Particle swarm optimization: Difference between revisions
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state =: pso^:40 state |
state =: pso^:40 state |
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smoutput 2 3 $ 'Iteration';'GlobalBestPosition';'GlobalBestValue';iter;gbpos;gbval |
smoutput |: 2 3 $ 'Iteration';'GlobalBestPosition';'GlobalBestValue';iter;gbpos;gbval |
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┌──────────────────┬──────────────────┐ |
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┌─────────┬──────────────────┬───────────────┐ |
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│Iteration │40 │ |
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│Iteration│GlobalBestPosition│GlobalBestValue│ |
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├──────────────────┼──────────────────┤ |
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├─────────┼──────────────────┼───────────────┤ |
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│GlobalBestPosition│_0.547599 _1.54788│ |
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│40 │_0.547804 _1.54794│_1.91322 │ |
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├──────────────────┼──────────────────┤ |
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└─────────┴──────────────────┴───────────────┘ |
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│GlobalBestValue │_1.91322 │ |
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└──────────────────┴──────────────────┘ |
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</lang> |
</lang> |
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Revision as of 16:53, 2 August 2015
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 McCormick function, and possibly other standard or well-known optimization test cases.
References:
J
<lang J> pso_init =: 3 : 0
'Min Max parameters nParticles' =. y smoutput 4 2 $ 'Min';Min;'Max';Max;'omega, phip, phig';parameters;'nParticles';nParticles Range =. Max - Min nDims =. #Min searchSpaceBounds =. |: (2,nDims) $ Min, Max rnd =. (1e6%~ ? (nParticles,nDims) $ 1e6) pos =. |: Min + Range * |: rnd bpos =. pos bval =. (#pos) $ _ vel =. ($pos) $ 0 0;_;_;Min;Max;parameters;pos;vel;bpos;bval NB. initial state
)
pso =: 3 : 0
NB. previous state 'iter gbpos gbval Min Max parameters pos vel bpos0 bval' =: y
NB. evaluate val =: pso_function"1 pos
NB. update better =: val < bval bpos =: (better * pos) + ((1-better) * bpos0) bval =: pso_function"1 bpos gbval =: <./,bval gmask =: gbval = bval gindex =: +/(gmask*(i.#gmask)) gbpos =: gindex { bpos
NB. migrate omega =: 0{parameters phip =: 1{parameters phig =: 2{parameters rp =: 1e6%~?(#pos)$1e6 rg =: 1e6%~?1e6 vel =: (omega*vel) + (phip * rp * (bpos-pos)) + (phig * rg * (gbpos -"1 1 pos)) pos =: pos + vel
NB. reset out-of-bounds particles pmask =: Min <"1 pos +. pos <"1 Max rnd =: (1e6%~ ? ($pos) $ 1e6) Range =: Max - Min newpos =: |: Min + Range * |: rnd pos =: (pmask * pos) + ((1-pmask) * newpos) iter =: >: iter
NB. new state iter;gbpos;gbval;Min;Max;parameters;pos;vel;bpos;bval
)
</lang> Apply to McCormick Function: <lang J>
load'trig' pso_function =: 3 : 0 (sin (0{y)+(1{y)) + (((0{y) - (1{y))^2) + (_1.5 * (0{y)) + (2.5 * (1{y)) + 1 )
state =: pso_init _1.5 _3 ; 4 4 ; 0 0.6 0.3; 100
┌─────────────────┬─────────┐ │Min │_1.5 _3 │ ├─────────────────┼─────────┤ │Max │4 4 │ ├─────────────────┼─────────┤ │omega, phip, phig│0 0.6 0.3│ ├─────────────────┼─────────┤ │nParticles │100 │ └─────────────────┴─────────┘
state =: pso^:40 state smoutput |: 2 3 $ 'Iteration';'GlobalBestPosition';'GlobalBestValue';iter;gbpos;gbval
┌──────────────────┬──────────────────┐ │Iteration │40 │ ├──────────────────┼──────────────────┤ │GlobalBestPosition│_0.547599 _1.54788│ ├──────────────────┼──────────────────┤ │GlobalBestValue │_1.91322 │ └──────────────────┴──────────────────┘ </lang>
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