遗传算法教程
遗传算法作为一种全局随机寻优的方法，是很有其特点的。有兴趣的朋友请在这儿讨论。 有交流才有进步！
遗传算法(Genetic Algorithm, GA)是近几年发展起来的一种崭新的全局优化算法，
它借用了生物遗传学的观点，通过自然选择、遗传、变异等作用机制，实现各个
个体的适应性的提高。这一点体现了自然界中"物竞天择、适者生存"进化过程。
1962年Holland教授首次提出了GA算法的思想，从而吸引了大批的研究者，迅速
推广到优化、搜索、机器学习等方面，并奠定了坚实的理论基础。
用遗传算法解决问题时，首先要对待解决问题的模型结构和参数进行编码，一般
用字符串表示，这个过程就将问题符号化、离散化了。也有在连续空
间定义的GA(Genetic Algorithm in Continuous Space, GACS)，暂不讨论。
一个串行运算的遗传算法(Seguential Genetic Algoritm, SGA)按如下过程进行：
(1) 对待解决问题进行编码；
(2) 随机初始化群体X(0):=(x1, x2, … xn)；
(3) 对当前群体X(t)中每个个体xi计算其适应度F(xi)，适应度表示了该个体的性
能好坏；
(4) 应用选择算子产生中间代Xr(t)；
(5) 对Xr(t)应用其它的算子，产生新一代群体X(t+1)，这些算子的目的在于扩展
有限个体的覆盖面，体现全局搜索的思想；
(6) t:=t+1；如果不满足终止条件继续(3)。
GA中最常用的算子有如下几种：
(1) 选择算子(selection/reproduction): 选择算子从群体中按某一概率成对
选择个体，某个体xi被选择的概率Pi与其适应度值成正比。最通常的实现
方法是轮盘赌(roulette wheel)模型。
(2) 交叉算子(Crossover): 交叉算子将被选中的两个个体的基因链按概率pc进
行交叉，生成两个新的个体，交叉位置是随机的。其中Pc是一个系统参数。
(3) 变异算子(Mutation): 变异算子将新个体的基因链的各位按概率pm进行变异，
对二值基因链(0,1编码)来说即是取反。
上述各种算子的实现是多种多样的，而且许多新的算子正在不断地提出，以改
进GA的某些性能。系统参数(个体数n,基因链长度l,交叉概率Pc,变异概率Pm等)对
算法的收敛速度及结果有很大的影响，应视具体问题选取不同的值。
GA的程序设计应考虑到通用性，而且要有较强的适应新的算子的能力。OOP中的
类的继承为我们提供了这一可能。
定义两个基本结构：基因(ALLELE)和个体(INDIVIDUAL)，以个体的集合作为群体
类TPopulation的数据成员，而TSGA类则由群体派生出来，定义GA的基本操作。
对任一个应用实例，可以在TSGA类上派生，并定义新的操作。
TPopulation类包含两个重要过程：
FillFitness: 评价函数，对每个个体进行解码(decode)并计算出其适应度值，
具体操作在用户类中实现。
Statistic: 对当前群体进行统计，如求总适应度sumfitness、平均适应度
average、最好个体fmax、最坏个体fmin等。
TSGA类在TPopulation类的基础上派生，以GA的系统参数为构造函数的参数，
它有4个重要的成员函数：
Select: 选择算子，基本的选择策略采用轮盘赌模型（如图2）。轮盘经任意
旋转停止后指针所指向区域被选中，所以fi值大的被选中的概率就大。
Crossover: 交叉算子，以概率Pc在两基因链上的随机位置交换子串。
Mutation: 变异算子，以概率Pm对基因链上每一个基因进行随机干扰(取反)。
Generate: 产生下代，包括了评价、统计、选择、交叉、变异等全部过程，每
运行一次，产生新的一代。
SGA的结构及类定义如下(用C++编写)：
typedef char ALLELE; // 基因类型
typedef struct{
ALLELE *chrom;
float fitness; // fitness of Chromosome
}INDIVIDUAL; // 个体定义
class TPopulation{ // 群体类定义
public:
int size; // Size of population: n
int lchrom; // Length of chromosome: l
float sumfitness, average;
INDIVIDUAL *fmin, *fmax;
INDIVIDUAL *pop;
TPopulation(int popsize, int strlength);
~TPopulation();
inline INDIVIDUAL &Individual(int i){ return pop;};
void FillFitness(); // 评价函数
virtual void Statistics(); // 统计函数
};
class TSGA : public TPopulation{ // TSGA类派生于群体类
public:
float pcross; // Probability of Crossover
float pmutation; // Probability of Mutation
int gen; // Counter of generation
TSGA(int size, int strlength, float pm=0.03, float pc=0.6):
TPopulation(size, strlength)
{gen=0; pcross=pc; pmutation=pm; } ;
virtual INDIVIDUAL& Select();
virtual void Crossover(INDIVIDUAL &parent1, INDIVIDUAL &parent2,
INDIVIDUAL &child1, INDIVIDUAL &child2);
virtual ALLELE Mutation(ALLELE alleleval);
virtual void Generate(); // 产生新的一代
};
};
用户GA类定义如下：
class TSGAfit : public TSGA{
public:
TSGAfit(int size,float pm=0.0333,float pc=0.6):TSGA(size,24,pm,pc){};
void print();
};
由于GA是一个概率过程，所以每次迭代的情况是不一样的；系统参数不同，迭代
情况也不同。在实验中参数一般选取如下：个体数n=50-200，变异概率Pm=0.03, 交叉
概率Pc=0.6。变异概率太大，会导致不稳定。
程序实例：（基于标准C）
//主程序
#include "sga.h"
main(argc,argv)
int argc;
char *argv[];
{
struct individual *temp;
FILE *fopen();
void copyright();
char *malloc();
/* determine input and output from program args */
numfiles = argc - 1;
switch(numfiles)
{
case 0:
infp = stdin;
outfp = stdout;
break;
case 1:
if((infp = fopen(argv,"r")) == NULL)
{
fprintf(stderr,"Input file %s not found\n",argv);
exit(-1);
}
outfp = stdout;
break;
case 2:
