一起来学演化计算-实数空间变异算子

时间:2022-07-23
本文章向大家介绍一起来学演化计算-实数空间变异算子，主要内容包括其使用实例、应用技巧、基本知识点总结和需要注意事项，具有一定的参考价值，需要的朋友可以参考一下。

  • [节选自] 文诗华. 多目标进化算法中变异算子的研究[D]. 湘潭大学. 这是来自郑金华教授的学生的硕士毕业论文。从入门演化计算时就读着郑老师的书走来的。在此对其表示最诚挚的敬意

实数搜索空间变异算子的实现

变异算子的设计原则

变异算子的研究概况

实数空间常用变异算子

均匀变异

非均匀变异

自适应变异

高斯变异

柯西变异

多项式变异

在Deb K , Goyal M . A Combined Genetic Adaptive Search (GeneAS) for Engineering Design[C]// 1996.原文中，其是这样描述的。

matlab实现多项式变异

% polynomial mutation
       % 多项式突变
       function object=mutate(object,p,dim,mum)
           rnvec_temp=p.rnvec;
           for i=1:dim
               % 因为问题的维度一般比较大，所以rand(1)<1/dim的概率很小
               if rand(1)<1/dim
                   u=rand(1);
                   if u <= 0.5
                       del=(2*u)^(1/(1+mum)) - 1;
                       rnvec_temp(i)=p.rnvec(i) + del*(p.rnvec(i));
                   else
                       del= 1 - (2*(1-u))^(1/(1+mum));
                       rnvec_temp(i)=p.rnvec(i) + del*(1-p.rnvec(i));
                   end
               end
           end  
           object.rnvec = rnvec_temp;          
       end

jmetal实现多项式变异

public void doMutation(double probability, Solution solution) throws JMException {
  double rnd, delta1, delta2, mut_pow, deltaq;
  double y, yl, yu, val, xy;
  XReal x = new XReal(solution);
  for (int var = 0; var < solution.numberOfVariables(); var++) {
   if (PseudoRandom.randDouble() <= probability) {//如果小于变异概率即可以进行变异操作
    y = x.getValue(var);
    yl = x.getLowerBound(var);
    yu = x.getUpperBound(var);
    delta1 = (y - yl) / (yu - yl);
    delta2 = (yu - y) / (yu - yl);
    rnd = PseudoRandom.randDouble();
    mut_pow = 1.0 / (eta_m_ + 1.0);
    if (rnd <= 0.5) {
     xy = 1.0 - delta1;
     val = 2.0 * rnd + (1.0 - 2.0 * rnd) * (Math.pow(xy, (distributionIndex_ + 1.0)));
     deltaq = java.lang.Math.pow(val, mut_pow) - 1.0;
    } else {
     xy = 1.0 - delta2;
     val = 2.0 * (1.0 - rnd) + 2.0 * (rnd - 0.5) * (java.lang.Math.pow(xy, (distributionIndex_ + 1.0)));
     deltaq = 1.0 - (java.lang.Math.pow(val, mut_pow));
    }
    y = y + deltaq * (yu - yl);
    if (y < yl)
     y = yl;
    if (y > yu)
     y = yu;
    x.setValue(var, y);
   }
  } // for

