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Particle swarm optimization: Difference between revisions

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Particle swarm optimization (view source)

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=={{header|C sharp|C#}}==
{{trans|java}}
<langsyntaxhighlight lang="csharp">using System;
 
namespace ParticleSwarmOptimization {
Line 245:
}
}
}</langsyntaxhighlight>
{{out}}
<pre>Test Function : McCormick
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=={{header|C++}}==
{{trans|D}}
<langsyntaxhighlight lang="cpp">#include <algorithm>
#include <functional>
#include <iostream>
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state.report("Michalewicz (2D)");
std::cout << "f(2.20, 1.57) : " << michalewicz({ 2.2, 1.57 }) << '\n';
}</langsyntaxhighlight>
{{out}}
<pre>Test Function : McCormick
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=={{header|D}}==
{{trans|Kotlin}}
<langsyntaxhighlight Dlang="d">import std.math;
import std.random;
import std.stdio;
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state.report("Michalewicz (2D)");
writefln("f(2.20, 1.57) : %.16f", michalewicz([2.2, 1.57]));
}</langsyntaxhighlight>
{{out}}
<pre>Test Function : McCormick
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=={{header|Go}}==
{{trans|Kotlin}}
<langsyntaxhighlight lang="go">package main
 
import (
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st.report("Michalewicz (2D)")
fmt.Println("f(2.20, 1.57) :", michalewicz([]float64{2.2, 1.57}))
</syntaxhighlight>
</lang>
 
{{out}}
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=={{header|J}}==
<langsyntaxhighlight Jlang="j">load 'format/printf'
 
pso_init =: verb define
Line 951:
)
 
reportState=: 'Iteration: %j\nGlobalBestPosition: %j\nGlobalBestValue: %j\n' printf 3&{.</langsyntaxhighlight>
Apply to McCormick Function:<langsyntaxhighlight Jlang="j"> require 'trig'
mccormick =: sin@(+/) + *:@(-/) + 1 + _1.5 2.5 +/@:* ]
 
Line 965:
Iteration: 40
GlobalBestPosition: _0.547399 _1.54698
GlobalBestValue: _1.91322</langsyntaxhighlight>
Apply to Michalewicz Function:
<langsyntaxhighlight Jlang="j"> michalewicz =: 3 : '- +/ (sin y) * 20 ^~ sin (>: i. #y) * (*:y) % pi'
michalewicz =: [: -@(+/) sin * 20 ^~ sin@(pi %~ >:@i.@# * *:) NB. tacit equivalent
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Iteration: 30
GlobalBestPosition: 2.20296 1.57083
GlobalBestValue: _1.8013</langsyntaxhighlight>
 
=={{header|Java}}==
{{trans|Kotlin}}
<langsyntaxhighlight lang="java">import java.util.Arrays;
import java.util.Objects;
import java.util.Random;
Line 1,177:
System.out.printf("f(2.20, 1.57) : %.15f\n", michalewicz(new double[]{2.20, 1.57}));
}
}</langsyntaxhighlight>
{{out}}
<pre>Test Function : McCormick
Line 1,195:
Translation of [[Particle_Swarm_Optimization#J|J]].
 
<langsyntaxhighlight JavaScriptlang="javascript">function pso_init(y) {
var nDims= y.min.length;
var pos=[], vel=[], bpos=[], bval=[];
Line 1,306:
state= repeat(function(y){return pso(mccormick,y)}, 40, state);
 
reportState(state);</langsyntaxhighlight>
 
Example displayed result (random numbers are involved so there will be a bit of variance between repeated runs:
 
<syntaxhighlight lang="javascript">
<lang Javascript>
Iteration: 0
GlobalBestPosition: Infinity
Line 1,317:
Iteration: 40
GlobalBestPosition: -0.5134004259016365,-1.5512442672625184
GlobalBestValue: -1.9114053788600853</langsyntaxhighlight>
 
