Particle swarm optimization: Difference between revisions
m
→{{header|Wren}}: Minor tidy
(julia example) |
m (→{{header|Wren}}: Minor tidy) |
||
(17 intermediate revisions by 9 users not shown) | |||
Line 4:
</p>
<p>
The goal of parameter selection is to ensure that the global minimum is discriminated from any local minima, and that the minimum is accurately determined, and that convergence is achieved with
<ul>
<li> McCormick function - bowl-shaped, with a single minimum
Line 40:
</p>
<br><br>
=={{header|C sharp|C#}}==
{{trans|java}}
<syntaxhighlight lang="csharp">using System;
namespace ParticleSwarmOptimization {
public struct Parameters {
public double omega, phip, phig;
public Parameters(double omega, double phip, double phig) : this() {
this.omega = omega;
this.phip = phip;
this.phig = phig;
}
}
public struct State {
public int iter;
public double[] gbpos;
public double gbval;
public double[] min;
public double[] max;
public Parameters parameters;
public double[][] pos;
public double[][] vel;
public double[][] bpos;
public double[] bval;
public int nParticles;
public int nDims;
public State(int iter, double[] gbpos, double gbval, double[] min, double[] max, Parameters parameters, double[][] pos, double[][] vel, double[][] bpos, double[] bval, int nParticles, int nDims) : this() {
this.iter = iter;
this.gbpos = gbpos;
this.gbval = gbval;
this.min = min;
this.max = max;
this.parameters = parameters;
this.pos = pos;
this.vel = vel;
this.bpos = bpos;
this.bval = bval;
this.nParticles = nParticles;
this.nDims = nDims;
}
public void Report(string testfunc) {
Console.WriteLine("Test Function : {0}", testfunc);
Console.WriteLine("Iterations : {0}", iter);
Console.WriteLine("Global Best Position : {0}", string.Join(", ", gbpos));
Console.WriteLine("Global Best Value : {0}", gbval);
}
}
class Program {
public static State PsoInit(double[] min, double[] max, Parameters parameters, int nParticles) {
var nDims = min.Length;
double[][] pos = new double[nParticles][];
for (int i = 0; i < nParticles; i++) {
pos[i] = new double[min.Length];
min.CopyTo(pos[i], 0);
}
double[][] vel = new double[nParticles][];
for (int i = 0; i < nParticles; i++) {
vel[i] = new double[nDims];
}
double[][] bpos = new double[nParticles][];
for (int i = 0; i < nParticles; i++) {
bpos[i] = new double[min.Length];
min.CopyTo(bpos[i], 0);
}
double[] bval = new double[nParticles];
for (int i = 0; i < nParticles; i++) {
bval[i] = double.PositiveInfinity;
}
int iter = 0;
double[] gbpos = new double[nDims];
for (int i = 0; i < nDims; i++) {
gbpos[i] = double.PositiveInfinity;
}
double gbval = double.PositiveInfinity;
return new State(iter, gbpos, gbval, min, max, parameters, pos, vel, bpos, bval, nParticles, nDims);
}
static Random r = new Random();
public static State Pso(Func<double[], double> fn, State y) {
var p = y.parameters;
double[] v = new double[y.nParticles];
double[][] bpos = new double[y.nParticles][];
for (int i = 0; i < y.nParticles; i++) {
bpos[i] = new double[y.min.Length];
y.min.CopyTo(bpos[i], 0);
}
double[] bval = new double[y.nParticles];
double[] gbpos = new double[y.nDims];
double gbval = double.PositiveInfinity;
for (int j = 0; j < y.nParticles; j++) {
// evaluate
v[j] = fn.Invoke(y.pos[j]);
// update
if (v[j] < y.bval[j]) {
y.pos[j].CopyTo(bpos[j], 0);
bval[j] = v[j];
}
else {
y.bpos[j].CopyTo(bpos[j], 0);
bval[j] = y.bval[j];
}
if (bval[j] < gbval) {
gbval = bval[j];
bpos[j].CopyTo(gbpos, 0);
}
}
double rg = r.NextDouble();
double[][] pos = new double[y.nParticles][];
double[][] vel = new double[y.nParticles][];