if((infp = fopen(argv,"r")) == NULL)
{
fprintf(stderr,"Cannot open input file %s\n",argv);
exit(-1);
}
if((outfp = fopen(argv,"w")) == NULL)
{
fprintf(stderr,"Cannot open output file %s\n",argv);
exit(-1);
}
break;
default:
fprintf(stderr,"Usage is: sga \n");
exit(-1);
}
/* print the author/copyright notice */
copyright();
if(numfiles == 0)
fprintf(outfp," Number of GA runs to be performed-> ");
fscanf(infp,"%d",&maxruns);
for(run=1; run<=maxruns; run++)
{
/* Set things up */
initialize();
for(gen=0; gen<maxgen; gen++)
{
fprintf(outfp,"\nRUN %d of %d: GENERATION %d->%d\n",
run,maxruns,gen,maxgen);
/*application dependent routines*/
application();
/* create a new generation */
generation();
/* compute fitness statistics on new populations */
statistics(newpop);
/* report results for new generation */
report();
/* advance the generation */
temp = oldpop;
oldpop = newpop;
newpop = temp;
}
freeall();
}
}
//头文件sga.h
/*--------------------------------------------------------------------------
--*/
/* sga.h - global declarations for main(), all variable declared herein must
*/
/* also be defined as extern variables in external.h !!!
*/
/*--------------------------------------------------------------------------
--*/
#define LINELENGTH 80 /* width of printou
t */
#define BITS_PER_BYTE 8 /* number of bits per byte on this machin
e */
#define UINTSIZE (BITS_PER_BYTE*sizeof(unsigned)) /* # of bits in unsigne
d */
#include <stdio.h>
/* file pointers */
FILE *outfp, *infp;
/* Global structures and variables */
struct individual
{
unsigned *chrom; /* chromosome string for the individua
l */
double fitness; /* fitness of the individua
l */
int xsite; /* crossover site at matin
g */
int parent; /* who the parents of offspring wer
e */
int *utility; /* utility field can be used as pointer to
a */
/* dynamically allocated, application-specific data structur
e */
};
struct bestever
{
unsigned *chrom; /* chromosome string for the best-ever individua
l */
double fitness; /* fitness of the best-ever individua
l */
int generation; /* generation which produced i
t */
};
struct individual *oldpop; /* last generation of individual
s */
struct individual *newpop; /* next generation of individual
s */
struct bestever bestfit; /* fittest individual so fa
r */
double sumfitness; /* summed fitness for entire populatio
n */
double max; /* maximum fitness of populatio
n */
double avg; /* average fitness of populatio
n */
double min; /* minumum fitness of populatio
n */
floatpcross; /* probability of crossove
r */
floatpmutation; /* probability of mutatio
n */
int numfiles; /* number of open file
s */
int popsize; /* population siz
e */
int lchrom; /* length of the chromosome per individua
l */
int chromsize; /* number of bytes needed to store lchrom strin
g */
int gen; /* current generation numbe
r */
int maxgen; /* maximum generation numbe
r */
int run; /* current run numbe
r */
int maxruns; /* maximum number of runs to mak
e */
int printstrings = 1; /* flag to print chromosome strings (default on
) */
int nmutation; /* number of mutations */
int ncross; /* number of crossovers */
/* Application-dependent declarations go after here... */
//头文件external.h
/*--------------------------------------------------------------------------
--*/
/* external.h - external global declarations from sga.h.
