一、布谷鸟算法简介
布谷鸟算法，英文叫做Cuckoo search (CS algorithm)。首先还是同样，介绍一下这个算法的英文含义， Cuckoo是布谷鸟的意思，啥是布谷鸟呢，是一种叫做布谷的鸟，o(∩_∩)o ，这种鸟她妈很懒，自己生蛋自己不养，一般把它的宝宝扔到别的种类鸟的鸟巢去。但是呢，当孵化后，遇到聪明的鸟妈妈，一看就知道不是亲生的，直接就被鸟妈妈给杀了。于是这群布谷鸟宝宝为了保命，它们就模仿别的种类的鸟叫，让智商或者情商极低的鸟妈妈误认为是自己的亲宝宝，这样它就活下来了。 布谷鸟搜索算法（Cuckoo Search, CS）是2009年Xin-She Yang 与Suash Deb在《Cuckoo Search via Levy Flights》一文中提出的一种优化算法。布谷鸟算法是一种集合了布谷鸟巢寄生性和莱维飞行（Levy Flights）模式的群体智能搜索技术，通过随机游走的方式搜索得到一个最优的鸟巢来孵化自己的鸟蛋。这种方式可以达到一种高效的寻优模式。
1 布谷鸟的巢寄生性
2 莱维飞行
图1.模拟莱维飞行轨迹示意图
3 布谷鸟搜索算法的实现过程
二、部分源代码
%% 数据的提取和预处理
% 载入测试数据上证指数(1990.12.19-2009.08.19)
% 数据是一个4579*6的double型的矩阵,每一行表示每一天的上证指数
% 6列分别表示当天上证指数的开盘指数,指数最高值,指数最低值,收盘指数,当日交易量,当日交易额.
clear
clc
load chapter_sh.mat;
% 提取数据
[m,n] = size(sh);
ts = sh(2:m,1); % 选取2到4579个交易日内每日的开盘指数作为因变量
tsx =sh(1:m-1,:); %选取1到4578个交易日
% 数据预处理,将原始数据进行归一化
ts = ts';
tsx = tsx';
% mapminmax为matlab自带的映射函数
% 对ts进行归一化
[TS,TSps] = mapminmax(ts,1,2); %归一化在区间[1 2]
% 对TSX进行转置,以符合libsvm工具箱的数据格式要求
TS = TS';
% mapminmax为matlab自带的映射函数
% 对tsx进行归一化
[TSX,TSXps] = mapminmax(tsx,1,2); %归一化在区间[1 2]
% 对TSX进行转置,以符合libsvm工具箱的数据格式要求
TSX = TSX';
Tol=1.0e-5;
n=25;%鸟巢个数
% Discovery rate of alien eggs/solutions
pa=0.25;
%为最大迭代次数限制
%% Simple bounds of the search domain
% Lower bounds
nd=2;
Lb=0.01*ones(1,nd);
% Upper bounds
Ub=100*ones(1,nd); %随机产生初始解
% Random initial solutions
for i=1:n,
nest(i,:)=Lb+(Ub-Lb).*rand(size(Lb));
end
%得到当前的最优解
% Get the current best
for i=1:n
fitness(i)=fun(nest(i,:));
end
fitness=10^10*ones(n,1);
[fmin,bestnest,nest,fitness]=get_best_nest(nest,nest,fitness,Ub,Lb);
for i=1:n
nest(i,find(nest(i,:)>Ub(1)))=Ub(1);
nest(i,find(nest(i,:)<Lb(1)))=Lb(1);
end
N_iter=0; %开始迭代
%% Starting iterations
for iter=1:1 %while (fmin>Tol),
% Generate new solutions (but keep the current best)
new_nest=get_cuckoos(nest,bestnest,Lb,Ub);
[fnew,best,nest,fitness]=get_best_nest(nest,new_nest,fitness,Ub,Lb);
% Update the counter
N_iter=N_iter+n;
% Discovery and randomization
new_nest=empty_nests(nest,Lb,Ub,pa) ;
% Evaluate this set of solutions
[fnew,best,nest,fitness]=get_best_nest(nest,new_nest,fitness,Ub,Lb);
% Update the counter again
N_iter=N_iter+n;
% Find the best objective so far
if fnew<fmin,
fmin=fnew;
bestnest=best;
end
end %% End of iterations(迭代)
% -----------------------------------------------------------------
% Cuckoo Search (CS) algorithm by Xin-She Yang and Suash Deb %
% Programmed by Xin-She Yang at Cambridge University %
% Programming dates: Nov 2008 to June 2009 %
% Last revised: Dec 2009 (simplified version for demo only) %
% -----------------------------------------------------------------
% Papers -- Citation Details:
% 1) X.-S. Yang, S. Deb, Cuckoo search via Levy flights,
% in: Proc. of World Congress on Nature & Biologically Inspired
% Computing (NaBIC 2009), December 2009, India,
% IEEE Publications, USA, pp. 210-214 (2009).
