How to apply bat algorithm to spring design problem?

This is what I did:

%[5 20 1 0]
% Main programs starts here
function [best,fmin,N_iter]=bat_algorithm_spring1(para)

   format long;

   % Lb=[0.05 0.25 2.0];  Ub=[1.0 1.3 15.0];

% Default parameters

n=para(1)  ;    % Population size, typically 10 to 40
N_gen=para(2);  % Number of generations
A=para(3) ;    % Loudness  (constant or decreasing)
r=para(4)  ;   % Pulse rate (constant or decreasing)
% This frequency range determines the scalings
% You should change these values if necessary
Qmin=0.0025;        % Frequency minimum
Qmax=88.4  ;    % Frequency maximum
% Iteration parameters
N_iter=0 ;      % Total number of function evaluations
% Dimension of the search variables
d=3       ;    % Number of dimensions 
% Lower limit/bounds/ a vector
Lb=0.0025*ones(1,d);
% Upper limit/bounds/ a vector
Ub=88.4*ones(1,d);

% Initializing arrays
Q=zeros(n,1) ;  % Frequency
v=zeros(n,d) ;  % Velocities
% Initialize the population/solutions

for i=1:n,
  Sol(i,:)=Lb+(Ub-Lb).*rand(1,d);
  Fitness(i)=objfun(Sol(i,:));
end
% Find the initial best solution
[fmin,I]=min(Fitness);
best=[0.09 0.35 11];

% Start the iterations -- Bat Algorithm (essential part)  %
for t=1:N_gen, 
% Loop over all bats/solutions
        for i=1:n,
          Q(i)=Qmin+(Qmax-Qmin)*rand;
          v(i,:)=v(i,:)+(Sol(i,:)-best)*Q(i);
          S(i,:)=Sol(i,:)+v(i,:);
          % Apply simple bounds/limits
           %Sol(i,:)=simplebounds(Sol(i,:),Lb,Ub);
          % Pulse rate
          if rand>r
          % The factor 0.001 limits the step sizes of random walks 
              S(i,:)=best+0.001*randn(1,d);
          end

       % Evaluate new solutions
             Fnew=objfun(S(i,:));
       % Update if the solution improves, or not too loud
             if (Fnew<=Fitness(i)) & (rand<A) ,
                  Sol(i,:)=S(i,:);
                  Fitness(i)=Fnew;
                 % A=0.025*A;
                  %r=r*(1-exp(-1*t));

             end

            % Update the current best solution
            if Fnew<=fmin,
                  best=S(i,:);
                  fmin=Fnew;
            end

          end

          N_iter=N_iter+n;
  end
  % Output/display
  disp(['Number of evaluations: ',num2str(N_iter)]);
  disp(['Best =',num2str(best),' fmin=',num2str(fmin)]);

% Application of simple limits/bounds
function s=simplebounds(s,Lb,Ub)
  % Apply the lower bound vector
  ns_tmp=s;
  I=ns_tmp<Lb;
  ns_tmp(I)=Lb(I);

    % Apply the upper bound vector   
    J=ns_tmp>Ub;
    ns_tmp(J)=Ub(J);
     %Update this new move 
    s=ns_tmp;

% Objective function
function f=objfun(x)
f=(2+x(3))*(x(1)^2)*x(2);

% Nonlinear constraints
function [g,geq]=nonfun(x)
% Inequality constraints
  g(1)=1-(((x(2)^3)*(x(3)))/(71785*(x(1)^4)));  
  % Notice the typo 7178 (instead of 71785)
  gtmp=((4*(x(2))^2)-(x(1)*x(2)))/(12566*(x(2)*(x(1)^3)-(x(1)^4)));
  g(2)=gtmp+(1/(5108*(x(1)^2)))-1;
  g(3)=1-((140.45*x(1))/((x(2)^2)*x(3)));
  g(4)=((x(1)+x(2))/1.5)-1;
% Equality constraints [none]
geq=[]

This converges lower than the real value. What could be wrong?

[Star Strider]

Reference: Bat algorithm

Answer 1

[Joe Ajay]

Hi, am too working on that; got the same problem here. Got any answers?