=={{header|Julia}}==
<langsyntaxhighlight lang="julia">using Optim
 
const mcclow = [-1.5, -3.0]
Line 1,339:
println(optimize(michalewicz, x0, ParticleSwarm(;lower=miclow, upper=micupp, n_particles=npar[2])))
@time optimize(michalewicz, x0, ParticleSwarm(;lower=miclow, upper=micupp, n_particles=npar[2]))
</langsyntaxhighlight>{{out}}
<pre>
Results of Optimization Algorithm
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=={{header|Kotlin}}==
{{trans|JavaScript}}
<langsyntaxhighlight lang="scala">// version 1.1.51
 
import java.util.Random
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state.report("Michalewicz (2D)")
println("f(2.20, 1.57) : ${michalewicz(doubleArrayOf(2.2, 1.57))}")
}</langsyntaxhighlight>
 
Sample output:
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f(2.20, 1.57) : -1.801140718473825
</pre>
 
=={{header|Nim}}==
{{trans|Kotlin}}
<syntaxhighlight lang="nim">import math, random, sequtils, sugar
 
type
 
Func = seq[float] -> float
 
Parameters = tuple[omega, phip, phig: float]
 
State = object
iter: int
gbpos: seq[float]
gbval: float
min, max: seq[float]
parameters: Parameters
pos, vel, bpos: seq[seq[float]]
bval: seq[float]
nParticles, nDims: int
 
 
func initState(min, max: seq[float]; parameters: Parameters; nParticles: int): State =
let nDims = min.len
State(iter: 0,
gbpos: repeat(Inf, nDims),
gbval: Inf,
min: min,
max: max,
parameters: parameters,
pos: repeat(min, nParticles),
vel: newSeqWith(nParticles,
newSeq[float](nDims)),
bpos: repeat(min, nParticles),
bval: repeat(Inf, nParticles),
nParticles: nParticles,
nDims: nDims)
 
 
proc report(state: State; testFunc: string) =
echo "Test Function: ", testfunc
echo "Iterations: ", state.iter
echo "Global Best Position: ", state.gbpos
echo "Global Best Value: ", state.gbval
 
 
proc pso(fn: Func; y: State): State =
let p = y.parameters
var v = newSeq[float](y.nParticles)
var bpos = repeat(y.min, y.nParticles)
var bval = newSeq[float](y.nParticles)
var gbpos = newSeq[float](y.nDims)
var gbval = Inf
 
for j in 0..<y.nParticles:
# evaluate.
v[j] = fn(y.pos[j])
# update.
if v[j] < y.bval[j]:
bpos[j] = y.pos[j]
bval[j] = v[j]
else:
bpos[j] = y.bpos[j]
bval[j] = y.bval[j]
if bval[j] < gbval:
gbval = bval[j]
gbpos = bpos[j]
 
let rg = rand(1.0)
var pos = newSeqWith(y.nParticles, newSeq[float](y.nDims))
var vel = newSeqWith(y.nParticles, newSeq[float](y.nDims))
for j in 0..<y.nParticles:
# migrate.
let rp = rand(1.0)
var ok = true
for k in 0..<y.nDims:
vel[j][k] = p.omega * y.vel[j][k] +
p.phip * rp * (bpos[j][k] - y.pos[j][k]) +
p.phig * rg * (gbpos[k] - y.pos[j][k])
pos[j][k] = y.pos[j][k] + vel[j][k]
ok = ok and y.min[k] < pos[j][k] and y.max[k] > pos[j][k]
if not ok:
for k in 0..<y.nDims:
pos[j][k]= y.min[k] + (y.max[k] - y.min[k]) * rand(1.0)
 
result = State(iter: 1 + y.iter,
gbpos: gbpos,
gbval: gbval,
min: y.min,
max: y.max,
parameters: y.parameters,
pos: pos,
vel: vel,
bpos: bpos,
bval: bval,
nParticles: y.nParticles,
nDims: y.nDims)
 
 
proc iterate(fn: Func; n: int; y: State): State =
result = y
if n == int.high:
while true:
let old = result
result = pso(fn, result)
if result == old: break
else:
for _ in 1..n:
result = pso(fn, result)
 