*/
/*--------------------------------------------------------------------------
--*/
#define LINELENGTH 80 /* width of printou
t */
#define BITS_PER_BYTE 8 /* number of bits per byte on this machin
e */
#define UINTSIZE (BITS_PER_BYTE*sizeof(unsigned)) /* # of bits in unsigne
d */
#include <stdio.h>
/* file pointers */
FILE *outfp, *infp;
/* Global structures and variables */
struct individual
{
unsigned *chrom; /* chromosome string for the individua
l */
double fitness; /* fitness of the individua
l */
int xsite; /* crossover site at matin
g */
int parent; /* who the parents of offspring wer
e */
int *utility; /* utility field can be used as pointer to
a */
/* dynamically allocated, application-specific data structur
e */
};
struct bestever
{
unsigned *chrom; /* chromosome string for the best-ever individua
l */
double fitness; /* fitness of the best-ever individua
l */
int generation; /* generation which produced i
t */
};
extern struct individual *oldpop; /* last generation of individual
s */
extern struct individual *newpop; /* next generation of individual
s */
extern struct bestever bestfit; /* fittest individual so fa
r */
extern double sumfitness; /* summed fitness for entire populatio
n */
extern double max; /* maximum fitness of populatio
n */
extern double avg; /* average fitness of populatio
n */
extern double min; /* minumum fitness of populatio
n */
extern floatpcross; /* probability of crossove
r */
extern floatpmutation; /* probability of mutatio
n */
extern int numfiles; /* number of open file
s */
extern int popsize; /* population siz
e */
extern int lchrom; /* length of the chromosome per individua
l */
extern int chromsize; /* number of bytes needed to store lchrom strin
g */
extern int gen; /* current generation numbe
r */
extern int maxgen; /* maximum generation numbe
r */
extern int run; /* current run numbe
r */
extern int maxruns; /* maximum number of runs to mak
e */
extern int printstrings;/* flag to print chromosome strings (default on
) */
extern int nmutation; /* number of mutations*/
extern int ncross; /* number of crossovers*/
/* Application-dependent external declarations go after here...*/
//初始化
/*--------------------------------------------------------------------------
--*/
/* initial.c - functions to get things set up and initialized
*/
/*--------------------------------------------------------------------------
--*/
#include "external.h"
initialize()
/* Initialization Coordinator */
{
/* get basic problem values from input file */
initdata();
/* define chromosome size in terms of machine bytes, ie*/
/* length of chromosome in bits (lchrom)/(bits-per-byte) */
/* chromsize must be known for malloc() of chrom pointer */
chromsize = (lchrom/UINTSIZE);
if(lchrom%UINTSIZE) chromsize++;
/* malloc space for global data structures */
initmalloc();
/* initialize application dependent variables*/
app_init();
/* initialize random number generator */
randomize();
/* initialize global counters/values */
nmutation = 0;
ncross = 0;
bestfit.fitness = 0.0;
bestfit.generation = 0;
/* initialize the populations and report statistics */
initpop();
statistics(oldpop);
initreport();
}
initdata()
/* data inquiry and setup */
{
charanswer;
if(numfiles == 0)
{
fprintf(outfp,"\n ------- SGA Data Entry and Initialization -------\
n");
fprintf(outfp," Enter the population size ------------> ");
}
fscanf(infp,"%d", &popsize);