for (int i = 0; i < y.nParticles; i++) {
pos[i] = new double[y.nDims];
vel[i] = new double[y.nDims];
}
for (int j = 0; j < y.nParticles; j++) {
// migrate
double rp = r.NextDouble();
bool ok = true;
for (int k = 0; k < y.nDims; k++) {
vel[j][k] = 0.0;
pos[j][k] = 0.0;
}
for (int k = 0; k < y.nDims; k++) {
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 (int k = 0; k < y.nDims; k++) {
pos[j][k] = y.min[k] + (y.max[k] - y.min[k]) * r.NextDouble();
}
}
}
var iter = 1 + y.iter;
return new State(iter, gbpos, gbval, y.min, y.max, y.parameters, pos, vel, bpos, bval, y.nParticles, y.nDims);
}
public static State Iterate(Func<double[], double> fn, int n, State y) {
State r = y;
if (n == int.MaxValue) {
State old = y;
while (true) {
r = Pso(fn, r);
if (r.Equals(old)) break;
old = r;
}
}
else {
for (int i = 0; i < n; i++) {
r = Pso(fn, r);
}
}
return r;
}
public static double Mccormick(double[] x) {
var a = x[0];
var b = x[1];
return Math.Sin(a + b) + (a - b) * (a - b) + 1.0 + 2.5 * b - 1.5 * a;
}
public static double Michalewicz(double[] x) {
int m = 10;
int d = x.Length;
double sum = 0.0;
for (int i = 1; i < d; i++) {
var j = x[i - 1];
var k = Math.Sin(i * j * j / Math.PI);
sum += Math.Sin(j) * Math.Pow(k, 2.0 * m);
}
return -sum;
}
static void Main(string[] args) {
var state = PsoInit(
new double[] { -1.5, -3.0 },
new double[] { 4.0, 4.0 },
new Parameters(0.0, 0.6, 0.3),
100
);
state = Iterate(Mccormick, 40, state);
state.Report("McCormick");
Console.WriteLine("f(-.54719, -1.54719) : {0}", Mccormick(new double[] { -.54719, -1.54719 }));
Console.WriteLine();
state = PsoInit(
new double[] { -0.0, -0.0 },
new double[] { Math.PI, Math.PI },
new Parameters(0.3, 0.3, 0.3),
1000
);
state = Iterate(Michalewicz, 30, state);
state.Report("Michalewicz (2D)");
Console.WriteLine("f(2.20, 1.57) : {0}", Michalewicz(new double[] { 2.20, 1.57 }));
}
}
}</syntaxhighlight>
{{out}}
<pre>Test Function : McCormick
Iterations : 40
Global Best Position : -0.546850526417689, -1.54649614884518
Global Best Value : -1.91322235333426
f(-.54719, -1.54719) : -1.91322295488227
Test Function : Michalewicz (2D)
Iterations : 30
Global Best Position : 2.20290514143486, 2.20798457238775
Global Best Value : -0.801303410096221
f(2.20, 1.57) : -0.801166387820286</pre>
=={{header|C++}}==
{{trans|D}}
<
#include <functional>
#include <iostream>
Line 317 ⟶ 535:
state.report("Michalewicz (2D)");
std::cout << "f(2.20, 1.57) : " << michalewicz({ 2.2, 1.57 }) << '\n';
}</
{{out}}
<pre>Test Function : McCormick
Line 330 ⟶ 548:
Global Best Value : -0.801303
f(2.20, 1.57) : -0.801166</pre>
=={{header|D}}==
{{trans|Kotlin}}
<
import std.random;
import std.stdio;
Line 716:
state.report("Michalewicz (2D)");
writefln("f(2.20, 1.57) : %.16f", michalewicz([2.2, 1.57]));
}</
{{out}}
<pre>Test Function : McCormick
Line 732:
=={{header|Go}}==
{{trans|Kotlin}}
<
import (
Line 888:
st.report("Michalewicz (2D)")
fmt.Println("f(2.20, 1.57) :", michalewicz([]float64{2.2, 1.57}))
</syntaxhighlight>
{{out}}
Line 907:
=={{header|J}}==
<
pso_init =: verb define
Line 951:
)
reportState=: 'Iteration: %j\nGlobalBestPosition: %j\nGlobalBestValue: %j\n' printf 3&{.</
Apply to McCormick Function:<
mccormick =: sin@(+/) + *:@(-/) + 1 + _1.5 2.5 +/@:* ]
Line 965:
Iteration: 40
GlobalBestPosition: _0.547399 _1.54698
GlobalBestValue: _1.91322</
Apply to Michalewicz Function:
<
michalewicz =: [: -@(+/) sin * 20 ^~ sin@(pi %~ >:@i.@# * *:) NB. tacit equivalent
Line 980:
Iteration: 30
GlobalBestPosition: 2.20296 1.57083
GlobalBestValue: _1.8013</
=={{header|Java}}==
{{trans|Kotlin}}
<
import java.util.Objects;
