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智能優化算法 ?神經網絡預測 雷達通信? 無線傳感器

信號處理 圖像處理 路徑規劃 元胞自動機 無人機? 電力系統

? 內容介紹

?布谷鳥搜索（Cuckoo Search, CS）算法是 2009 年 Xin-She Yang 與 Susash Deb 提出的一種新型的啟發算法[61]。算法靈感來源于一些布谷鳥種屬（Cuckoo Species）的專性寄生哺育（BroodParasitism）行為，即這些種群不會像絕大多數鳥類一樣自己筑巢哺育后代，而是通常把蛋產于宿主鳥巢內，由宿主代養，這種行為被稱為巢寄生。此類布谷鳥會觀察宿主鳥所產的卵并對其進行模仿，按照宿主鳥卵的顏色形狀來產卵，導致宿主鳥辨別出布谷鳥卵的幾率微乎其微，布谷鳥卵混在宿主鳥卵中，孵化后由宿主鳥哺育并與宿主雛鳥爭奪生存資源。然而，布谷鳥卵一旦被宿主鳥識破情況便不同，宿主將完全摧毀鳥巢或是僅僅將布谷鳥卵摧毀。因此布谷鳥在繁殖季會尋找孵化周期類似、雛鳥習性類似以及卵外觀類似的宿主鳥。布谷鳥通常會趁宿主外出時將卵產于巢內，有時會將宿主卵推出巢后進行產卵，使布谷雛鳥獨享生存資源，以提高生存幾率。此外，布谷鳥等動物的覓食過程是也是一種有啟發性的隨機行為過程。所在位置確定移動的下一個目標點，所選取的數學模型決定移動方向。根據當前位置與到下一個位置的轉移概率，它們會飛向或是走向搜索路徑。鳥類的這種飛行行為，在很多研究中被證明為萊維飛行（Levy Flight）的典型特征

? 部分代碼

%% 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)? ? %

% Multiobjective cuckoo search (MOCS) added in July 2012,? ? ? ? ?%

% Then, MOCS was updated in Sept 2015.? ? ? ? ? ? ? ? ? ? ?Thanks %

% -----------------------------------------------------------------

%% References -- 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

%% 3) X.-S. Yang, S. Deb, Multi-objective cuckoo search for?

% Design optimization, Computers & Operations Research,?

% vol. 40, no. 6, 1616-1624 (2013).

% ----------------------------------------------------------------%

% 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 Optimization Algoirthms,? ? ? ? %?

%? ? ?Elsevier Press, 2014.? "? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %

% --------------------------------------------------------------- %

% =============================================================== %

%% Notes:? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?%

% 1) The constraint-handling is not included in this demo code.? ?%

% The main idea to show how the essential steps of cuckoo search? %

% and multi-objective cuckoo search (MOCS) can be done.? ? ? ? ? ?%

% 2) Different implementations may lead to slightly different? ? ?%

% behavour and/or results, but there is nothing wrong with it,? ? %

% as it is the nature of random walks and all metaheuristics.? ? ?%

% --------------------------------------------------------------- %

function [bestnest,fmin]=mocs_new(inp)

if nargin<1,

inp=[100 1000 0.25]; % pop_size, #iteraion, pa

end? ??

% Number of nests (or the population size)

n=inp(1);

% Number of iterations/generations

N_IterTotal=inp(2);

% Discovery rate of alien eggs/solutions

pa=inp(3);

d=30;? ?% Dimensionality of the problem

% Simple lower bounds

Lb=0*ones(1,d);?

% Simple upper bounds

Ub=1*ones(1,d);

% Number of objectives

m=2;

%% Initialize the population

for i=1:n,

? ?Sol(i,:)=Lb+(Ub-Lb).*rand(1,d);?

? ?f(i,1:m) = obj_funs(Sol(i,:), m);

end

% Store the fitness or objective values

f_new=f;

%% Sort the initialized population

x=[Sol f];? % combined into a single input

% Non-dominated sorting for the initila population

Sorted=solutions_sorting(x, m,d);

% Decompose into solutions, fitness, rank and distances

nest=Sorted(:,1:d);

f=Sorted(:,(d+1):(d+m));

RnD=Sorted(:,(d+m+1):end);

%% Starting iterations

for t=1:N_IterTotal,

? ? % Generate new solutions (but keep the current best)

? ? ?new_nest=get_cuckoos(nest,nest(1,:), Lb,Ub);? ?

? %? ?new_nest=nest;

? ? ?% Discovery and randomization

? ? ?new_nest=empty_nests(nest,Lb,Ub,pa) ;

? ? ?

? ? % Evaluate this set of solutions

? ? ? for i=1:n,

? ? ? %% Evalute the fitness/function values of the new population

? ? ? ? f_new(i, 1:m) = obj_funs(new_nest(i,1:d),m);

? ? ? ??

? ? ? ? if (f_new(i,1:m) <= f(i,1:m)),??

? ? ? ? ? ? f(i,1:m)=f_new(i,1:m);

? ? ? ? ? ? nest(i,:)=new_nest(i,:);

? ? ? ? end

? ? ? ? % Update the current best (stored in the first row)

? ? ? ? if (f_new(i,1:m) <= f(1,1:m)),?

? ? ? ? ? ? nest(1,1:d) = new_nest(i,1:d);?

? ? ? ? ? ? f(1,:)=f_new(i,:);

? ? ? ? end? ? ? ? ?

? ? ? end? % end of for loop

? ? ??