if((popsize%2) != 0)
{
fprintf(outfp, "Sorry! only even population sizes are allowed. \n In
crem
nt
ing popsize by one.\n");
popsize++;
};
if(numfiles == 0)
fprintf(outfp," Enter chromosome length --------------> ");
fscanf(infp,"%d", &lchrom);
if(numfiles == 0)
fprintf(outfp," Print chromosome strings? (y/n) ------> ");
fscanf(infp,"%s",answer);
if(strncmp(answer,"n",1) == 0) printstrings = 0;
if(numfiles == 0)
fprintf(outfp," Enter maximum number of generations --> ");
fscanf(infp,"%d", &maxgen);
if(numfiles == 0)
fprintf(outfp," Enter crossover probability ----------> ");
fscanf(infp,"%f", &pcross);
if(numfiles == 0)
fprintf(outfp," Enter mutation probability -----------> ");
fscanf(infp,"%f", &pmutation);
/* any application-dependent global input */
app_data();
}
initpop()
/* Initialize a population at random */
{
int j, j1, k, stop;
unsigned mask = 1;
for(j = 0; j < popsize; j++)
{
for(k = 0; k < chromsize; k++)
{
oldpop.chrom = 0;
if(k == (chromsize-1))
stop = lchrom - (k*UINTSIZE);
else
stop = UINTSIZE;
/* A fair coin toss */
for(j1 = 1; j1 <= stop; j1++)
{
oldpop.chrom = oldpop.chrom<<1;
if(flip(0.5))
oldpop.chrom = oldpop.chrom|mask;
}
}
oldpop.parent = 0; /* Initialize parent info. */
oldpop.parent = 0;
oldpop.xsite = 0;
objfunc(&(oldpop));/* Evaluate initial fitness */
}
}
initreport()
/* Initial report */
{
void skip();
skip(outfp,1);
fprintf(outfp," SGA Parameters\n");
fprintf(outfp," -------------------------------------------------\n");
fprintf(outfp," Total Population size = %d\n",popsize);
fprintf(outfp," Chromosome length (lchrom) = %d\n",lchrom);
fprintf(outfp," Maximum # of generations (maxgen)= %d\n",maxgen);
fprintf(outfp," Crossover probability (pcross) = %f\n", pcross);
fprintf(outfp," Mutationprobability (pmutation)= %f\n", pmutation);
skip(outfp,1);
/* application dependant report */
app_initreport();
fflush(outfp);
}
//繁衍
/*--------------------------------------------------------------------------
--*/
/* generate.c - create a new generation of individuals
*/
/*--------------------------------------------------------------------------
--*/
#include "external.h"
generation()
{
int mate1, mate2, jcross, j = 0;
/* perform any preselection actions necessary before generation */
preselect();
/* select, crossover, and mutation */
do
{
/* pick a pair of mates */
mate1 = select();
mate2 = select();
/* Crossover and mutation */
jcross = crossover(oldpop.chrom, oldpop.chrom,
newpop.chrom, newpop.chrom);
mutation(newpop.chrom);
mutation(newpop.chrom);
/* Decode string, evaluate fitness, & record */
/* parentage date on both children */
objfunc(&(newpop));
newpop.parent = mate1+1;
newpop.xsite = jcross;
newpop.parent = mate2+1;
objfunc(&(newpop));
newpop.parent = mate1+1;
newpop.xsite = jcross;
newpop.parent = mate2+1;
/* Increment population index */
j = j + 2;
}
while(j < (popsize-1));
}
//一些不重要的函数
/*--------------------------------------------------------------------------
--*/
/* utility.c - utility routines, contains copyright,repchar, skip
*/
/*--------------------------------------------------------------------------
--*/
#include "external.h"
void copyright()
{
void repchar(), skip();
int iskip;
int ll = 59;
iskip = (LINELENGTH - ll)/2;
skip(outfp,1);
repchar(outfp," ",iskip); repchar(outfp,"-",ll); skip(outfp,1);
repchar(outfp," ",iskip);
fprintf(outfp,"| SGA-C (v1.1) - A Simple Genetic Algorithm