import java.util.Random;
Line 1,305 ⟶ 1,177:
System.out.printf("f(2.20, 1.57) : %.15f\n", michalewicz(new double[]{2.20, 1.57}));
}
}</
{{out}}
<pre>Test Function : McCormick
Line 1,318 ⟶ 1,190:
Global Best value : -0.801303410098550
f(2.20, 1.57) : -0.801166387820286</pre>
=={{header|JavaScript}}==
Translation of [[Particle_Swarm_Optimization#J|J]].
<syntaxhighlight lang="javascript">function pso_init(y) {
var nDims= y.min.length;
var pos=[], vel=[], bpos=[], bval=[];
for (var j= 0; j<y.nParticles; j++) {
pos[j]= bpos[j]= y.min;
var v= []; for (var k= 0; k<nDims; k++) v[k]= 0;
vel[j]= v;
bval[j]= Infinity}
return {
iter: 0,
gbpos: Infinity,
gbval: Infinity,
min: y.min,
max: y.max,
parameters: y.parameters,
pos: pos,
vel: vel,
bpos: bpos,
bval: bval,
nParticles: y.nParticles,
nDims: nDims}
}
function pso(fn, state) {
var y= state;
var p= y.parameters;
var val=[], bpos=[], bval=[], gbval= Infinity, gbpos=[];
for (var j= 0; j<y.nParticles; j++) {
// evaluate
val[j]= fn.apply(null, y.pos[j]);
// update
if (val[j] < y.bval[j]) {
bpos[j]= y.pos[j];
bval[j]= val[j];
} else {
bpos[j]= y.bpos[j];
bval[j]= y.bval[j]}
if (bval[j] < gbval) {
gbval= bval[j];
gbpos= bpos[j]}}
var rg= Math.random(), vel=[], pos=[];
for (var j= 0; j<y.nParticles; j++) {
// migrate
var rp= Math.random(), ok= true;
vel[j]= [];
pos[j]= [];
for (var k= 0; k < y.nDims; k++) {
vel[j][k]= p.omega*y.vel[j][k] + p.phip*rp*(bpos[j]-y.pos[j]) + p.phig*rg*(gbpos-y.pos[j]);
pos[j][k]= y.pos[j]+vel[j][k];
ok= ok && y.min[k]<pos[j][k] && y.max>pos[j][k];}
if (!ok)
for (var k= 0; k < y.nDims; k++)
pos[j][k]= y.min[k] + (y.max[k]-y.min[k])*Math.random()}
return {
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}
}
function display(text) {
if (document) {
var o= document.getElementById('o');
if (!o) {
o= document.createElement('pre');
o.id= 'o';
document.body.appendChild(o)}
o.innerHTML+= text+'\n';
window.scrollTo(0,document.body.scrollHeight);
}
if (console.log) console.log(text)
}
function reportState(state) {
var y= state;
display('');
display('Iteration: '+y.iter);
display('GlobalBestPosition: '+y.gbpos);
display('GlobalBestValue: '+y.gbval);
}
function repeat(fn, n, y) {
var r=y, old= y;
if (Infinity == n)
while ((r= fn(r)) != old) old= r;
else
for (var j= 0; j<n; j++) r= fn(r);
return r
}
function mccormick(a,b) {
return Math.sin(a+b) + Math.pow(a-b,2) + (1 + 2.5*b - 1.5*a)
}
state= pso_init({
min: [-1.5,-3], max:[4,4],
parameters: {omega: 0, phip: 0.6, phig: 0.3},
nParticles: 100});
reportState(state);
state= repeat(function(y){return pso(mccormick,y)}, 40, state);
reportState(state);</syntaxhighlight>
Example displayed result (random numbers are involved so there will be a bit of variance between repeated runs:
<syntaxhighlight lang="javascript">
Iteration: 0
GlobalBestPosition: Infinity
GlobalBestValue: Infinity
Iteration: 40
GlobalBestPosition: -0.5134004259016365,-1.5512442672625184
GlobalBestValue: -1.9114053788600853</syntaxhighlight>
=={{header|Julia}}==
<
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]))
</
<pre>
Results of Optimization Algorithm
Line 1,377:
* Objective Calls: 1001001
* Gradient Calls: 0
</pre>
=={{header|Kotlin}}==
{{trans|JavaScript}}
<
import java.util.Random
Line 1,539 ⟶ 1,538:
state.report("Michalewicz (2D)")
println("f(2.20, 1.57) : ${michalewicz(doubleArrayOf(2.2, 1.57))}")
}</
Sample output:
Line 1,555 ⟶ 1,554:
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}}==
<
* Test for McCormick function
*--------------------------------------------------------------------*/
Line 1,592 ⟶ 1,747:
