【优化算法】多目标花朵授粉算法（MOFPA）【含Matlab源码 1594期】

一、获取代码方式

获取代码方式1：
完整代码已上传我的资源：【优化算法】多目标花朵授粉算法（MOFPA）【含Matlab源码 1594期】

获取代码方式2：
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二、花朵授粉算法简介

介绍了一种新的元启发式群智能算法——花朵授粉算法（flower pollinate algorithm，FPA）和一种新型的差分进化变异策略——定向变异（targeted mutation，TM）策略。针对FPA存在的收敛速度慢、寻优精度低、易陷入局部最优等问题，提出了一种基于变异策略的改进型花朵授粉算法——MFPA。该算法通过改进TM策略，并应用到FPA的局部搜索过程中，以增强算法的局部开发能力。

三、部分源代码

% --------------------------------------------------------------------    %
% Multiobjective flower pollenation algorithm (MOFPA)                     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Notes: This demo program contains the very basic components of          %
% the multiobjective flower pollination algorithm (MOFPA)                 %
% for bi-objective optimization. It usually works well for                %
% unconstrained functions only. For functions/problems with               %
% limits/bounds and constraints, constraint-handling techniques           %
% should be implemented to deal with constrained problems properly.       %
%                                                                         %   %% Notes: --------------------------------------------------------------- %
% n=# of the solutions in the population
% m=# of objectives, d=# of dimensions
% S or Sol has a size of n by d
% f = objective values of [n by m]
% RnD = Rank of solutions and crowding Distances, so size of [n by 2]    %function [best,fmin,N_iter]=mofpa(para)
% Default parameters
if nargin<1,para=[100 1000 0.8];
end
n=para(1);           % Population size, typically 10 to 25
Iter_max=para(2);    % Max number of iterations
p=para(3);           % probabibility switch% Number of objectives
m=2;
% Rank and distance matrix
RnD=zeros(n,2);
% Dimension of the search variables
d=30;
% Simple lower and upper bounds
Lb=0*ones(1,d);    Ub=1*ones(1,d);%% 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
Sol=Sorted(:,1:d);
f=Sorted(:,(d+1):(d+m));
RnD=Sorted(:,(d+m+1):end);% Start the iterations -- Flower Algorithm
for t=1:Iter_max,% Loop over all flowers/solutionsfor i=1:n,% Pollens are carried by insects and thus can move in% large scale, large distance.% This L should replace by Levy flights  % Formula: x_i^{t+1}=x_i^t+ L (x_i^t-gbest)if rand>p,%% L=rand;L=Levy(d);     % The best is stored as the first row Sol(1,:) of the sorted solutions dS=L.*(Sol(i,:)-Sol(1,:));S(i,:)=Sol(i,:)+dS;% Check if the simple limits/bounds are OKS(i,:)=simplebounds(S(i,:),Lb,Ub);% If not, then local pollenation of neighbor flowers elseepsilon=rand;% Find random flowers in the neighbourhoodJK=randperm(n);% As they are random, the first two entries also random% If the flower are the same or similar species, then% they can be pollenated, otherwise, no action.% Formula: x_i^{t+1}+epsilon*(x_j^t-x_k^t)S(i,:)=Sol(1,:)+epsilon*(Sol(JK(1),:)-Sol(JK(2),:));% Check if the simple limits/bounds are OKS(i,:)=simplebounds(S(i,:),Lb,Ub);endend % end of for loop%% Evalute the fitness/function values of the new populationfor i=1:n,f_new(i, 1:m) = obj_funs(S(i,1:d),m);if (f_new(i,1:m) <= f(i,1:m)),  f(i,1:m)=f_new(i,1:m);end% Update the current best (stored in the first row)if (f_new(i,1:m) <= f(1,1:m)), Sol(1,1:d) = S(i,1:d); f(1,:)=f_new(i,:);endend % end of for loop%% ! It's very important to combine both populations, otherwise,
%% the results may look odd and will be very inefficient. !
%% The combined population consits of both the old and new solutions
%% So the total size of the combined population for sorting is 2*nX(1:n,:)=[S f_new];            % Combine new solutionsX((n+1):(2*n),:)=[Sol f];      % Combine old solutionsSorted=solutions_sorting(X, m, d);%% Select n solutions among a combined population of 2*n solutionsnew_Sol=Select_pop(Sorted, m, d, n);% Decompose into solutions, fitness and rankingSol=new_Sol(:,1:d);             % Sorted solutionsf=new_Sol(:,(d+1):(d+m));       % Sorted objective valuesRnD=new_Sol(:,(d+m+1):end);     % Sorted ranks and distances%% Running display at each 100 iterationsif ~mod(t,100), disp(strcat('Iterations t=',num2str(t))); plot(f(:, 1), f(:, 2),'ro','MarkerSize',3); % axis([0 1 -0.8 1]);xlabel('f_1'); ylabel('f_2');drawnow;end   end  % end of iterations%% End of the main program %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Application of simple constraints or bounds
function s=simplebounds(s,Lb,Ub)% Apply the lower boundns_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;% Draw n Levy flight sample
function L=Levy(d)
% Levy exponent and coefficient
% For details, see Chapter 11 of the following book:
% Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, (2014).
beta=3/2;
sigma=(gamma(1+beta)*sin(pi*beta/2)/(gamma((1+beta)/2)*beta*2^((beta-1)/2)))^(1/beta);u=randn(1,d)*sigma;v=randn(1,d);step=u./abs(v).^(1/beta);
L=0.1*step; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Make sure all the new solutions are within the limits
function [ns]=findlimits(ns,Lb,Ub)% Apply the lower boundns_tmp=ns;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 ns=ns_tmp;

四、运行结果

五、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.

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