How to store results from a function in a workspace

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Anoire BEN JDIDIA
Anoire BEN JDIDIA 2018-8-31
编辑： Stephen23 2018-8-31
Hi, Actually Im using this code
% ============================================================= %
% Files of the Matlab programs included in the book: %
% Xin-She Yang, Nature-Inspired Metaheuristic Algorithms, %
% Second Edition, Luniver Press, (2010). www.luniver.com %
% ============================================================= %
% The Accelerated Particle Swarm Optimization (APSO): %
% APSO was deloveloped by Xin-She Yang at Cambridge University %
% in 2008. For detail, please refer to Chapter 5 (section 5.3) %
% of the following book by %
% Xin-She Yang, Nature-Inspired Metaheuristic Algorithms, %
% First Edition, Luniver Press, (2008). Also in Chapter 8 %
% (section 8.3, page 65) of the second edition (2010). %
% ------------------------------------------------------------- %
% Optimization of a welded beam using Accelerated PSO
function apso_weld
% This welded beam example can be found in Section 4.4 of the book
%%Lower and upper bounds
Lb=[0.1 0.1 0.1 0.1];
Ub=[2.0 10.0 10.0 2.0];
% Default parameters [number of particles, number of iterations]
para=[25 150 0.95];
% Call the accelerated PSO optimizer
[gbest,fmin]=pso_mincon(@cost,@constraint,Lb,Ub,para);
% Display results
Bestsolution=gbest
fmin
%%== Modify the following to use your own functions ===============
% Welded beam optimization. For detailed description, see
% X. S. Yang, Chapter 4 (section 4.4) of Nature-Inspired
% Metaheuristic Algorithms, 2nd Edition, Luniver Press, (2010).
%%Objective function
function f=cost(x)
f=1.10471*x(1)^2*x(2)+0.04811*x(3)*x(4)*(14.0+x(2));
% Nonlinear constraints
function [g,geq]=constraint(x)
% Inequality constraints
Q=6000*(14+x(2)/2);
D=sqrt(x(2)^2/4+(x(1)+x(3))^2/4);
J=2*(x(1)*x(2)*sqrt(2)*(x(2)^2/12+(x(1)+x(3))^2/4));
alpha=6000/(sqrt(2)*x(1)*x(2));
beta=Q*D/J;
tau=sqrt(alpha^2+2*alpha*beta*x(2)/(2*D)+beta^2);
sigma=504000/(x(4)*x(3)^2);
delta=65856000/(30*10^6*x(4)*x(3)^3);
F=4.013*(30*10^6)/196*sqrt(x(3)^2*x(4)^6/36)*(1-x(3)*sqrt(30/48)/28);
g(1)=tau-13600;
g(2)=sigma-30000;
g(3)=x(1)-x(4);
g(4)=0.10471*x(1)^2+0.04811*x(3)*x(4)*(14+x(2))-5.0;
g(5)=0.125-x(1);
g(6)=delta-0.25;
g(7)=6000-F;
% If no equality constraint at all, put geq=[] as follows
geq=[];
%%=== End of your own functions ==============================
%%=== APSO Solver starts here ================================
% No need to modify the following, unless you want to improve
% the perfornance of this accelerated PSO.
function [gbest,fbest]=pso_mincon(fhandle,fnonlin,Lb,Ub,para)
if nargin<=4,
para=[20 150 0.95];
end
% Populazation size, time steps and gamma
n=para(1); time=para(2); gamma=para(3);
% -----------------------------------------------------------------
%%Scalings
scale=abs(Ub-Lb);
% Validation constraints
if abs(length(Lb)-length(Ub))>0,
disp('Constraints must have equal size');
return
end
% -----------------------------------------------------------
% Setting parameters alpha, beta
% Randomness amplitude of roaming particles alpha=[0,1]
% Speed of convergence (0->1)=(slow->fast); % beta=0.5
alpha=0.2; beta=0.5;
% A potential improvement of convergence is to use a variable
% alpha & beta. For example, to use a reduced alpha, we have
% gamma in [0.7, 1];
% -----------------------------------------------------------
%%------------- Start Particle Swarm Optimization -----------
% generating the initial locations of n particles
best=init_pso(n,Lb,Ub);
fbest=1.0e+100;
% ----- Iterations starts ------
for t=1:time,
% Find which particle is the global best
for i=1:n,
fval=Fun(fhandle,fnonlin,best(i,:));
% Update the best
if fval<=fbest,
gbest=best(i,:);
fbest=fval;
end
end