res=rxcalcsin(x+y,16,'R')+(x-y)**2-1.5*x+2.5*y+1
Return res
::requires rxmath library</
{{out}}
<pre>-1.5 -2.5 -1.243197504692072
Line 1,610 ⟶ 1,765:
and differs from published -1.9133</pre>
=={{header|
{{trans|
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
use constant
use constant Inf => 1e10;
sub pso_init {
my(%y) = @_;
my $d = @{$y{'min'}};
my $n = $y{'n'};
$y{'gbval'} = Inf;
$y{'gbpos'} = [(Inf) x $d];
$y{'bval'} = [(Inf) x $n];
$y{'bpos'} = [($y{'min'}) x $n];
$y{'pos'} = [($y{'min'}) x $n];
$y{'vel'} = [([(0) x $d]) x $n];
%y
}
sub pso {
my $d = @{$y{'min'}};
my @bpos = ($y{'min'}) x $n;
my $gbval = Inf;
my (@pos, @vel, @v, @gbpos, @bval);
for my $j (0 .. $n-1) {
$v[$j] = &$fn(@{$y{'pos'}[$j]}); # evaluate
# update
if ($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] < $gbval) {
@gbpos = @{$bpos[$j]};
$gbval = $bval[$j];
}
}
# migrate
for my $j (0 .. $n-1) {
my $rand_p = rand;
my $ok = 1;
for my $k (0 .. $d-1) {
$vel[$j][$k] = $$p{'omega'} * $y{'vel'}[$j][$k]
+ $$p{'phi_p'} * $rand_p * ($bpos[$j][$k] - $y{'pos'}[$j][$k])
+ $$p{'phi_g'} * $rand_g * ($gbpos[$k] - $y{'pos'}[$j][$k]);
$pos[$j][$k] = $y{'pos'}[$j][$k] + $vel[$j][$k];
$ok = ($y{'min'}[$k] < $pos[$j][$k]) && ($pos[$j][$k] < $y{'max'}[$k]) && $ok;
}
next if $ok;
$pos[$j][$_] = $y{'min'}[$_] + ($y{'max'}[$_] - $y{'min'}[$_]) * rand for 0 .. $d-1;
}
return {gbpos => \@gbpos, gbval => $gbval, bpos => \@bpos, bval => \@bval, pos => \@pos, vel => \@vel,
min => $y{'min'}, max => $y{'max'}, p=> $y{'p'}, n => $n};
}
sub report {
my($function_name, %state) = @_;
say $function_name;
say 'Global best position: ' . sprintf "%.5f %.5f", @{$state{'gbpos'}};
say 'Global best value: ' . sprintf "%.5f", $state{'gbval'};
say '';
}
# McCormick
sub mccormick {
my($a,$b) = @_;
sin($a+$b) + ($a-$b)**2 + (1 + 2.5*$b - 1.5*$a)
}
my %state = pso_init( (
min => [-1.5, -3],
max => [4, 4],
n => 100,
p => {omega => 0, phi_p => 0.6, phi_g => 0.3},
) );
%state = %{pso(\&mccormick, %state)} for 1 .. 40;
report('McCormick', %state);
# Michalewicz
sub michalewicz {
my(@x) = @_;
my $sum;
my $m = 10;
for my $i (1..@x) {
my $j = $x[$i - 1];
my $k = sin($i * $j**2/PI);
$sum += sin($j) * $k**(2*$m)
}
-$sum
}
%state = pso_init( (
min => [0, 0],
max => [PI, PI],
n => 1000,
p => {omega => 0.3, phi_p => 0.3, phi_g => 0.3},
) );
%state = %{pso(\&michalewicz, %state)} for 1 .. 30;
report('Michalewicz', %state);</syntaxhighlight>
{{out}}
<pre>McCormick
Global best position: -0.54675 -1.54665
Global best value: -1.91322
Michalewicz
Global best position: 2.20293 1.57080
Global best value: -1.80130</pre>
=={{header|Phix}}==
{{trans|Kotlin}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<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>
<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: #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>
<span style="color: #008080;">constant</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
Test Function : %s
Iterations : %d
Global Best Position : %s
Global Best Value : %f
"""</span>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<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>
<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>
<span style="color: #004080;">atom</span> <span style="color: #000000;">gbval</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">inf</span>
<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>
<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>
<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>