 
func mccormick(x: seq[float]): float =
let a = x[0]
let b = x[1]
result = sin(a + b) + (a - b) * (a - b) + 1.0 + 2.5 * b - 1.5 * a
 
 
func michalewicz(x: seq[float]): float =
const M = 10
for i in 1..x.len:
let j = x[i - 1]
let k = sin(i.toFloat * j * j / PI)
result -= sin(j) * k^(2 * M)
 
 
randomize()
 
var state = initState(min = @[-1.5, -3],
max = @[4.0, 4.0],
parameters = (0.0, 0.6, 0.3),
nParticles = 100)
 
state = iterate(mccormick, 40, state)
state.report("McCormick")
echo "f(-.54719, -1.54719): ", mccormick(@[-0.54719, -1.54719])
echo()
state = initState(min = @[0.0, 0.0],
max = @[PI, PI],
parameters = (0.3, 0.3, 0.3),
nParticles = 1000)
state = iterate(michalewicz, 30, state)
state.report("Michalewicz (2D)")
echo "f(2.20, 1.57): ", michalewicz(@[2.2, 1.57])</syntaxhighlight>
 
{{out}}
<pre>Test Function: McCormick
Iterations: 40
Global Best Position: @[-0.5470347980396687, -1.547176688676891]
Global Best Value: -1.913222920248667
f(-.54719, -1.54719): -1.913222954882274
 
Test Function: Michalewicz (2D)
Iterations: 30
Global Best Position: @[2.202898715299719, 1.570804023976923]
Global Best Value: -1.801303406946448
f(2.20, 1.57): -1.801140718473825</pre>
 
=={{header|ooRexx}}==
<langsyntaxhighlight lang="oorexx">/* REXX ---------------------------------------------------------------
* Test for McCormick function
*--------------------------------------------------------------------*/
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res=rxcalcsin(x+y,16,'R')+(x-y)**2-1.5*x+2.5*y+1
Return res
::requires rxmath library</langsyntaxhighlight>
{{out}}
<pre>-1.5 -2.5 -1.243197504692072
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=={{header|Perl}}==
{{trans|Raku}}
<langsyntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
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) );
%state = %{pso(\&michalewicz, %state)} for 1 .. 30;
report('Michalewicz', %state);</langsyntaxhighlight>
{{out}}
<pre>McCormick
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=={{header|Phix}}==
{{trans|Kotlin}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<lang Phix>enum OMEGA, PHIP, PHIG
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
enum ITER,GBPOS,GBVAL,MIN,MAX,PARAMS,POS,VEL,BPOS,BVAL,NPARTICLES,NDIMS
<span style="color: #008080;">enum</span> <span style="color: #000000;">OMEGA</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">PHIP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">PHIG</span>
 
<span style="color: #008080;">enum</span> <span style="color: #000000;">ITER</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">GBPOS</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">GBVAL</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">MIN</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">MAX</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">PARAMS</span><span style="color: #0000FF;">,</span>
constant inf = 1e308*1e308
<span style="color: #000000;">POS</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">VEL</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">BPOS</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">BVAL</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">NPARTICLES</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">NDIMS</span>
 
constant fmt = """
<span style="color: #008080;">constant</span> <span style="color: #000000;">inf</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e308</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1e308</span>
Test Function : %s
Iterations : %d
<span style="color: #008080;">constant</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
Global Best Position : %s
Global Test Function Best Value : %fs
Iterations : %d
"""
Global Best Position : %s
 
Global Best Value : %f
procedure report(sequence state, string testfunc)
"""</span>
printf(1,fmt,{testfunc,state[ITER],sprint(state[GBPOS]),state[GBVAL]})
end procedure
<span style="color: #008080;">procedure</span> <span style="color: #000000;">report</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">testfunc</span><span style="color: #0000FF;">)</span>
 