% http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.1594v1.pdf
% 2) X.-S. Yang, S. Deb, Engineering optimization by cuckoo search,
% Int. J. Mathematical Modelling and Numerical Optimisation,
% Vol. 1, No. 4, 330-343 (2010).
% http://arxiv.org/PS_cache/arxiv/pdf/1005/1005.2908v2.pdf
% ----------------------------------------------------------------%
% This demo program only implements a standard version of %
% Cuckoo Search (CS), as the Levy flights and generation of %
% new solutions may use slightly different methods. %
% The pseudo code was given sequentially (select a cuckoo etc), %
% but the implementation here uses Matlab's vector capability, %
% which results in neater/better codes and shorter running time. %
% This implementation is different and more efficient than the %
% the demo code provided in the book by
% "Yang X. S., Nature-Inspired Metaheuristic Algoirthms, %
% 2nd Edition, Luniver Press, (2010). " %
% --------------------------------------------------------------- %
% =============================================================== %
% Notes: %
% Different implementations may lead to slightly different %
% behavour and/or results, but there is nothing wrong with it, %
% as this is the nature of random walks and all metaheuristics. %
% -----------------------------------------------------------------
function [bestnest,fmin]=cuckoo_search(n) %n为鸟巢数目
if nargin<1, % nargin是用来判断输入变量个数的函数
% Number of nests (or different solutions)
n=25;
end
% Discovery rate of alien eggs/solutions
pa=0.25;
%% Change this if you want to get better results
% Tolerance
Tol=1.0e-5; %为最大迭代次数限制
%% Simple bounds of the search domain
% Lower bounds
nd=15;
Lb=-5*ones(1,nd);
% Upper bounds
Ub=5*ones(1,nd);
%随机产生初始解
% Random initial solutions
for i=1:n,
nest(i,:)=Lb+(Ub-Lb).*rand(size(Lb));
end
%得到当前的最优解
% Get the current best
fitness=10^10*ones(n,1);
[fmin,bestnest,nest,fitness]=get_best_nest(nest,nest,fitness);
N_iter=0; %开始迭代
%% Starting iterations
while (fmin>Tol),
% Generate new solutions (but keep the current best)
new_nest=get_cuckoos(nest,bestnest,Lb,Ub);
[fnew,best,nest,fitness]=get_best_nest(nest,new_nest,fitness);
% Update the counter
N_iter=N_iter+n;
% Discovery and randomization
new_nest=empty_nests(nest,Lb,Ub,pa) ;
% Evaluate this set of solutions
[fnew,best,nest,fitness]=get_best_nest(nest,new_nest,fitness);
% Update the counter again
N_iter=N_iter+n;
% Find the best objective so far
if fnew<fmin,
fmin=fnew;
bestnest=best;
end
end %% End of iterations(迭代)
%% Post-optimization processing
%% Display all the nests
disp(strcat('Total number of iterations=',num2str(N_iter)));
fmin
bestnest
%% --------------- All subfunctions are list below ------------------
%% Get cuckoos by ramdom walk
function nest=get_cuckoos(nest,best,Lb,Ub)
% Levy flights
n=size(nest,1);
% Levy exponent and coefficient
% For details, see equation (2.21), Page 16 (chapter 2) of the book
% X. S. Yang, Nature-Inspired Metaheuristic Algorithms, 2nd Edition, Luniver Press, (2010).
