Schwefel

Problem definition

Objective function
f = @(x) 418.9829*2 - (x(:,1).*sin(sqrt(abs(x(:,1)))) + x(:,2).*sin(sqrt(abs(x(:,2)))))
Optimization settings
o = struct	

% initializing struct

o.d = 2

% dimension of decision variable

o.lb = -500

% lower bounds

o.ub = 500

% upper bounds

Graphic representation
[x,y] = meshgrid(linspace(o.lb,o.ub,50))
surf(x,y,f([x(:),y(:)]))

Problem properties

convexity smoothness minimum
0 f(420.9687,420.9687) = 0

Optimization example with ga

Algorithm options
o.maxit = 23	

% 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 = [420.9687 420.9687 0]	

% solution

info.animate = true

% plot animation

info.animfreq = 2

% frame frequency

info.np = 21

% number of points for meshgrid

optimview('ga',info)

References

[1] H. P. Schwefel, "Numerical Optimization for Computer Models", John Wiley Sons, 1981

Related functions

ga | meshgrid | surf