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">testfunc</span><span style="color: #0000FF;">,</span><span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ITER</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">GBPOS</span><span style="color: #0000FF;">]),</span><span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">GBVAL</span><span style="color: #0000FF;">]})</span>
function psoInit(sequence mins, maxs, params, integer nParticles)
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
integer nDims = length(mins), iter=0
atom gbval = inf
<span style="color: #008080;">function</span> <span style="color: #000000;">psoInit</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">mins</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">params</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">nParticles</span><span style="color: #0000FF;">)</span>
sequence gbpos = repeat(inf,nDims),
<span style="color: #004080;">integer</span> <span style="color: #000000;">nDims</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mins</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">iter</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span>
pos = repeat(mins,nParticles),
<span style="color: #004080;">atom</span> <span style="color: #000000;">gbval</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">inf</span>
vel = repeat(repeat(0,nDims),nParticles),
<span style="color: #004080;">sequence</span> <span style="color: #000000;">gbpos</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">inf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nDims</span><span style="color: #0000FF;">),</span>
bpos = repeat(mins,nParticles),
<span style="color: #000000;">pos</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mins</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nParticles</span><span style="color: #0000FF;">),</span>
bval = repeat(inf,nParticles)
<span style="color: #000000;">vel</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nDims</span><span style="color: #0000FF;">),</span><span style="color: #000000;">nParticles</span><span style="color: #0000FF;">),</span>
return {iter,gbpos,gbval,mins,maxs,params,pos,vel,bpos,bval,nParticles,nDims}
<span style="color: #000000;">bpos</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mins</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nParticles</span><span style="color: #0000FF;">),</span>
end function
<span style="color: #000000;">bval</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">inf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nParticles</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">iter</span><span style="color: #0000FF;">,</span><span style="color: #000000;">gbpos</span><span style="color: #0000FF;">,</span><span style="color: #000000;">gbval</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mins</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">params</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pos</span><span style="color: #0000FF;">,</span><span style="color: #000000;">vel</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bpos</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bval</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nParticles</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nDims</span><span style="color: #0000FF;">}</span>
function pso(integer fn, sequence state)
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
integer particles = state[NPARTICLES],
dims = state[NDIMS]
<span style="color: #008080;">function</span> <span style="color: #000000;">pso</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">)</span>
sequence p = state[PARAMS],
<span style="color: #004080;">integer</span> <span style="color: #000000;">particles</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">NPARTICLES</span><span style="color: #0000FF;">],</span>
v = repeat(0,particles),
<span style="color: #000000;">dims</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">NDIMS</span><span style="color: #0000FF;">]</span>
bpos = repeat(state[MIN],particles),
<span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">PARAMS</span><span style="color: #0000FF;">],</span>
bval = repeat(0,particles),
<span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">particles</span><span style="color: #0000FF;">),</span>
gbpos = repeat(0,dims)
<span style="color: #000000;">bpos</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MIN</span><span style="color: #0000FF;">],</span><span style="color: #000000;">particles</span><span style="color: #0000FF;">),</span>
atom gbval = inf
<span style="color: #000000;">bval</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">particles</span><span style="color: #0000FF;">),</span>
for j=1 to particles do
<span style="color: #000000;">gbpos</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dims</span><span style="color: #0000FF;">)</span>
-- evaluate
<span style="color: #004080;">atom</span> <span style="color: #000000;">gbval</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">inf</span>
v[j] = call_func(fn,{state[POS][j]})
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">particles</span> <span style="color: #008080;">do</span>
-- update
<span style="color: #000080;font-style:italic;">-- evaluate</span>
if v[j] < state[BVAL][j] then
<span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">fn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POS</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span>
bpos[j] = state[POS][j]
<span style="color: #000080;font-style:italic;">-- update</span>
bval[j] = v[j]
<span style="color: #008080;">if</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">BVAL</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
else
<span style="color: #000000;">bpos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POS</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
bpos[j] = state[BPOS][j]
<span style="color: #000000;">bval</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
bval[j] = state[BVAL][j]
<span style="color: #008080;">else</span>
end if
<span style="color: #000000;">bpos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">BPOS</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
if bval[j] < gbval then
<span style="color: #000000;">bval</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">BVAL</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
gbval = bval[j]
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
gbpos = bpos[j]
<span style="color: #008080;">if</span> <span style="color: #000000;">bval</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">gbval</span> <span style="color: #008080;">then</span>
end if
<span style="color: #000000;">gbval</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bval</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
end for
<span style="color: #000000;">gbpos</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bpos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
atom rg = rnd()
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
sequence pos = repeat(repeat(0,dims),particles),
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
vel = repeat(repeat(0,dims),particles)
<span style="color: #004080;">atom</span> <span style="color: #000000;">rg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">rnd</span><span style="color: #0000FF;">()</span>
for j=1 to particles do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">pos</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dims</span><span style="color: #0000FF;">),</span><span style="color: #000000;">particles</span><span style="color: #0000FF;">),</span>
-- migrate
<span style="color: #000000;">vel</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dims</span><span style="color: #0000FF;">),</span><span style="color: #000000;">particles</span><span style="color: #0000FF;">)</span>
atom rp = rnd()
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">particles</span> <span style="color: #008080;">do</span>
bool ok = true
<span style="color: #000080;font-style:italic;">-- migrate</span>
vel[j] = repeat(0,dims)
<span style="color: #004080;">atom</span> <span style="color: #000000;">rp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">rnd</span><span style="color: #0000FF;">()</span>
pos[j] = repeat(0,dims)
<span style="color: #004080;">bool</span> <span style="color: #000000;">ok</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
for k=1 to dims do
<span style="color: #000000;">vel</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dims</span><span style="color: #0000FF;">)</span>
vel[j][k] = p[OMEGA] * state[VEL][j][k] +
<span style="color: #000000;">pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dims</span><span style="color: #0000FF;">)</span>
p[PHIP] * rp * (bpos[j][k] - state[POS][j][k]) +
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">dims</span> <span style="color: #008080;">do</span>
p[PHIG] * rg * (gbpos[k] - state[POS][j][k])
