Griewank
Problem definition
Objective function
f = @(x) (x(:,1).^2 + x(:,2).^2)/4000 - cos(x(:,1)).*cos(x(:,2)./sqrt(2)) + 1
Optimization settings
o = struct% initializing struct
o.d = 2% dimension of decision variable
o.lb = -600% lower bounds
o.ub = 600% upper bounds
Graphic representation
[x,y] = meshgrid(o.lb:40:o.ub) surf(x,y,f([x(:),y(:)]))
Zoom around global minimum
[x,y] = meshgrid(-6:0.3:6) surf(x,y,f([x(:),y(:)]))
Problem properties
| convexity | smoothness | minimum |
| 0 | ∞ | f(0,0) = 0 |
Optimization example with ga
Algorithm options
o.maxit = 60% 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 = [0 0 0]% solution
info.animate = true% plot animation
info.animfreq = 4% frame frequency
info.np = 21% number of points for meshgrid
optimview('ga',info)
References
[1] A. O. Griewank, "Generalized Decent for Global Optimization", J. Opt. Th. Appl. 34, 1139, 1981