Double mutation genetic algorithm and its application to the critical slip surface search
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摘要:
针对传统的优化算法难以在具有变量多、约束条件复杂、局部极值点多的边坡临界滑动面搜索中取得较好效果的问题，提出双重变异遗传算法（DMGA）。一方面，该算法通过探测变异操作提升算法的局部寻优能力，通过直接变异操作提升算法的全局寻优能力，两者的结合使算法能够在搜索的广度与深度上达到较好的平衡；另一方面，算法采用考虑个体适应度值与进化代数的自适应交叉概率及自适应变异概率，使算法在进化的早期能够增加种群的多样性，在进化的后期能够保护较优的个体不受破坏。将该算法与简化Bishop法相结合，对澳大利亚计算机应用协会（ACADS）提供的考核题及一个海堤边坡工程实例进行分析，计算结果表明：（1）对于均质边坡和非均质边坡，该方法均能准确搜索到边坡的临界滑动面及相应的安全系数；（2）与仅进行直接变异或探测变异的遗传算法相比，双重变异遗传算法具有更强的全局搜索能力及更好的鲁棒性，具有广阔的应用前景。
Abstract:Considering the fact that the optimization function of the critical slip surface search problem has many variables, complex constraints and many local extremum points, it is difficult for the traditional optimization method to achieve better search results. Therefore, a genetic algorithm based on double mutation strategy is proposed to search the critical slip surface of slope. On one hand, the algorithm improves the local optimization ability of the algorithm by detecting mutation operation and the global optimization ability of the algorithm by direct mutation operation. The combination of detection mutation operation and direct mutation operation enables the algorithm to achieve a good balance between the breadth and depth of the search. On the other hand, the algorithm adopts adaptive crossover probability and adaptive mutation probability considering individual fitness value and evolution times, so that the algorithm can increase the diversity of population in the early stage of evolution. The algorithm can protect the better individuals from destruction in the later stage of evolution. The algorithm is combined with the simplified Bishop method to calculate the examination questions provided by ACADS and a seawall slope problem. The results show that (1) for both homogeneous and heterogeneous slopes, this method can accurately search the critical slip surface of the slope and calculate the corresponding safety factor. (2) Compared with genetic algorithms that only carry out direct mutation or detect mutation, the double mutation genetic algorithm has stronger global search ability and better robustness, and has a broad application prospect.
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Key words:
- genetic algorithm /
- slope stability /
- simplified Bishop method /
- critical slip surface
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土号 黏聚力
/ kPa内摩擦角
/（°）重度
/（kN·m−3）1#土 0.0 38.0 19.5 2#土 5.3 23.0 19.5 3#土 7.2 20.0 19.5 
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表 2 考核题1（a）的计算结果（DMGA）
Table 2. Calculated results of EX1（a）（DMGA）
序号 F R/m xo/m yo/m 1 0.985 3 28.967 −0.637 28.960 2 0.985 2 28.824 −0.501 28.820 3 0.985 2 29.003 −0.564 28.998 4 0.985 2 28.231 −0.291 28.230 5 0.985 5 29.899 −0.882 29.886 6 0.985 7 30.246 −1.044 30.228 7 0.985 5 27.486 −0.026 27.486 8 0.985 2 29.040 −0.591 29.034 9 0.985 9 30.390 −0.999 30.374 10 0.985 6 30.035 −0.950 30.020 
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表 3 考核题1（c）的计算结果（DMGA）
Table 3. Calculated results of EX1（c）（DMGA）
序号 F R/m xo/m yo/m 1 1.396 6 19.365 4.300 18.799 2 1.397 8 19.749 4.200 19.036 3 1.395 4 18.344 4.412 17.659 4 1.400 1 20.140 3.818 19.699 5 1.399 9 20.255 4.129 19.609 6 1.397 1 18.740 4.169 17.994 7 1.394 9 18.400 4.551 17.809 8 1.396 1 18.921 4.027 18.439 9 1.397 2 18.766 4.300 17.899 10 1.400 3 20.086 3.893 19.699 
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表 4 考核题1（a）、1（c）的计算结果统计分析
Table 4. Statistical analysis of computation results of EX1（a）and EX1（c）
考核题 算法 最小安全
系数最大安全
系数平均安全
系数安全系数的
标准差1（a） DMGA 0.985 2 0.993 7 0.985 7 0.001 3 DIMGA 0.985 3 1.029 9 0.995 8 0.011 3 DEMGA 0.985 2 1.116 0 1.010 7 0.036 5 1（c） DMGA 1.394 9 1.407 0 1.397 9 0.003 0 DIMGA 1.397 9 1.438 7 1.412 5 0.009 1 DEMGA 1.395 3 1.471 1 1.413 2 0.026 0
