编码和种群生成 ：
function [pop] = initializega(num,bounds,evalFN,evalOps,options) % pop - the initial, evaluated, random population
% num - the size of the population, i.e. the number to create % bounds - the number of permutations in an individual (e.g., number % of cities in a tsp
% evalFN - the evaluation fn, usually the name of the .m file for evaluation % evalOps- any options to be passed to the eval function defaults [ ] % options- options to the initialize function, ie. [eps, float/binary, prec] % where eps is the epsilon value and the second option is 1 for % orderOps, prec is the precision of the variables defaults [1e-6 1] 交叉
function [c1,c2] = arithXover(p1,p2,bounds,Ops)
% Arith crossover takes two parents P1,P2 and performs an interpolation % along the line formed by the two parents. %
% function [c1,c2] = arithXover(p1,p2,bounds,Ops)
% p1 - the first parent ( [solution string function value] ) % p2 - the second parent ( [solution string function value] ) % bounds - the bounds matrix for the solution space
% Ops - Options matrix for arith crossover [gen #ArithXovers] 选择
normGeomSelect：NormGeomSelect is a ranking selection function based on the normalized geometric distribution. （基于正态分布的序列选择函数） 变异
function[newPop] = normGeomSelect(oldPop,options)
% NormGeomSelect is a ranking selection function based on the normalized % geometric distribution. %
% function[newPop] = normGeomSelect(oldPop,options) % newPop - the new population selected from the oldPop % oldPop - the current population % options - options to normGeomSelect [gen probability_of_selecting_best]
一些辅助函数：
f2b ：Return the binary representation of the float number fval（将浮点数转化为二进制数）
b2f：Return the float number corresponing to the binary representation of bval. （将二进制
数转化为 浮点数）
nonUnifMutation： Non uniform mutation changes one of the parameters of the parent based on a non-uniform probability distribution. This Gaussian distribution starts wide, and narrows to a point distribution as the current generation approaches the maximum generation. （基于非均一概率分布进行非均一变异）
maxGenTerm：Returns 1, i.e. terminates the GA when the maximal_generation is reached. （当迭代次数大于最大迭代次数时，终止遗传算法，返回 为1，否则返回为0。）
roulette：roulette is the traditional selection function with the probability of surviving equal to the fittness of i / sum of the fittness of all individuals
应用举例
1. 计算下列函数的最大值。
f(x)=x+10*sin(5x)+7cos(4x) , x∈[0,9] 方式1 >>gademo 方式2
step 1 编写目标函数gademo1eval1.m
function [sol, val] = gaDemo1Eval(sol,options) x=sol(1);
val = x + 10*sin(5*x)+7*cos(4*x); step 2 生成初始种群，大小为10
initPop=initializega(10,[0, 9],'gademo1eval1',[],[1e-6,1]); step 3 25次遗传迭代
[x,endPop,bpop,trace] = ga([0 9],'gademo1eval1',[],initPop,... [1e-6 1 1],'maxGenTerm',25,... 'normGeomSelect',[0.08],... ['arithXover'],[2],... 'nonUnifMutation',[2, 25 ,3]) % Output Arguments:
% x - the best solution found during the course of the run % endPop - the final population
% bPop - a trace of the best population (解的变化)
% traceInfo - a matrix of best and means of the ga for each generation (种群平均值的变化) %
% Input Arguments:
% bounds - a matrix of upper and lower bounds on the variables % evalFN - the name of the evaluation .m function
% evalOps - options to pass to the evaluation function ([NULL]) % startPop - a matrix of solutions that can be initialized % from initialize.m
% opts - [epsilon, prob_ops ,display] change required to consider two solutions different, prob_ops 0 if you want to apply the
% genetic operators probabilisticly to each solution, 1 if you are supplying a deterministic number of operator applications and display is 1 to output progress 0 for quiet. ([1e-6 1 0])
% termFN - name of the .m termination function
% termOps - options string to be passed to the termination function ([100]). % selectFN - name of the .m selection function (['normGeomSelect']) % selectOpts - options string to be passed to select after % select(pop,#,opts) ([0.08])
% xOverFNS - a string containing blank seperated names of Xover.m files (['arithXover heuristicXover simpleXover'])
% xOverOps - A matrix of options to pass to Xover.m files with the first column being the number of that xOver to perform similiarly for mutation ([2 0;2 3;2 0])
% mutFNs - a string containing blank seperated names of mutation.m files (['boundaryMutation multiNonUnifMutation ...
% nonUnifMutation unifMutation'])
% mutOps - A matrix of options to pass to Xover.m files with the first column being the number of that xOver to perform similiarly for mutation ([4 0 0;6 100 3;4 100 3;4 0 0])
2. 求sin(x) 在0到3.14之间的最大值.
function [sol, val] = sin1(sol,options) x=sol(1); val =sin(x);
initPop=initializega(10,[0, 3.14],'sin1',[],[1e-6,1]);
[x, endPop,bpop,trace] = ga([0 3.14],'sin1',[],initPop,... [1e-6 1 1],'maxGenTerm',25,... 'normGeomSelect',[0.08],... ['arithXover'],[2],... 'nonUnifMutation',[2, 25 ,3])
3 求解非线性规划问题
max f(x) s.t. gi(x)<=0,i=1,...,m hi(x)=0,i=m+1,...,n x∈Ω ？不可行的后代？ 拒绝策略 修复策略 惩罚策略
e.g. min f(x)=(x1-2)2+(x2-1)2
s.t. g1(x)=x1-2x2+1>=0 g2(x)=x12/4-x22+1>=0 分析：取加法形式的适值函数： val(x)=f(x)+p(x)
惩罚函数 p(x)由两部分组成，可变乘法因子和 违反约束乘法，其表达式如下：
改进遗传算子策略
其中ri是约束i的可变惩罚系数。 步骤如下：
function [sol,eval]=f552(sol,options) x1=sol(1); x2=sol(2);
r1=0.1; r2=0.8; %约束条件 g1=x1-2*x2+1; g2=x1.^2/4-x2.^2+1; %加惩罚项的适值
if (g1>=0)&(g2>=0) eval=(x1-2).^2+(x2-1).^2; else eval=(x1-2).^2+(x2-1).^2+r1*g1+r2*g2; end eval=-eval;
%%%%%%%%%%%%%%%%%%%%%%%%%%% %维数n=2 %设置参数边界
bounds = ones(2,1)*[-1 1];%??????
%遗传算法优化 [p,endPop,bestSols,trace]=ga(bounds,'f552'); p %性能跟踪
plot(trace(:,1),trace(:,3),'b-') hold on
plot(trace(:,1),trace(:,2),'r-') xlabel('Generation'); ylabel('Fittness');
legend('解的变化','种群平均值的变化');