<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>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<span style="color: #004080;">atom</span> <span style="color: #000000;">gbval</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">inf</span>
<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>
<span style="color: #000080;font-style:italic;">-- evaluate</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;">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>
<span style="color: #000080;font-style:italic;">-- update</span>
<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>
<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>
<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>
<span style="color: #008080;">else</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: #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>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<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>
<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>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<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>
<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>
<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>
<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>
<span style="color: #000080;font-style:italic;">-- migrate</span>
<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>
<span style="color: #004080;">bool</span> <span style="color: #000000;">ok</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</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: #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;">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>
<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>
<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>
<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>
<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>
<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>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">ok</span> <span style="color: #008080;">then</span>
<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>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<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>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<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>
<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>
<span style="color: #000000;">old</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">state</span>
<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>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<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>
<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>
<span style="color: #000000;">old</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">else</span>
<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>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<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>
<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>
<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>
<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>
<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>
<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>
<span style="color: #004080;">atom</span> <span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.0</span>
<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>
<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>
<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>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">total</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</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: #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>
<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>
<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>
<span style="color: #004080;">integer</span> <span style="color: #000000;">nParticles</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</span>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<span style="color: #000000;">nParticles</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000</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>
<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>
<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>
<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>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 1,763 ⟶ 2,042:
f(2.20291, 1.57080) : -1.801303
</pre>
=={{header|Python}}==
{{trans|D}}
<syntaxhighlight lang="python">import math
import random
INFINITY = 1 << 127
MAX_INT = 1 << 31
class Parameters:
def __init__(self, omega, phip, phig):
self.omega = omega
self.phip = phip
self.phig = phig
class State:
def __init__(self, iter, gbpos, gbval, min, max, parameters, pos, vel, bpos, bval, nParticles, nDims):
self.iter = iter
self.gbpos = gbpos
self.gbval = gbval
self.min = min
self.max = max
self.parameters = parameters
self.pos = pos
self.vel = vel
self.bpos = bpos
self.bval = bval
self.nParticles = nParticles
self.nDims = nDims
def report(self, testfunc):
print "Test Function :", testfunc
print "Iterations :", self.iter
print "Global Best Position :", self.gbpos
print "Global Best Value : %.16f" % self.gbval
def uniform01():
v = random.random()
assert 0.0 <= v and v < 1.0
return v
def psoInit(min, max, parameters, nParticles):
nDims = len(min)
pos = [min[:]] * nParticles
vel = [[0.0] * nDims] * nParticles
bpos = [min[:]] * nParticles
bval = [INFINITY] * nParticles
iter = 0
gbpos = [INFINITY] * nDims
gbval = INFINITY
return State(iter, gbpos, gbval, min, max, parameters, pos, vel, bpos, bval, nParticles, nDims);
def pso(fn, y):
p = y.parameters
v = [0.0] * (y.nParticles)
bpos = [y.min[:]] * (y.nParticles)
bval = [0.0] * (y.nParticles)
gbpos = [0.0] * (y.nDims)
gbval = INFINITY
for j in xrange(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][:]
rg = uniform01()
pos = [[None] * (y.nDims)] * (y.nParticles)
vel = [[None] * (y.nDims)] * (y.nParticles)
for j in xrange(0, y.nParticles):
# migrate
rp = uniform01()
ok = True
vel[j] = [0.0] * (len(vel[j]))
pos[j] = [0.0] * (len(pos[j]))
for k in xrange(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 xrange(0, y.nDims):
pos[j][k] = y.min[k] + (y.max[k] - y.min[k]) * uniform01()
iter = 1 + y.iter
return State(iter, gbpos, gbval, y.min, y.max, y.parameters, pos, vel, bpos, bval, y.nParticles, y.nDims);
def iterate(fn, n, y):
r = y
old = y
if n == MAX_INT:
while True:
r = pso(fn, r)
if r == old:
break
old = r
else:
for _ in xrange(0, n):
r = pso(fn, r)
return r
def mccormick(x):
(a, b) = x
return math.sin(a + b) + (a - b) * (a - b) + 1.0 + 2.5 * b - 1.5 * a
def michalewicz(x):
m = 10
d = len(x)
sum = 0.0
for i in xrange(1, d):
j = x[i - 1]
k = math.sin(i * j * j / math.pi)
sum += math.sin(j) * k ** (2.0 * m)
return -sum
def main():
state = psoInit([-1.5, -3.0], [4.0, 4.0], Parameters(0.0, 0.6, 0.3), 100)
state = iterate(mccormick, 40, state)
state.report("McCormick")
print "f(-.54719, -1.54719) : %.16f" % (mccormick([-.54719, -1.54719]))
print
state = psoInit([0.0, 0.0], [math.pi, math.pi], Parameters(0.3, 0.3, 0.3), 1000)
state = iterate(michalewicz, 30, state)