|\n");
repchar(outfp," ",iskip);
fprintf(outfp,"| (c) David E. Goldberg 1986, All Rights Reserved
|\n");
repchar(outfp," ",iskip);
fprintf(outfp,"| C version by Robert E. Smith, U. of Alabama
|\n");
repchar(outfp," ",iskip);
fprintf(outfp,"| v1.1 modifications by Jeff Earickson, Boeing Company
|\n");
repchar(outfp," ",iskip); repchar(outfp,"-",ll); skip(outfp,2);
}
void repchar (outfp,ch,repcount)
/* Repeatedly write a character to stdout */
FILE *outfp;
char *ch;
int repcount;
{
int j;
for (j = 1; j <= repcount; j++) fprintf(outfp,"%s", ch);
}
void skip(outfp,skipcount)
/* Skip skipcount lines */
FILE *outfp;
int skipcount;
{
int j;
for (j = 1; j <= skipcount; j++) fprintf(outfp,"\n");
}
int ithruj2int(i,j,from)
/* interpret bits i thru j of a individual as an integer */
/* j MUST BE greater than or equal to i AND j-i < UINTSIZE-1*/
/* from is a chromosome, represented as an array of unsigneds */
int i,j;
unsigned *from;
{
unsigned mask, temp;
int bound_flag;
int iisin, jisin;
int i1, j1, out;
if(j < i)
{
fprintf(stderr,"Error in ithruj2int: j < i\n");
exit(-1);
}
if(j-i+1 > UINTSIZE)
{
fprintf(stderr,"Error in ithruj2int: j-i+1 > UINTSIZE\n");
exit(-1);
}
iisin = i/UINTSIZE;
jisin = j/UINTSIZE;
i1 = i - (iisin*UINTSIZE);
j1 = j - (jisin*UINTSIZE);
if(i1 == 0)
{
iisin = iisin-1;
i1 = i - (iisin*UINTSIZE);
};
if(j1 == 0)
{
jisin = jisin-1;
j1 = j - (jisin*UINTSIZE);
};
/* check if bits fall across a word boundary */
if(iisin == jisin)
bound_flag = 0;
else
bound_flag = 1;
if(bound_flag == 0)
{
mask = 1;
mask = (mask<<(j1-i1+1))-1;
mask = mask<<(i1-1);
out = (from&mask)>>(i1-1);
return(out);
}
else
{
mask = 1;
mask = (mask<<j1)-1;
temp = from&mask;
mask = 1;
mask = (mask<<(UINTSIZE-i1+1))-1;
mask = mask<<(i1-1);
out = ((from&mask)>>(i1-1)) | (temp<<(UINTSIZE-i1+1));
return(out);
}
}
//适应度统计
/*--------------------------------------------------------------------------
--*/
/* statistic.c - compute the fitness statistics
*/
/*--------------------------------------------------------------------------
--*/
#include "external.h"
statistics(pop)
/* Calculate population statistics */
struct individual *pop;
{
int i, j;
sumfitness = 0.0;
min = pop.fitness;
max = pop.fitness;
/* Loop for max, min, sumfitness */
for(j = 0; j < popsize; j++)
{
sumfitness = sumfitness + pop.fitness; /* Accumulat
e */
if(pop.fitness > max) max = pop.fitness; /* New maximu
m */
if(pop.fitness < min) min = pop.fitness; /* New minimu
m */
/* new global best-fit individual */
if(pop.fitness > bestfit.fitness)
{
for(i = 0; i < chromsize; i++)
bestfit.chrom = pop.chrom;
bestfit.fitness = pop.fitness;
bestfit.generation = gen;
}
}
/* Calculate average */
avg = sumfitness/popsize;
/* get application dependent stats */
app_stats(pop);
}
//选择
/*--------------------------------------------------------------------------
--*/
/* rselect.c:roulette wheel selection.
*/
/*--------------------------------------------------------------------------
--*/
#include "external.h"
select_memory()
{
}
select_free()
{
}
preselect()
{
int j;
sumfitness = 0;
for(j = 0; j < popsize; j++) sumfitness += oldpop.fitness;
}
int select()
/* roulette-wheel selection 轮盘赌选择*/
{
extern float randomperc();
float sum, pick;
int i;
pick = randomperc();
sum = 0;
if(sumfitness != 0)
{
for(i = 0; (sum < pick) && (i < popsize); i++)
sum += oldpop.fitness/sumfitness;
}
else
i = rnd(1,popsize);
return(i-1);
}