用浮点数编码解决遗传算法问题

1、遗传算法作业一：用浮点数编码解决以下问题。55f(XrX2) =迟 icos( + 1)x1 + i icos(+ 1)x2 + ii=1i=1其中-10乞xx2乞10求mirf(N，Xz)二：构造过程。第一步：确定决策变量和约束条件。题目中已给出了该问题的决策变量及约束条件。第二步：建立优化模型。既是题目给出所要求的。第三步：确定编码方法。第四步：确定解码方法。第五步：确定个体评价方法。这里可将个体的适应度直接取为对应的目标函数值，并且不再对它做其他变化处理，即有:F(X)=f(x1,x2)第六步：设计遗传算子。选择运算使用比例运算算子；交叉运算是用单点交叉算子；变异运算使用基本位变异算子。

2、第七步：确定遗传算法的运行参数。对于本例，设计基本遗传算法的运行参数如下: int cur_best; /* 最佳个体 */MAXGENS=80POPSIZE=20NVARS=2PXOVER=0.2PMUTATION=0.1三：代码如下。#i nclude "stdafx.h"#in clude <stdio.h>#in clude <stdlib.h>#in clude <math.h>#defi ne MAXGENS 80#defi ne POPSIZE 20#defi ne NVARS 2#defi ne PXOVER 0.2#de

3、fi ne PMUTATION 0.1#defi ne FALSE 0#defi ne TRUE 1int gen erati on;/*最大世代数*/*种群大小*/*变量个数*/*交叉概率*/*变异概率*/*最大世代数*/*种群大小*/*变量个数*/*交叉概率*/*变异概率*/*当前世代*/struct genotypedouble geneNV ARS;double fitness;double upperNV ARS;double lowerNV ARS;double rfitness;double cfitness;struct genotype populationPOPSIZE+1

4、;struct genotype newpopulationPOPSIZE+1;void initialize(void);double randval(double, double);void evaluate(void);void keep_the_best(void);void elitist(void);void select(void);void crossover(void);void Xover(int,int);void swap(double *, double *);void mutate(void);void report(void);void initialize(vo

5、id)int i, j;double lbound, ubound;for (i = 0; i < NV ARS; i+) scanf("%lf",&lbound);scanf("%lf",&ubound);for (j = 0; j < POPSIZE; j+)populationj.fitness = 0;populationj.rfitness = 0;populationj.cfitness = 0;populationj.loweri = lbound;populationj.upperi= ubound;popul

6、ationj.genei = randval(populationj.loweri, populationj.upperi); double randval(double low, double high)double val;val = (double)(rand()%1000)/1000.0)*(high - low) + low;return(val);void evaluate(void)int mem;int i;int X=0;int Y=0;double xNV ARS+1;for (mem = 0; mem < POPSIZE; mem+)for (i = 0; i &l

7、t; NV ARS; i+)xi+1 = populationmem.genei;for(i=1;i<=5;i+)X=X+(i*cos(i+1)*x1+i);Y=Y+(i*cos(i+1)*x2+i); populationmem.fitness = (-1)*X*Y;void keep_the_best()int mem;int i;cur_best = 0;for (mem = 0; mem < POPSIZE; mem+)if (populationmem.fitness > populationPOPSIZE.fitness) cur_best = mem;popul

8、ationPOPSIZE.fitness = populationmem.fitness; for (i = 0; i < NV ARS; i+)populationPOPSIZE.genei = populationcur_best.genei;void elitist()int i;double best, worst;int best_mem, worst_mem;best = population0.fitness;worst = population0.fitness;for (i = 0; i < POPSIZE - 1; +i)if(populationi.fitne

9、ss > populationi+1.fitness)if (populationi.fitness >= best)best = populationi.fitness; best_mem = i;if (populationi+1.fitness <= worst) worst = populationi+1.fitness;worst_mem = i + 1;elseif (populationi.fitness <= worst)worst = populationi.fitness;worst_mem = i;if (populationi+1.fitness

10、 >= best)best = populationi+1.fitness;best_mem = i + 1;if (best >= populationPOPSIZE.fitness)for (i = 0; i < NV ARS; i+)populationPOPSIZE.genei = populationbest_mem.genei; populationPOPSIZE.fitness = populationbest_mem.fitness;elsefor (i = 0; i < NV ARS; i+)populationworst_mem.genei = po

11、pulationPOPSIZE.genei; populationworst_mem.fitness = populationPOPSIZE.fitness;void select(void)int mem, i, j, k;double sum = 0;double p;for (mem = 0; mem < POPSIZE; mem+)sum += populationmem.fitness;for (mem = 0; mem < POPSIZE; mem+)populationmem.rfitness = populationmem.fitness/sum; populati

12、on0.cfitness = population0.rfitness; for (mem = 1; mem < POPSIZE; mem+)populationmem.cfitness = populationmem-1.cfitness + populationmem.rfitness; for (i = 0; i < POPSIZE; i+)p = rand()%1000/1000.0;if (p < population0.cfitness) newpopulationi = population0;else for (j = 0; j < POPSIZE;j+