% -----------------------------------------------------------
% Randomness reduction
alpha=newPara(alpha,gamma);
% Move all particles to new locations
best=pso_move(best,gbest,alpha,beta,Lb,Ub);
% Output the results to screen
str=strcat('Best estimates: gbest=',num2str(gbest));
str=strcat(str,' iteration='); str=strcat(str,num2str(t));
disp(str);
end %%%%%end of main program
% -------------------------------------------------
% All subfunctions are listed here
%
% Intial locations of particles
function [guess]=init_pso(n,Lb,Ub)
ndim=length(Lb);
for i=1:n,
guess(i,1:ndim)=Lb+rand(1,ndim).*(Ub-Lb);
end
% Move all the particles toward (xo,yo)
function ns=pso_move(best,gbest,alpha,beta,Lb,Ub)
% This scale is important as it increases the mobility of particles
n=size(best,1); ndim=size(best,2);
scale=(Ub-Lb);
for i=1:n,
ns(i,:)=best(i,:)+beta*(gbest-best(i,:))+alpha.*randn(1,ndim).*scale;
end
ns=findrange(ns,Lb,Ub);
% Application of simple lower and upper bounds
function ns=findrange(ns,Lb,Ub)
n=length(ns);
for i=1:n,
% Apply the lower bound
ns_tmp=ns(i,:);
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(i,:)=ns_tmp;
end
% Reduction of the randomness
function alpha=newPara(alpha,gamma);
% More elaborate scheme can be used.
alpha=alpha*gamma;
% ---------------------------------------------------------------------
% Computing the d-dimensional objective function with constraints
function z=Fun(fhandle,fnonlin,u)
% Objective
z=fhandle(u);
% Apply nonlinear constraints by the penalty method
% Z=f+sum_k=1^N lam_k g_k^2 *H(g_k) where lam_k >> 1
z=z+getconstraints(fnonlin,u);
function Z=getconstraints(fnonlin,u)
% Penalty constant >> 1
PEN=10^15;
lam=PEN; lameq=PEN;
Z=0;
% Get nonlinear constraints
[g,geq]=fnonlin(u);
% Apply all inequality constraints as a penalty function
for k=1:length(g),
Z=Z+ lam*g(k)^2*getH(g(k));
end
% Apply all equality constraints (when geq=[], length->0)
for k=1:length(geq),
Z=Z+lameq*geq(k)^2*geteqH(geq(k));
end
% Test if inequalities hold so as to get the value of the Index function
% H(g) which is something like the Index in the interior-point methods
function H=getH(g)
if g<=0,
H=0;
else
H=1;
end
% Test if equalities hold
function H=geteqH(g)
if g==0,
H=0;
else
H=1;
end
%%-----------------------------------------------------------------------
%%End of this program ---------------------------------------------------
the problem that bestsolution and fmin are not stored in the workspace to plot their evaluation in each iteration . Any help please to store the value of bestsolution and fmin in each iteration

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Stephen23
Stephen23 2018-8-31
编辑：Stephen23 2018-8-31
Without function output arguments, you are not going to get any function outputs. Its author simply displayed some values, which is not very useful. The function help clearly explains how to write a function with output arguments. In your case, change the function definition to return the required variables:
function apso_weld
to
function [gbest, fmin] = apso_weld()
And then when you call the function it must have two output arguments:
[A,B] = apso_weld()
I would also recommend that you completely remove these three lines, which are totally useless for anything (except perhaps debugging):
% Display results
Bestsolution=gbest
fmin
"Any help please to store the value of bestsolution and fmin in each iteration"
Each iteration of what?
If you want the intermediate results at each iteration step of the (apparently) optimization function pso_mincon, then you will have to contact its author or adapt the code yourself. Take a look at just below the comment "Output the results to screen": that seems a likely place to start investigating which values to store.

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