%% Combined population consits of both the old and new solutions

%% So the total number of solutions for sorting is 2*n

%% ! It's very important to combine both populations, otherwise,

%% the results may look odd and will be very inefficient. !

? ? ? ?X(1:n,:)=[new_nest f_new];? ? ? % Combine new solutions

? ? ? ?X((n+1):(2*n),:)=[nest f];? ? ? % Combine old solutions

? ? ? ?Sorted=solutions_sorting(X, m, d);?

? ? ? ?%% Select n solutions from a combined population of 2*n solutions

? ? ? ?new_Sol=Select_pop(Sorted, m, d, n);

? ? ? ?% Decompose the sorted solutions into solutions, fitness & ranking

? ? ? ?nest=new_Sol(:,1:d);? ? ? ? ? ?% Sorted solutions/variables

? ? ? ?f=new_Sol(:,(d+1):(d+m));? ? ? % Sorted objective values

? ? ? ?RnD=new_Sol(:,(d+m+1):end);? ? % Sorted ranks and distances

? ? ? ?

? %% Running display at each 100 iterations

? ?if ~mod(t,100),?

? ? ?disp(strcat('Iterations t=',num2str(t)));?

? ? ?plot(f(:, 1), f(:, 2),'rs','MarkerSize',3);?

? ? ?axis([0 1 -0.8 1]);

? ? ?xlabel('f_1'); ylabel('f_2');

? ? ?drawnow;

? ?end? ?

end %% End of iterations

%% --------------- All subfunctions are list below ------------------? ? ?%

%% Get cuckoos by ramdom walk

function nest=get_cuckoos(nest,best,Lb,Ub)

n=size(nest,1);

% For details, please see the chapters of the following Elsevier book:??

% X. S. Yang, Nature-Inspired Optimization Algorithms, Elsevier, (2014).

beta=3/2;? % Levy exponent in Levy flights

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,:);

? ? %% Levy flights by Mantegna's algorithm

? ? u=randn(size(s))*sigma;

? ? v=randn(size(s));

? ? step=u./abs(v).^(1/beta);

? ? stepsize=0.1*step.*(s-best);

? ? % Now the actual random walks or flights

? ? s=s+stepsize.*randn(size(s));

? ?% Apply simple bounds/limits

? ?nest(j,:)=simplebounds(s,Lb,Ub);

end

%% 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,d]=size(nest);

% The solutions represented by cuckoos to be discovered or not?

% with a probability pa. This action is implemented as a status vector

K=rand(size(nest))>pa;?

%% New solution by biased/selective random walks

stepsize=rand(1,d).*(nest(randperm(n),:)-nest(randperm(n),:));

new_nest=nest+stepsize.*K;

for j=1:size(new_nest,1)

? ? s=new_nest(j,:);

? ? new_nest(j,:)=simplebounds(s,Lb,Ub);??

end

% Application of simple bounds

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;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Objective functions?

function f = obj_funs(x, m)

% Zitzler-Deb-Thiele's funciton No 3 (ZDT function 3)

% M = # of objectives

% d = # of variables/dimensions

d=length(x);? % d=30 for ZDT 3

% First objective f1

f(1) = x(1);

g=1+9/29*sum(x(2:d));

h=1-sqrt(f(1)/g)-f(1)/g*sin(10*pi*f(1));

% Second objective f2

f(2) = g*h;

%%%%%%%%%%%%%%%%%% end of the definitions of obojectives %%%%%%%%%%%%%%%%%%

function new_Sol = Select_pop(nest, m, ndim, npop)

% The input population to this part has twice (ntwice) of the needed?

% population size (npop). Thus, selection is done based on ranking and?

% crowding distances, calculated from the non-dominated sorting

ntwice= size(nest,1);

% Ranking is stored in column Krank

Krank=m+ndim+1;

% Sort the population of size 2*npop according to their ranks

[~,Index] = sort(nest(:,Krank)); sorted_nest=nest(Index,:);

% Get the maximum rank among the population

RankMax=max(nest(:,Krank));?

%% Main loop for selecting solutions based on ranks and crowding distances

K = 0;? % Initialization for the rank counter?

% Loop over all ranks in the population

for i =1:RankMax,??

? ? % Obtain the current rank i from sorted solutions

? ? RankSol = max(find(sorted_nest(:, Krank) == i));

? ? % In the new cuckoos/solutions, there can be npop solutions to fill

? ? if RankSol<npop,

? ? ? ?new_Sol(K+1:RankSol,:)=sorted_nest(K+1:RankSol,:);

? ? end?

? ? % If the population after addition is large than npop, re-arrangement

? ? % or selection is carried out

? ? if RankSol>=npop

? ? ? ? % Sort/Select the solutions with the current rank?

? ? ? ? candidate_nest = sorted_nest(K + 1 : RankSol, :);

? ? ? ? [~,tmp_Rank]=sort(candidate_nest(:,Krank+1),'descend');

? ? ? ? % Fill the rest (npop-K) cuckoo/solutions up to npop solutions?

? ? ? ? for j = 1:(npop-K),?

? ? ? ? ? ? new_Sol(K+j,:)=candidate_nest(tmp_Rank(j),:);

? ? ? ? end

? ? end

? ? % Record and update the current rank after adding new cuckoo solutions

? ? K = RankSol;

end

? 運行結果

? 參考文獻

[1]尚志勇. 基于改進布谷鳥搜索算法的配送中心選址問題研究. (Doctoral dissertation, 河南大學).

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