 } // doMutation

[42] Andenbrandt C A. An Extension the Theory of Convergence and a Proof of the Time Complexity of Genetic Algorithms. In [343], 53~68,1993. [43] C. A. Magele, K.Preis, W.Renhart, etc. Higher order evolution strategies for the global optimization of electromagnetic devices. IEEE Trans. On Magnetics,1993,29(2) :1775~1778. [44] C. Kappler. “Are evolutionary algorithms improved by large mutation?”, in Parallel Problem Solving from Nature( PPSN) IV (H.M Voigt, W Ebeling,I.Rochenberg, and H.P.Schwefeleds.Vo1.1141 of Lecture Notes in Computer Science,(Berlin), Springer-Verlag,1996:346~355. [45] Dai Xiaoming. Zou Runmin, Sun Rong etc. Convergence properties of non-crossover genetic algorithm. Proceedings of the 4th World Congress on Intelligent control and automation, Shanghai, China,2002:1882~1826. [46] Dirk Büche, Sibylle Müller, and Petros Koumoutsakos. Self-Adaptation for Multi-objective Evolutionary Algorithms, in Carlos M. Fonseca, Peter J. Fleming,Eckart Zitzler, Kalyanmoy Deb and Lothar Thiele (editors), EvolutionaryMulti-Criterion Optimization. Second International Conference, EMO 2003, pp.267–281, Springer. Lecture Notes in Computer Science. Volume 2632, Faro,Portugal, April 2003 . [47] Fogarty T C. Varying the Probability of Mutation in the Genetic Algorithms. In[335],104~109,1989. [48] Farhang-Mehr Ali and Shapour Azarm. An Information-Theoretic Metric forAssessing Multi-Objective Optimization Solution Set Quality. ASME,Transactions, Journal of Mechanical Design, 2003. [49] G. Rudolph. An evolutionary algorithm for integer programming, Int’1 conf. 1994 in Parallel problem solving from nature,Y David, R. Männer and H.P.Schwefel eds.,Vo1.3:139~148. [50] H.G Beyer. The theory of evolution strategies. Natural computing series. Springer,Heidelberg, 2001. [51] Hashem, M.M.A.; Watanabe, M.; Izumi, K. Evolution strategy a new time-variant mutation for fine local tuning SICE ‘97. Proceedings of the 36th SICE Annual Conference. International Session Papers, 1997:1099~1104. [52] Hesser J and Männer R. Investigation of the M-Heuristic for Optimal Mutation Probability. In [340], 115~125, 1992. [53] I.D.Falco ， A.D.Coippa ， E.Tarantino. Mutation-based genetic algorithm: performance evaluation. Applied Soft Computing, (2002): 285~299. [54] I. Rechenberg. Evolutionsstrategie: Optimierung texhnischer Systeme nach Prinzipien der biologischen Evolution. Stuttgart,Germany: Frogmann Holzboog, 1973. [55] J.Smith. Self-adaptation in evolutionary algorithm. Ph .D. dissertation, Univ. of the West of England, Bristol, 1997. [56] J.Smith. Operator and parameter adaptation in genetic algorithms. Soft computing.1997, 1(2):81~87. [57] K.C.Tan, C.K. Goh, Y.J. Yang, T.H. Lee. Evolving better population distribution and exploration in evolutionary multi-objective optimization, European Journal of Operational Research , 2006, 171 (2) : 463~495. [58] K. Deb and M. Goyal. A combined genetic adaptive search (GeneAS) for engineering design. Computer Science and Informatics, 1996, 26(4): 30-45. [59] Kalyanmoy Deb. Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester, UK, 2001. [60] K Deb, Mohan M, Mishra S. A fast multi-objective evolutionary algorithm for finding well-spread Pareto-optimal solutions [R]. KanGAL Report. No 2003002. [61] L.Hildebrand; B.Reusch, Fathi, M.; Directed mutation—a new self-adaptation for evolution strategies. Evolutionary Computation, 1999. CEC99. Proceedings of the 1999 Congress on, Volume:2, 1999:1550~1557. [62] Marco Laumanns, Günter Rudolph, Hans-Paul Schwefel. Mutation Control and Convergence in Evolutionary Multi-objective Optimization, In R. Matousek and P. Osmera (eds.), Proceedings of the 7th International Mendel Conference on Soft Computing (MENDEL 2001), Brno University of Technology, pp. 24–29, Brno, Czech Republic, June 2001. [63] Matthieu Basseur, Franck Seynhaeve, El-ghazali Talbi. Design of Multi-objective evolutionary algorithms: Application to the flow-shop scheduling