Bohachevsky1
Problem definition
Objective function
f = @(x) x(:,1).^2 + 2*x(:,2).^2 - 0.3*cos(3*pi*x(:,1)) - 0.4*cos(4*pi*x(:,2)) + 0.7
Optimization settings
o = struct% initializing struct
o.lb = -50% lower bounds
o.ub = 50% upper bounds
Graphic representation
[x,y] = meshgrid(o.lb:10:o.ub) surf(x,y,f([x(:),y(:)]))
Problem properties
| convexity | smoothness | minimum |
| 1 | ∞ | f(0,0) = 0 |
Optimization example with fminsearch
Optimization
rng(0)% for tractability
x0 = [44,44]% initial guess
[xmin,fmin,info] = fminsearch(f,x0,o)% running minimization
Animation
rng(0) x0 = [44,44] [~,~,info] = fminsearch(f,x0,o) info.sol = [0 0 0]% solution
info.animate = true% plot animation
info.animfreq = 5% frame frequency
optimview('fminsearch',info)
References
[1] I. O. Bohachevsky, M. E. Johnson, M. L. Stein, "General Simulated Annealing for
Function Optimization", Technometrics, vol. 28, no. 3, pp. 209-217, 1986