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表 5 考核题1（a）、1（c）算法收敛过程对比表
Table 5. Comparison of convergence processes of EX1（a）and EX1（c）
考核题 算法 收敛
代数最大适应度值 安全
系数1（a） DMGA 66 0.50371 0.985 3 DIMGA 116 0.50321 0.987 2 DEMGA 110 0.49375 1.025 3 1（c） DMGA 72 0.41726 1.396 6 DIMGA 151 0.41605 1.403 6 DEMGA 27 0.41673 1.399 6
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[1] 胡卸文, 张志鹏, 黄润秋, 等. 基于圆弧型滑面搜索的松散堆积体边坡坍岸宽度预测方程[J]. 水文地质工程地质,2009,36(2):47 − 51. [HU Xiewen, ZHANG Zhipeng, HUANG Runqiu, et al. Bank collapse predictive equation of the loose accumulation slope based on circular sliding surface search[J]. Hydrogeology & Engineering Geology,2009,36(2):47 − 51. (in Chinese with English abstract) doi: 10.3969/j.issn.1000-3665.2009.02.010
[2] 汪民乐, 高晓光, 范阳涛. 先进遗传算法及其工程应用[M]. 西安: 西北工业大学出版社, 2019.
WANG Minle, GAO Xiaoguang, FAN Yangtao. Advanced genetic algorithm and engineering application [M]. Xi’an: Northwestern Polytechnical University Press, 2019. (in Chinese)
[3] 贺子光, 姚翔龙, 赵法锁, 等. 改进GEP方法在边坡非圆临界滑动面搜索中的应用[J]. 长江科学院院报,2017,34(1):91 − 97. [HE Ziguang, YAO Xianglong, ZHAO Fasuo, et al. Improved genetic expression programming applied to searching for non-circular critical slip surface of slope[J]. Journal of Yangtze River Scientific Research Institute,2017,34(1):91 − 97. (in Chinese with English abstract) doi: 10.11988/ckyyb.20150985
[4] 梁冠亭, 陈昌富, 朱剑锋, 等. 基于M-P法的抗滑桩支护边坡稳定性分析[J]. 岩土力学,2015,36(2):451 − 456. [LIANG Guanting, CHEN Changfu, ZHU Jianfeng, et al. Stability analysis of pile stabilized slope based on Morgenstern-Price method[J]. Rock and Soil Mechanics,2015,36(2):451 − 456. (in Chinese with English abstract)
[5] 朱剑锋, 陈昌富, 徐日庆. 土钉墙内部稳定性分析自适应禁忌变异遗传算法[J]. 岩土力学,2010,31(5):1663 − 1669. [ZHU Jianfeng, CHEN Changfu, XU Riqing. Application of ATMGA to interior stability analysis of soil-nailing wall[J]. Rock and Soil Mechanics,2010,31(5):1663 − 1669. (in Chinese with English abstract) doi: 10.3969/j.issn.1000-7598.2010.05.054
[6] 宁社教, 姚磊华, 赵永年. 用改进的十进制遗传算法确定土质边坡最危险滑面[J]. 工程地质学报,2008,16(1):109 − 115. [NING Shejiao, YAO Leihua, ZHAO Yongnian. Application of improved decimal strings genetic algorithm to searching for the most critical slip surface of soil slope[J]. Journal of Engineering Geology,2008,16(1):109 − 115. (in Chinese with English abstract) doi: 10.3969/j.issn.1004-9665.2008.01.020
[7] 石露, 李小春, 任伟, 等. 蚁群算法与遗传算法融合及其在边坡临界滑动面搜索中的应用[J]. 岩土力学,2009,30(11):3486 − 3492. [SHI Lu, LI Xiaochun, REN Wei, et al. Hybrid of ant colony algorithm and genetic algorithm and its application to searching critical slope slip surface[J]. Rock and Soil Mechanics,2009,30(11):3486 − 3492. (in Chinese with English abstract) doi: 10.3969/j.issn.1000-7598.2009.11.045
[8] 万文, 曹平, 冯涛, 等. 基于加速混合遗传算法搜索复杂边坡的最危险滑动面[J]. 岩土工程学报,2006,28(4):475 − 479. [WAN Wen, CAO Ping, FENG Tao, et al. Searching for the most dangerous failure surface of complex slope based on accelerating hybrid genetic algorithm[J]. Chinese Journal of Geotechnical Engineering,2006,28(4):475 − 479. (in Chinese with English abstract) doi: 10.3321/j.issn:1000-4548.2006.04.010
[9] 乐超, 徐超. 加筋土边坡安全评价的简化水平条分法[J]. 水文地质工程地质,2013,40(2):74 − 78. [LE Chao, XU Chao. Simplified horizontal slice method of reinforced soil slopes safety analysis[J]. Hydrogeology & Engineering Geology,2013,40(2):74 − 78. (in Chinese with English abstract)
[10] 毕港, 陈征宙, 姜玉平, 等. 一种边坡多滑动面搜索的新方法[J]. 水文地质工程地质,2011,38(6):24 − 28. [BI Gang, CHEN Zhengzhou, JIANG Yuping, et al. A new method for searching all possible circular slips of a slope[J]. Hydrogeology & Engineering Geology,2011,38(6):24 − 28. (in Chinese with English abstract)
[11] 佴磊, 徐燕, 代树林, 等. 边坡工程[M]. 北京: 科学出版社, 2010.