13、)if (p >= populationj.cfitness && p<populationj+1.cfitness) newpopulationi = populationj+1; for (i = 0; i < POPSIZE; i+)populationi = newpopulationi;void crossover(void)int i, mem, one;int first = 0; double x;for (mem = 0; mem < POPSIZE; +mem)x = rand()%1000/1000.0;if (x < PXO

14、VER) +first;if (first % 2 = 0)Xover(one, mem); elseone = mem;void Xover(int one, int two)int i;int point;if(NV ARS > 1)if(NV ARS = 2)point = 1;elsepoint = (rand() % (NV ARS - 1) + 1;for (i = 0; i < point; i+)swap(&populationone.genei, &populationtwo.genei);void swap(double *x, double *

15、y)double temp;temp = *x;*x = *y;*y = temp;void mutate(void)int i, j;double lbound, hbound;double x;for (i = 0; i < POPSIZE; i+)for (j = 0; j < NV ARS; j+)x = rand()%1000/1000.0;if (x < PMUTATION)lbound = populationi.lowerj;hbound = populationi.upperj; populationi.genej = randval(lbound, hbo

16、und); void report(void)int i;double best_val;double avg;double stddev;double sum_square;double square_sum;double sum;sum = 0.0;sum_square = 0.0;for (i = 0; i < POPSIZE; i+)sum += populationi.fitness;sum_square += populationi.fitness * populationi.fitness; avg = sum/(double)POPSIZE; square_sum = a

17、vg * avg * POPSIZE; stddev = sqrt(sum_square - square_sum)/(POPSIZE - 1); best_val = populationPOPSIZE.fitness;printf("n%5d,%6.3f, %6.3f, %6.3f nn", generation, best_val, avg, stddev); int main() int i; generation = 0; printf("n generation best average standard n"); printf("

18、 number value fitness deviation n"); initialize(); evaluate(); keep_the_best();while(generation<MAXGENS) generation+; select(); crossover(); mutate(); report(); evaluate(); elitist(); printf("nn Simulation completedn"); printf("n Best member: n"); for (i = 0; i < NV AR

19、S; i+)printf ("n var(%d) = %3.3f",i,populationPOPSIZE.genei); printf("nn Best fitness = %3.3f",populationPOPSIZE.fitness); 四：结果。 generation best average standard number value fitness deviation-1010 -10101,35.000, -159.600, 49.378 2,40.000, -162.500, 51.527 3,63.000, -227.800, 107

20、.370 4,338.000, 288.000, 0.000 5,338.000, -1127.000, 722.9456,338.000, -496.200, 188.442 7,338.000, -1949.400, 1010.274 8,338.000, -1228.750, 417.198 9,338.000, -737.400, 321.81410,338.000, -620.500, 201.032 11,338.000, -381.050, 149.048 12,338.000, -492.800, 201.228 13,338.000, -687.950, 264.773 14

21、,338.000, -534.750, 188.388 15,338.000, -683.700, 253.797 16,338.000, -1771.600, 457.733 17,338.000, -1523.000, 489.257 18,338.000, -1231.600, 422.400 19,338.000, -918.600, 412.579 20,338.000, -715.200, 432.551 21,338.000, -822.700, 516.523 22,338.000, -508.350, 253.088 23,338.000, -143.400, 103.914

22、 24,338.000, -336.750, 121.766 25,338.000, -314.800, 238.319 26,338.000, -423.600, 229.694 27,338.000, -381.650, 226.027 28,338.000, -308.400, 167.353 29,338.000, -380.600, 103.331 30,338.000, -1646.000, 1005.859 31,338.000, -4075.900, 1982.759 32,338.000, -1589.300, 956.300 33,338.000, -1566.700, 5

23、89.679 34,338.000, -493.050, 162.640 35,338.000, -251.550, 177.270 36,338.000, -201.550, 40.163 37,338.000, -412.650, 159.800 38,338.000, -144.850, 63.644 39,338.000, -244.450, 45.629 40,338.000, -172.850, 69.363 41,338.000, -37.000, 18.070 42,338.000, -79.000, 31.573 43,338.000, -68.400, 20.556 44,

24、338.000, -79.000, 30.042 45,338.000, 338.000, 0.000 46,338.000, -467.100, 154.784 47,338.000, -365.600, 108.007 48,338.000, -160.150, 70.261 49,338.000, -357.000, 129.672 50,338.000, -364.000, 138.034 51,338.000, -231.200, 62.732 52,338.000, -394.000, 81.458 53,338.000, -373.550, 168.63554,338.000, -206.000, 67.17455,338.000, -101.800, 33.82956,338.000, -186.800, 51.19457,338.000, 99.500, 141.27558,338.000, 142.800, 147.30459,3