Bird

Problem definition

Objective function
f = @(x) sin(x(:,1)).*exp(1-cos(x(:,2))).^2 + cos(x(:,2)).*exp(1-sin(x(:,1))).^2 + (x(:,1)-x(:,2)).^2
Optimization settings
o = struct	

% initializing struct

o.d = 2

% dimension of decision variable

o.lb = -2*pi

% lower bounds

o.ub = 2*pi

% upper bounds

Graphic representation
[x,y] = meshgrid(o.lb:0.5:o.ub)
surf(x,y,f([x(:),y(:)]))

Problem properties

convexity smoothness minimum
0 f(4.70104,3.15294) = -106.764537

Optimization example with ga

Algorithm options
o.maxit = 21	

% number of iterations

Optimization
rng(0)	

% for tractability

[xmin,fmin,popPos,popCost] = ga(f,o)

% running minimization

Animation
rng(0)
[~,~,~,~,info] = ga(f,o)
info.sol = [4.70104 3.15294 -106.764537]	

% solution

info.animate = true

% plot animation

info.animfreq = 2

% frame frequency

info.np = 21

% number of points for meshgrid

optimview('ga',info)

References

[1] S. K. Mishra, "Global Optimization By Differential Evolution and Particle Swarm Methods: Evaluation On Some Benchmark Functions", Munich Research Papers in Economics

Related functions

ga | meshgrid | surf