NAI Lei, XU Yan, DAI Shulin, et al. Slope engineering [M]. Beijing: Science Press, 2010. (in Chinese)
[12] 陈宝林. 最优化理论与算法[M]. 2版. 北京: 清华大学出版社, 2005.
CHEN Baolin. Optimization theory and algorithm [M].2nd ed. Beijing: Tsinghua University Press, 2005. (in Chinese)
[13] 刘全, 王晓燕, 傅启明, 等. 双精英协同进化遗传算法[J]. 软件学报,2012,23(4):765 − 775. [LIU Quan, WANG Xiaoyan, FU Qiming, et al. Double elite coevolutionary genetic algorithm[J]. Journal of Software,2012,23(4):765 − 775. (in Chinese with English abstract) doi: 10.3724/SP.J.1001.2012.04040
[14] 魏彤, 龙琛. 基于改进遗传算法的移动机器人路径规划[J]. 北京航空航天大学学报,2020,46(4):703 − 711. [WEI Tong, LONG Chen. Path planning for mobile robot based on improved genetic algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics,2020,46(4):703 − 711. (in Chinese with English abstract)
[15] 潘正君, 康立山, 陈毓屏. 演化计算[M]. 北京: 清华大学出版社, 1998.
PAN Zhengjun, KANG Lishan, CHEN Yuping. Evolutionary computation [M]. Beijing: Tsinghua University Press, 1998. (in Chinese)
[16] 卢明奇, 曾风波. 基于自适应遗传算法的钢筋混凝土桥墩抗震设计方法[J]. 土木工程学报,2020,53(7):73 − 77. [LU Mingqi, ZENG Fengbo. Seismic design method for reinforcement concrete piers based on adaptive genetic algorithm[J]. China Civil Engineering Journal,2020,53(7):73 − 77. (in Chinese with English abstract)
[17] 玄光男, 程润伟. 遗传算法与工程优化[M]. 于歆杰, 周根贵, 译. 北京: 清华大学出版社, 2004.
MITSUO Gen, CHENG Runwei. Genetic algorithms and engineering optimization[M]. YU Xinjie, ZHOU Gengui, trans. Beijing: Tsinghua University Press, 2004. (in Chinese)
[18] 陈祖煜, 土质边坡稳定性分析——原理·方法·程序[M]. 北京: 中国水利水电出版社, 2003.
CHEN Zuyu. Soil slope stability analysis——theory, methods and programs[M]. Beijing: China Water Conservancy and Hydropower Press, 2003. (in Chinese)
[19] 邹广电. 边坡稳定分析条分法的一个全局优化算法[J]. 岩土工程学报,2002,24(3):309 − 312. [ZOU Guangdian. A global optimization method of the slice method for slope stability analysis[J]. Chinese Journal of Geotechnical Engineering,2002,24(3):309 − 312. (in Chinese with English abstract) doi: 10.3321/j.issn:1000-4548.2002.03.009
[20] 张明瑞, 陈征宙, 刘裕华, 等. 引入退火机制的智能单粒子算法在复杂边坡最危险滑动面搜索中的应用[J]. 工程地质学报,2011,19(2):181 − 186. [ZHANG Mingrui, CHEN Zhengzhou, LIU Yuhua, et al. Application of intelligent single particle optimizer with simulated annealing mechanism to searching for critical slip surface of complex slope[J]. Journal of Engineering Geology,2011,19(2):181 − 186. (in Chinese with English abstract) doi: 10.3969/j.issn.1004-9665.2011.02.006
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