<span style="color: #000000;">vel</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">OMEGA</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VEL</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span>
pos[j][k] = state[POS][j][k] + vel[j][k]
<span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">PHIP</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">rp</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">bpos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POS</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">+</span>
ok = ok and state[MIN][k] < pos[j][k] and state[MAX][k] > pos[j][k]
<span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">PHIG</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">rg</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">gbpos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POS</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span>
end for
<span style="color: #000000;">pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POS</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">vel</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
if not ok then
<span style="color: #000000;">ok</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ok</span> <span style="color: #008080;">and</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MIN</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">and</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MAX</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">></span> <span style="color: #000000;">pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
for k=1 to dims do
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
pos[j][k]= state[MIN][k] + (state[MAX][k] - state[MIN][k]) * rnd()
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">ok</span> <span style="color: #008080;">then</span>
end for
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">dims</span> <span style="color: #008080;">do</span>
end if
<span style="color: #000000;">pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MIN</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MAX</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MIN</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">rnd</span><span style="color: #0000FF;">()</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
integer iter = 1 + state[ITER]
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
return {iter, gbpos, gbval, state[MIN], state[MAX], state[PARAMS],
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
pos, vel, bpos, bval, particles, dims}
<span style="color: #004080;">integer</span> <span style="color: #000000;">iter</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ITER</span><span style="color: #0000FF;">]</span>
end function
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">iter</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">gbpos</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">gbval</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MIN</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">MAX</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">PARAMS</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">pos</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">vel</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bpos</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bval</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">particles</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dims</span><span style="color: #0000FF;">}</span>
function iterate(integer fn, n, sequence state)
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
sequence r = state,
old = state
<span style="color: #008080;">function</span> <span style="color: #000000;">iterate</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">)</span>
if n=-1 then
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">,</span>
while true do
<span style="color: #000000;">old</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span>
r = pso(fn, r)
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
if (r == old) then exit end if
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
old = r
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pso</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
end while
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">r</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">old</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
else
<span style="color: #000000;">old</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
for i=1 to n do
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
r = pso(fn, r)
<span style="color: #008080;">else</span>
end for
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
end if
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pso</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
return r
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
function mccormick(sequence x)
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
atom {a, b} = x
return sin(a + b) + (a - b) * (a - b) + 1.0 + 2.5 * b - 1.5 * a
<span style="color: #008080;">function</span> <span style="color: #000000;">mccormick</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
constant r_mccormick = routine_id("mccormick")
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">a</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">a</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">1.0</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">2.5</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">1.5</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function michalewicz(sequence x)
integer m = 10,
<span style="color: #008080;">function</span> <span style="color: #000000;">michalewicz</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
d = length(x)
<span style="color: #004080;">integer</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">,</span>
atom total = 0.0
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
for i=1 to d do
<span style="color: #004080;">atom</span> <span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.0</span>
atom j = x[i],
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">d</span> <span style="color: #008080;">do</span>
k = sin(i * j * j / PI)
<span style="color: #004080;">atom</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span>
total += sin(j) * power(k, 2.0 * m)
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">/</span> <span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #000000;">total</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.0</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
return -total
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end function
<span style="color: #008080;">return</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">total</span>
constant r_michalewicz = routine_id("michalewicz")
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
procedure main()
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
sequence mins = {-1.5, -3.0},
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mins</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">3.0</span><span style="color: #0000FF;">},</span>
maxs = {4.0, 4.0},
<span style="color: #000000;">maxs</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">4.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.0</span><span style="color: #0000FF;">},</span>
params = {0.0, 0.6, 0.3}
<span style="color: #000000;">params</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.3</span><span style="color: #0000FF;">}</span>
integer nParticles = 100
<span style="color: #004080;">integer</span> <span style="color: #000000;">nParticles</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</span>
sequence state = psoInit(mins,maxs,params,nParticles)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">state</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">psoInit</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mins</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">params</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nParticles</span><span style="color: #0000FF;">)</span>
state = iterate(r_mccormick, 40, state)
<span style="color: #000000;">state</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">iterate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mccormick</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">40</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">)</span>
report(state,"McCormick")
<span style="color: #000000;">report</span><span style="color: #0000FF;">(</span><span style="color: #000000;">state</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"McCormick"</span><span style="color: #0000FF;">)</span>
atom {x,y} = state[GBPOS]
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">GBPOS</span><span style="color: #0000FF;">]</span>
printf(1,"f(%.4f, %.4f) : %f\n\n",{x,y,mccormick({x,y})})
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"f(%.4f, %.4f) : %f\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mccormick</span><span style="color: #0000FF;">({</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">})})</span>
 
