Particle swarm optimization
Particle Swarm Optimization (PSO) is an optimization method in which multiple candidate solutions ('particles') migrate through the solution space under the influence of local and global best known positions. PSO does not require that the objective function be differentiable and can optimize over very large problem spaces, but is not guaranteed to converge.
The method should be demonstrated by application of the 2D Rosenbrock function, and possibly other standard or well-known optimization test cases.
References:
ooRexx
<lang oorexx>/* REXX ---------------------------------------------------------------
- Test for McCormick function
- --------------------------------------------------------------------*/
Numeric Digits 16 Parse Value '-.5 -1.5 1' With x y d fmin=1e9 Call refine x,y Do r=1 To 10
d=d/5 Call refine xmin,ymin End
Say 'which is better (less) than' Say ' f(-.54719,-1.54719)='f(-.54719,-1.54719) Say 'and differs from published -1.9133' Exit
refine: Parse Arg xx,yy Do x=xx-d To xx+d By d/2
Do y=yy-d To yy+d By d/2 f=f(x,y) If f<fmin Then Do Say x y f fmin=f xmin=x ymin=y End End End
Return
f: Parse Arg x,y res=rxcalcsin(x+y,16,'R')+(x-y)**2-1.5*x+2.5*y+1 Return res
- requires rxmath library</lang
- Output:
-1.5 -2.5 -1.243197504692072 -1.0 -2.0 -1.641120008059867 -0.5 -1.5 -1.909297426825682 -0.54 -1.54 -1.913132979507516 -0.548 -1.548 -1.913221840016527 -0.5480 -1.5472 -1.913222034492829 -0.5472 -1.5472 -1.913222954970650 -0.54720000 -1.54719872 -1.913222954973731 -0.54719872 -1.54719872 -1.913222954978670 -0.54719872 -1.54719744 -1.913222954978914 -0.54719744 -1.54719744 -1.913222954981015 -0.5471975424 -1.5471975424 -1.913222954981036 which is better (less) than f(-.54719,-1.54719)=-1.913222954882273 and differs from published -1.9133