Cross-in-tray
Problem definition
Objective function
f = @(x) -0.0001*(abs(sin(x(:,1)).*sin(x(:,2)).*exp(abs(100 - (x(:,1).^2 + x(:,2).^2).^0.5/pi))) + 1).^0.1
Optimization settings
o = struct% initializing struct
o.lb = -3% lower bounds
o.ub = 3% upper bounds
Graphic representation
[x,y] = meshgrid(o.lb:0.25:o.ub) surf(x,y,f([x(:),y(:)]))
Problem properties
| convexity | smoothness | minimum |
| 0 | ∞ | f(-1.3494, -1.3494) = -2.06261 |
Optimization example with fminsearch
Optimization
rng(0)% for tractability
x0 = [0.5,-2]% initial guess
[xmin,fmin,info] = fminsearch(f,x0,o)% running minimization
Animation
rng(0) x0 = [0.5,-2] [~,~,info] = fminsearch(f,x0,o) info.sol = [-1.3494 -1.3494 -2.06261]% solution
info.animate = true% plot animation
info.animfreq = 5% frame frequency
info.np = 40% number of points for meshgrid
optimview('fminsearch',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