJFDTOTAL-KXTS201510014.htm
    [13] 肖黎彬, 王鹏, 陈磊, 郭又铭.量子谐振子优化算法.计算机应用, 2013, 32(S2):1-4, 44 http://www.cnki.com.cn/Article/CJFDTOTAL-JSJY2012S2000.htm

    Xiao Li-Bin, Wang Peng, Chen Lei, Guo You-Ming. Quantum harmonic oscillator optimization algorithm. Journal of Computer Applications, 2013, 32(S2):1-4, 44 http://www.cnki.com.cn/Article/CJFDTOTAL-JSJY2012S2000.htm
    [14] Mallat S G. A theory for multiresolution signal decomposition:the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, 11(7):674-693 doi: 10.1109/34.192463
    [15] 左斌, 胡云安, 施建洪.极值搜索算法的研究与进展.海军航空工程学院学报, 2006, 21(6):611-617 http://www.cnki.com.cn/Article/CJFDTOTAL-HJHK200606003.htm

    Zuo Bin, Hu Yun-An, Shi Jian-Hong. Research and development of extremum seeking algorithm. Journal of Naval Aeronautical Engineering Institute, 2006, 21(6):611-617 http://www.cnki.com.cn/Article/CJFDTOTAL-HJHK200606003.htm
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  • 收稿日期:  2015-07-02
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