Ackley

Problem definition

Objective function
f = @(x) -20*exp(-0.2*sqrt(0.5*sum(x.^2,2))) - exp(0.5*(cos(2*pi*x(:,1))+cos(2*pi*x(:,2)))) + exp(1) + 20
Optimization settings
o = struct	
% initializing struct

o.lb = -2	
% lower bounds

o.ub = 2	
% upper bounds
Graphic representation 
[x,y] = meshgrid(o.lb:0.2:o.ub)
surf(x,y,f([x(:),y(:)]))

Problem properties

convexity smoothness minimum
0 0 f(0,0) = 0

Optimization example with fminsearch

Optimization 
rng(0)	
% for tractability 

x0 = [2,2]	
% initial guess 

[xmin,fmin,info] = fminsearch(f,x0,o)	
% running minimization
Animation 
rng(0)
x0 = [2,2]
[~,~,info] = fminsearch(f,x0,o)
info.sol = [0 0 0]	
% solution 

info.animate = true	
% plot animation 

info.animfreq = 5	
% frame frequency 

info.np = 21	
% number of points for meshgrid 

optimview('fminsearch',info)

References

[1] T. Back, H. P. Schwefel, An Overview of Evolutionary Algorithm for Parameter Optimization, Evolutionary Computation, vol. 1, no. 1, pp. 1-23, 1993

Related functions

fminsearch | meshgrid | surf