problem, in Congress on Evolutionary Computation (CEC’2002), Vol. 2, pp. 1151–1156, IEEE Service Center, Piscataway, New Jersey, May 2002. [64] Matthieu Basseur, Franck Seynhaeve, El-ghazali Talbi. Adaptive mechanisms for multiobjective evolutionary algorithms, in IMACS multiconference, Computational Engineering in Systems Applications (CESA’03), paper S3-R-00-222, IEEE Service Center, Piscataway, New Jersey, July 2003 . [65] Michalewicz Z. Genetic Algorithms + Data Structures= Programs. Springer-Verlag, Berlin.1992. [66] Miqing Li and Jinhua Zheng. Spread Assessment for Evolutionary Multi-Objective Optimization, Evolutionary Multi-Criterion Optimization, 5th International Conference (EMO 2009), Nantes, France 216-230, 2009. [67] Miqing Li, Jinhua Zheng and Guixia Xiao. Uniformity Assessment for Evolutionary Multi-Objective Optimization, in Proceedings of IEEE Congress on Evolutionary Computation (CEC’2008), Hongkong, 625-632, 2008. [68] T.Bäck and H.P. Schwefel. Evolutionary computation: an overview. In Proc. of the 1996 IEEE Int’1 Conf. on Evolutionary Computation (ICEC1996) Nagoya Japan, IEEE Press, New York, NY, 1996:20~29. [69] Sang Hwan Lee, Hyo Byung Jun, Kwee Bo Sim. Performance improvement of evolution strategies using reinforcement learning. Fuzzy Systems Conference Proceedings, 1999.IEEE’ 99.1999 IEEE International, V olume:2 ,2 2~25. [70] S.D.Müller, N.N.Schraudlph, P.D.Koumoutsakos. Step size adaptation in evolutions trategies using reinforcement learning. Evolutionary Computation, 2002 .CEC’02. Proceedings of the 2002 Congress, Volume:l ,2002:151~156. [71] Q .Zhou and Yanda Li. Directed variation in evolution strategies. IEEE trans. On Evolutionary computation, 2003,7 (4):356~366. [72] Yu Yongquan; Huang Ying; Zeng Bi; Chen Xianchu; Learning fuzzy model for nonlinear system using evolution strategies with adaptive direction mutation. Fuzzy Systems, 2003. FUZZ '03. The 12th IEEE International Conference, Volume: 1, 2003:237~241. [73] X.Yao and Y.Liu. “Fast evolution strategies”, Proc.4th, IEEE conf in Evolutionary Programming VI, P.J Angeline, R.Reynolds,J.McDonnell, and R.Eberthart, eds. Berlin, Germany Springer~Verlag, 1997:151~161. [74] 林丹, 李敏强, 寇纪淞. 进化规划和进化策略中变异算子的若干研究[J]. 天 津大学学报, 2000,33(5):627~630. [75] 王云诚, 唐焕文. 单峰函数最优化问题的一个快速收敛进化策略[J]. 小型微 型计算机系统, 2002, 23 (11):1390~1392. [76] 刘若辰, 杜海峰, 焦李成. 基于柯西变异的免疫单克隆策略[J]. 西安电子科技大学学报, 2004, 31 (4):551~556. [77] 王战权 , 赵 朝 义 . 进 化 策 略 中 变 异 算 子 的 改 进 研 究 [J]. 计算机仿真,1999,16(3):8 ~11. [78] 王战权, 赵朝义, 夏云庆. 进化策略中基于柯西分布的变异算子改进探讨[J]. 系统工程, 1999,17 (4): 49~54. [79] Yong Liang, Kwong Sak Leung. Two-way mutation evolution strategies. CEC’02 .Proceedings of the 2002 Congress on Evolutionary Computation, Volume: 1,2002: 789~794. [80] R.Hinterding ， Z.Michalewicz and A.E.Eiben. Adaptation in evolutionary computation. In Proc. 2nd IEEE Conf. Evolutionary computation. Piscataway, N J: IEEE Press, 1997:65~69. [81] 潘正君. 基于演化计算的并行问题求解[D]. 武汉:武汉大学博士学位论文,1996. [82] Varun Aggarwal， Una-May O’Reilly. COSMO: A Correlation SensitiveMutation Operator for Multi-Objective Optimization, Proceedings of the 9th annual conference on Genetic and evolutionary computation, New York: ACM , 2007: 741~748. [83] 潘正君, 康立山, 陈毓屏. 演化计算[M]. 北京: 清华大学出版社, 1998.5. [84] P.J.Angeline. Adaptive and self-adaptive evolutionary computation. In Computation intelligence: a dynamic system perspective. M. Palaniswami, YAttikiouzel etc. eds. New York: IEEE Press, 1995:152~161. [85] Pan Z J, Kang L S, Nie S X. Evolving Both the Topology and weights of Neural Networks. Parallel Algorithms and Applications, Vol.9, 299~307, 1996. [86] Zbigniew Michalewicz, David B.Fogel. How to Solve It: Modern Heuristics. Springer-Verlag, Berlin.2000. [87] X. Yao and Y. Liu. “Fast evolution strategies”, Proc.4th, IEEE conf in Evolutionary Programming VI, P.J Angeline, R.Reynolds, J.McDonnell, and R.Eberthart, eds. Berlin, Germany Springer-Verlag, 1997:151-163.

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