经典遗传算法原理与应用

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,遗传算法原理与应用,SN:,SNO:,主要内容,遗传算法基本原理,2,遗传算法概述,1,遗传算法的应用及一些问题,3,1、优化方法,遗传算法概述,传统的优化方法局部优化,共轭梯度法、拟牛顿法、单纯形方法,全局优化方法,GA、漫步法Random Walk、模拟退火法,2、遗传算法优点,遗传算法GA模拟自然选择和自然遗传过程中发生的繁殖、交叉和基因突变现象，在每次迭代中都保存一组候选解，并按某种指标从解群中选取较优的个体，利用遗传算子(选择、交叉和变异)对这些个体进行组合，产生新一代的候选解群，重复此过程，直到满足某种收敛指标为止。其遗传进化操作过程简单，容易理解。,遗传算法根本原理,1、根本思想,模拟自然界优胜劣汰的进化现象，把搜索空间映射为遗传空间，把可能的解编码成一个向量染色体，向量的每个元素称为基因。通过不断计算各染色体的适应值，选择最好的染色体，获得最优解。,2、遗传算法的根本运算,选择运算,交换操作,变异,选择运算,从旧的种群中选择适应度高的染色体，放入匹配集缓冲区，为以后染色体交换、变异，产生新的染色体作准备。,选择方法适应度比例法转轮法,某染色体被选的概率：Pc,x,i,为种群中第,i个染色体，,f(,xi,)为第i个染色体的适应度值。,具体步骤,1计算各染色体适应度值,2累计所有染色体适应度值，记录中间累加值S-mid 和最后累加值 sum=f(xi),3产生一个随机数 N，0 N sum,4选择对应中间累加值S-mid 的第一个染色体进入交换集,5 重复3和4，直到获得足够的染色体。,举例：,具有,6个染色体的二进制编码、适应度值、,P,c,累计值。,染色体的适应度和所占的比例,用转轮方法进行选择,染色体被选的概率,染色体编号,1,2,3,4,5,6,7,8,9,10,适应度,8,2,17,7,2,12,11,7,3,7,被选概率,0.1,0.02,0.22,0.09,0.02,0.16,0.14,0.09,0.03,0.09,适应度累计,8,10,27,34,36,48,59,66,69,76,被选的染色体个数,随机数,23,49,76,13,1,27,57,所选染色体号码,3,7,10,3,1,3,7,交换操作,方法,:随机选择二个染色体(双亲染色体),随机指定一点或多点,进行交换,可得二个新的染色体(子辈染色体).,新的子辈染色体,:A,11010001,B,01011110,变异,模拟生物在自然界环境变化,引起基因的突变.在染色体二进制编码中,1变成0;或0变成1.突变产生染色体的多样性,防止进化中早期成熟,陷入局部极值点,突变的概率很低.,GA,流程,简单遗传算法GA的根本参数,种群规模 P:参与进化的染色体总数.,代沟,G:二代之间不相同的染色体数目,无重叠G=1;有重叠 0 G 1,选择方法,:转轮法,精英选择法,竞争法.,交换率,:,P,c,一般为,60100%.,变异率,:,P,m,一般为,0.110%,实例,1、产生初始种群,0001100000 0101111001 0000000101 1001110100 1010101010,8 5 2 10 7 1110010110 1001011011 1100000001 1001110100 000101001 12 5 19 10 14,2、计算适应度,3、选择,个体,染色体,适应度,选择概率,累积概率,1,0001100000,8,2,0101111001,5,3,0000000101,2,4,1001110100,10,5,1010101010,7,6,1110010110,12,7,1001011011,5,8,1100000001,19,9,1001110100,10,10,0001010011,14,8,852107125191014,0.086957,0.054348,5,852107125191014,0.021739,0.108696,0.076087,0.130435,0.054348,0.206522,0.108696,0.152174,3、选择,个体,染色体,适应度,选择概率,累积概率,1,0001100000,8,2,0101111001,5,3,0000000101,2,4,1001110100,10,5,1010101010,7,6,1110010110,12,7,1001011011,5,8,1100000001,19,9,1001110100,10,10,0001010011,14,0.086957,0.054348,0.021739,0.108696,0.076087,0.130435,0.054348,0.206522,0.108696,0.152174,0.086957,0.141304,0.163043,0.271739,0.347826,0.478261,0.532609,0.739130,0.847826,1.000000,3、选择,在,01之间产生一个,随机数：,0.545929,0.784567,0.446930,0.507893,0.291198,0.716340,0.270901,0.371435,0.854641,个体,染色体,适应度,选择概率,累积概率,1,0001100000,8,2,0101111001,5,3,0000000101,2,4,1001110100,10,5,1010101010,7,6,1110010110,12,7,1001011011,5,8,1100000001,19,9,1001110100,10,10,0001010011,14,0.086957,0.086957,0.054348,0.141304,0.021739,0.108696,0.076087,0.130435,0.054348,0.206522,0.108696,0.152174,0.271739,0.347826,0.478261,0.532609,0.739130,0.847826,1.000000,0.163043,淘,淘汰,4、交叉,0001100000 1110010110 1100000001 1001110100 1010101010,1110010110 1001011011 1001110100 1100000001 0001010011,0001100000 1110010110 1100000001 1001110100,0001,1110,100000,010110,111,100,0010110,1011011,110000,100111,0100,0001,1001110100,1100000001,1010101,0001010,010,011,5、变异,0001100000 1110010110 1100000001 1001110100 1010101010,1110010110 1001011011 1100000001 1001110100 0001010011,0001,1110,100000,010110,111,100,0010110,1011011,110000,1001,1,1,0100,0001,1001110100,1100000001,1010101,0001010,010,011,0001100000 1110010110 1100000001 1001110100 1010101010,1110010110 1001011011 1100000001 1001110100 0001010011,0001,1110,100000,010110,111,100,0010110,1011011,110000,1001,0,1,0100,0001,1001110100,1100000001,1010101,0001010,010,011,6、至下一代，适应度计算选择交叉变异，直至满足终止条件,。,遗传算法的应用及一些问题,1、,遗传算法的应用领域,1组合优化 2函数优化,3自动控制 4生产调度,5图像处理 6机器学习,7人工生命 8数据挖掘,2、遗传算法在应用中的一些问题,1知识的编码,二进制和十进制的比较：二进制有更多图式和更大的搜索范围；十进制更接近于实际操作。,2适应度函数,适应度函数值必须非负，根据情况做适当的处理。,如图,3全局最优和收敛性。,根据图式定理，对于具有“欺骗性函数，GA有可能落入局部最优点。,举例：,3位欺骗函数,Thank you!,