beta=3/2;
sigma=(gamma(1+beta)*sin(pi*beta/2)/(gamma((1+beta)/2)*beta*2^((beta-1)/2)))^(1/beta);
for j=1:n,
s=nest(j,:);
% This is a simple way of implementing Levy flights
% For standard random walks, use step=1;
%% Levy flights by Mantegna's algorithm
u=randn(size(s))*sigma;
v=randn(size(s));
step=u./abs(v).^(1/beta);
% In the next equation, the difference factor (s-best) means that
% when the solution is the best solution, it remains unchanged.
stepsize=0.01*step.*(s-best);
% Here the factor 0.01 comes from the fact that L/100 should the typical
% step size of walks/flights where L is the typical lenghtscale;
% otherwise, Levy flights may become too aggresive/efficient,
% which makes new solutions (even) jump out side of the design domain
% (and thus wasting evaluations).
% Now the actual random walks or flights
s=s+stepsize.*randn(size(s));
% Apply simple bounds/limits
nest(j,:)=simplebounds(s,Lb,Ub);
end
%% Find the current best nest
function [fmin,best,nest,fitness]=get_best_nest(nest,newnest,fitness)
% Evaluating all new solutions
for j=1:size(nest,1),
fnew=fobj(newnest(j,:));
if fnew<=fitness(j),
fitness(j)=fnew;
nest(j,:)=newnest(j,:);
end
end
% Find the current best
[fmin,K]=min(fitness) ;
best=nest(K,:);
%% Replace some nests by constructing new solutions/nests
function new_nest=empty_nests(nest,Lb,Ub,pa)
% A fraction of worse nests are discovered with a probability pa
n=size(nest,1);
% Discovered or not -- a status vector
K=rand(size(nest))>pa;
% In the real world, if a cuckoo's egg is very similar to a host's eggs, then
% this cuckoo's egg is less likely to be discovered, thus the fitness should
% be related to the difference in solutions. Therefore, it is a good idea
% to do a random walk in a biased way with some random step sizes.
%% New solution by biased/selective random walks
stepsize=rand*(nest(randperm(n),:)-nest(randperm(n),:));
new_nest=nest+stepsize.*K;
% Application of simple constraints
function s=simplebounds(s,Lb,Ub)
% Apply the lower bound
ns_tmp=s;
I=ns_tmp<Lb;
ns_tmp(I)=Lb(I);
% Apply the upper bounds
J=ns_tmp>Ub;
ns_tmp(J)=Ub(J);
% Update this new move
s=ns_tmp;
%% You can replace the following by your own functions
% A d-dimensional objective function
function z=fobj(x)
%% d-dimensional sphere function sum_j=1^d (u_j-1)^2.
% with a minimum at (1,1, ...., 1);
sum=0;
global nd;
for i=1:nd
sum=sum+x(i)^2;
end
z=sum;
三、运行结果
四、matlab版本及参考文献
1 matlab版本 2014a
2 参考文献 [1] 包子阳,余继周,杨杉.智能优化算法及其MATLAB实例（第2版）[M].电子工业出版社，2016. [2]张岩,吴水根.MATLAB优化算法源代码[M].清华大学出版社，2017. [3]周品.MATLAB 神经网络设计与应用[M].清华大学出版社，2013. [4]陈明.MATLAB神经网络原理与实例精解[M].清华大学出版社，2013. [5]方清城.MATLAB R2016a神经网络设计与应用28个案例分析[M].清华大学出版社，2018.