mins = {0.0, 0.0}
<span style="color: #000000;">mins</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0</span><span style="color: #0000FF;">}</span>
maxs = {PI, PI}
<span style="color: #000000;">maxs</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">PI</span><span style="color: #0000FF;">}</span>
params = {0.3, 0.3, 0.3}
<span style="color: #000000;">params</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.3</span><span style="color: #0000FF;">}</span>
nParticles = 1000
<span style="color: #000000;">nParticles</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000</span>
state = psoInit(mins,maxs,params,nParticles)
<span style="color: #000000;">state</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">psoInit</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mins</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">params</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nParticles</span><span style="color: #0000FF;">)</span>
state = iterate(r_michalewicz, 30, state)
<span style="color: #000000;">state</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">iterate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">michalewicz</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">30</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">)</span>
report(state,"Michalewicz (2D)")
<span style="color: #000000;">report</span><span style="color: #0000FF;">(</span><span style="color: #000000;">state</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Michalewicz (2D)"</span><span style="color: #0000FF;">)</span>
{x,y} = state[GBPOS]
<span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span><span style="color: #0000FF;">[</span><span style="color: #000000;">GBPOS</span><span style="color: #0000FF;">]</span>
printf(1,"f(%.5f, %.5f) : %f\n\n",{x,y,michalewicz({x,y})})
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"f(%.5f, %.5f) : %f\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">michalewicz</span><span style="color: #0000FF;">({</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">})})</span>
end procedure
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
main()</lang>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 1,887 ⟶ 2,045:
=={{header|Python}}==
{{trans|D}}
<langsyntaxhighlight lang="python">import math
import random
 
