Drop-Wave
Problem definition
Objective function
f = @(x) -(1+cos(12*(sqrt(x(:,1).^2 + x(:,2).^2))))./(0.5*(x(:,1).^2 + x(:,2).^2) + 2)
Optimization settings
o = struct% initializing struct
o.d = 2% dimension of decision variable
o.lb = -5.12% lower bounds
o.ub = 5.12% 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 | ∞ | f(0,0) = -1 |
Optimization example with ga
Algorithm options
o.maxit = 250% 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 -1]% solution
info.animate = true% plot animation
info.animfreq = 15% frame frequency
info.np = 21% number of points for meshgrid
optimview('ga',info)
References
[1] M. Molga and C. Smutnicki, "Test functions for optimization needs", 2005