Line 2,018 ⟶ 2,176:
print "f(2.20, 1.57) : %.16f" % (michalewicz([2.2, 1.57]))
 
main()</langsyntaxhighlight>
{{out}}
<pre>Test Function : McCormick
Line 2,033 ⟶ 2,191:
 
=={{header|Racket}}==
<langsyntaxhighlight lang="racket">#lang racket/base
(require racket/list racket/math)
 
Line 2,111 ⟶ 2,269:
(PSO (Michalewitz 5) 1000 30 (box 0) (box pi) #:ω 0.3 #:φ_p 0.3 #:φ_g 0.3 #:> <)
(displayln "Michalewitz 10d [-9.66015]")
(PSO (Michalewitz 10) 1000 30 (box 0) (box pi) #:ω 0.3 #:φ_p 0.3 #:φ_g 0.3 #:> <)</langsyntaxhighlight>
{{out}}
 
Line 2,147 ⟶ 2,305:
(formerly Perl 6)
{{trans|J (via Javascript, Kotlin, D, Python)}}
<syntaxhighlight lang="raku" perl6line>sub pso-init (%y) {
my $d = @(%y{'min'});
my $n = %y{'n'};
Line 2,245 ⟶ 2,403:
} );
%state = pso(&michalewicz, %state) for 1 .. 30;
report 'Michalewicz', %state;</langsyntaxhighlight>
{{out}}
<pre>McCormick
Line 2,270 ⟶ 2,428:
 
Note that REXX uses decimal floating point, not binary.
<langsyntaxhighlight lang="rexx">/*REXX program calculates Particle Swarm Optimization as it migrates through a solution.*/
numeric digits length( pi() ) - length(.) /*use the number of decimal digs in pi.*/
parse arg x y d #part sDigs . /*obtain optional arguments from the CL*/
Line 2,305 ⟶ 2,463:
pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865; return pi
r2r: return arg(1) // ( pi() * 2) /*normalize radians ───► a unit circle.*/
sin: procedure; arg x; x= r2r(x); z=x; xx= x*x; do k=2 by 2 until p=z; p=z; x= -x* xx/ (k*(k+1)); z= z+x; end; return z</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
<pre>
Line 2,373 ⟶ 2,531:
Output note: &nbsp; the published global minimum (referenced above, as well as the function's arguments) can be found at:
::::: &nbsp; <u>[http://www.sfu.ca/~ssurjano/mccorm.html http://www.sfu.ca/~ssurjano/mccorm.html]</u>
 
<br><br>
=={{header|Wren}}==
{{trans|Kotlin}}
{{libheader|Wren-dynamic}}
<syntaxhighlight lang="wren">import "random" for Random
import "./dynamic" for Tuple
 
var Parameters = Tuple.create("Parameters", ["omega", "phip", "phig"])
 
var fields = [
"iter", "gbpos", "gbval", "min", "max", "parameters",
"pos", "vel", "bpos", "bval", "nParticles", "nDims"
]
 
var State = Tuple.create("State", fields)
 
var report = Fn.new { |state, testfunc|
System.print("Test Function : %(testfunc)")
System.print("Iterations : %(state.iter)")
System.print("Global Best Position : %(state.gbpos)")
System.print("Global Best Value : %(state.gbval)")
}
 
var psoInit = Fn.new { |min, max, parameters, nParticles|
var nDims = min.count
var pos = List.filled(nParticles, null)
var vel = List.filled(nParticles, null)
var bpos = List.filled(nParticles, null)
var bval = List.filled(nParticles, 1/0)
for (i in 0...nParticles) {
pos[i] = min.toList
vel[i] = List.filled(nDims, 0)
bpos[i] = min.toList
}
var iter = 0
var gbpos = List.filled(nDims, 1/0 )
var gbval = 1/0
return State.new(iter, gbpos, gbval, min, max, parameters,
pos, vel, bpos, bval, nParticles, nDims)
}
 
var r = Random.new()
 
var pso = Fn.new { |fn, y|
var p = y.parameters
var v = List.filled(y.nParticles, 0)
var bpos = List.filled(y.nParticles, null)
for (i in 0...y.nParticles) bpos[i] = y.min.toList
var bval = List.filled(y.nParticles, 0)
var gbpos = List.filled(y.nDims, 0)
var gbval = 1/0
for (j in 0...y.nParticles) {
// evaluate
v[j] = fn.call(y.pos[j])
// update
if (v[j] < y.bval[j]) {
bpos[j] = y.pos[j]
bval[j] = v[j]
} else {
bpos[j] = y.bpos[j]
bval[j] = y.bval[j]
}
if (bval[j] < gbval) {
gbval = bval[j]
gbpos = bpos[j]
}
}
var rg = r.float()
var pos = List.filled(y.nParticles, null)
var vel = List.filled(y.nParticles, null)
for (i in 0...y.nParticles) {
pos[i] = List.filled(y.nDims, 0)
vel[i] = List.filled(y.nDims, 0)
}
for (j in 0...y.nParticles) {
// migrate
var rp = r.float()
var ok = true
for (k in 0...y.nDims) {
vel[j][k] = p.omega * y.vel[j][k] +
p.phip * rp * (bpos[j][k] - y.pos[j][k]) +
p.phig * rg * (gbpos[k] - y.pos[j][k])
pos[j][k] = y.pos[j][k] + vel[j][k]
ok = ok && y.min[k] < pos[j][k] && y.max[k] > pos[j][k]
}
if (!ok) {
for (k in 0...y.nDims) {
pos[j][k]= y.min[k] + (y.max[k] - y.min[k]) * r.float()
}
}
}
var iter = 1 + y.iter
return State.new(
iter, gbpos, gbval, y.min, y.max, y.parameters,
pos, vel, bpos, bval, y.nParticles, y.nDims
)
}
 
var iterate = Fn.new { |fn, n, y|
var r = y
var old = y
if (n == 2147483647) {
while (true) {
r = pso.call(fn, r)
if (r == old) break
old = r
}
} else {
for (i in 1..n) r = pso.call(fn, r)
}
return r
}
 
var mccormick = Fn.new { |x|
var a = x[0]
var b = x[1]
return (a + b).sin + (a - b) * (a - b) + 1 + 2.5 * b - 1.5 * a
}
 
var michalewicz = Fn.new { |x|
var m = 10
var d = x.count
var sum = 0
for (i in 1..d) {
var j = x[i - 1]
var k = (i * j * j / Num.pi).sin
sum = sum + j.sin * k.pow(2 * m)
}
return -sum
}
 
var state = psoInit.call([-1.5, -3], [4, 4], Parameters.new(0, 0.6, 0.3), 100)
state = iterate.call(mccormick, 40, state)
report.call(state, "McCormick")
System.print("f(-0.54719, -1.54719) : %(mccormick.call([-0.54719, -1.54719]))")
System.print()
state = psoInit.call([0, 0], [Num.pi, Num.pi], Parameters.new(0.3, 0.3, 0.3), 1000)
state = iterate.call(michalewicz, 30, state)
report.call(state, "Michalewicz (2D)")
System.print("f(2.20, 1.57) : %(michalewicz.call([2.2, 1.57]))")</syntaxhighlight>
 
{{out}}
Sample run:
<pre>
Test Function : McCormick
Iterations : 40
Global Best Position : [-0.54763537556709, -1.5469760587453]
Global Best Value : -1.9132225000184
f(-0.54719, -1.54719) : -1.9132229548823
 
Test Function : Michalewicz (2D)
Iterations : 30
Global Best Position : [2.2029075565418, 1.570796180786]
Global Best Value : -1.8013034100303
f(2.20, 1.57) : -1.8011407184738
</pre>
PureFox
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