state.report("Michalewicz (2D)")
print "f(2.20, 1.57) : %.16f" % (michalewicz([2.2, 1.57]))
main()</syntaxhighlight>
{{out}}
<pre>Test Function : McCormick
Iterations : 40
Global Best Position : [-0.5471069930124911, -1.5471582891466962]
Global Best Value : -1.9132229450518705
f(-.54719, -1.54719) : -1.9132229548822739
Test Function : Michalewicz (2D)
Iterations : 30
Global Best Position : [2.2029052187108036, 0.9404640520657541]
Global Best Value : -0.8013034100970750
f(2.20, 1.57) : -0.8011663878202856</pre>
=={{header|Racket}}==
<
(require racket/list racket/math)
Line 1,843 ⟶ 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 #:> <)</
{{out}}
Line 1,875 ⟶ 2,301:
1.8558804696523914)
-6.432092623300999</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{trans|J (via Javascript, Kotlin, D, Python)}}
<syntaxhighlight lang="raku" line>sub pso-init (%y) {
my $d = @(%y{'min'});
my $n = %y{'n'};
%y{'gbval'} = Inf;
%y{'gbpos'} = [Inf xx $d];
%y{'bval'} = [Inf xx $n];
%y{'bpos'} = [%y{'min'} xx $n];
%y{'pos'} = [%y{'min'} xx $n];
%y{'vel'} = [[0 xx $d] xx $n];
%y;
}
sub pso (&fn, %y) {
my %p = %y{'p'};
my $n = %y{'n'};
my $d = @(%y{'min'});
my @bpos = %y{'min'} xx $n;
my $gbval = Inf;
my $rand-g = rand;
my (@pos, @vel, @v, @gbpos, @bval);
for 0 ..^ $n -> \j {
@v[j] = &fn(%y{'pos'}[j]); # evaluate
# 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];
}
}
# migrate
for 0 ..^ $n -> \j {
my $rand-p = rand;
my $ok = True;
for 0 ..^ $d -> \k {
@vel[j;k] = %p{'ω'} × %y{'vel'}[j;k]
+ %p{'φ-p'} × $rand-p × (@bpos[j;k] - %y{'pos'}[j;k])
+ %p{'φ-g'} × $rand-g × (@gbpos[k] - %y{'pos'}[j;k]);
@pos[j;k] = %y{'pos'}[j;k] + @vel[j;k];
$ok = %y{'min'}[k] < @pos[j;k] < %y{'max'}[k] if $ok;
}
next if $ok;
@pos[j;$_] = %y{'min'}[$_] + (%y{'max'}[$_] - %y{'min'}[$_]) × rand for 0 ..^ $d;
}
return {gbpos => @gbpos, gbval => $gbval, bpos => @bpos, bval => @bval, pos => @pos, vel => @vel,
min => %y{'min'}, max => %y{'max'}, p=> %y{'p'}, n => $n}
}
sub report ($function-name, %state) {
say $function-name;
say '🌐 best position: ' ~ %state{'gbpos'}.fmt('%.5f');
say '🌐 best value: ' ~ %state{'gbval'}.fmt('%.5f');
say '';
}
sub mccormick (@x) {
my ($a,$b) = @x;
sin($a+$b) + ($a-$b)**2 + (1 + 2.5×$b - 1.5×$a)
}
my %state = pso-init( {
min => [-1.5, -3],
max => [4, 4],
n => 100,
p => {ω=> 0, φ-p=> 0.6, φ-g=> 0.3},
} );
%state = pso(&mccormick, %state) for 1 .. 40;
report 'McCormick', %state;
sub michalewicz (@x) {
my $sum;
my $m = 10;
for 1..@x -> $i {
my $j = @x[$i-1];
my $k = sin($i × $j**2/π);
$sum += sin($j) × $k**(2×$m)
}
-$sum
}
%state = pso-init( {
min => [0, 0],
max => [π, π],
n => 1000,
p => {ω=> 0.3, φ-p=> 0.3, φ-g=> 0.3},
} );
%state = pso(&michalewicz, %state) for 1 .. 30;
report 'Michalewicz', %state;</syntaxhighlight>
{{out}}
<pre>McCormick
🌐 best position: -0.54714 -1.54710
🌐 best value: -1.91322
Michalewicz
🌐 best position: 2.20291 1.57080
🌐 best value: -1.80130</pre>
=={{header|REXX}}==
Line 1,891 ⟶ 2,428:
Note that REXX uses decimal floating point, not binary.
<
numeric digits length( pi() ) -
parse arg x y d #part sDigs . /*obtain optional arguments from the CL*/
if x=='' | x=="," then x= -0.5 /*Not specified? Then use the default.*/
Line 1,903 ⟶ 2,440:
show= sDigs + 3 /*adjust number decimal digits for show*/
say "══iteration══" center('X',show,"═") center('Y',show,"═") center('D',show,"═")
#= 0; call refine x,
do until refine(minX, minY) /*perform until the mix is "refined". */
d=d * .2 /*decrease the difference in the mix. .*/
end /*until*/ /* [↑] stop refining if no difference.*/
$= 15 + show*2; say /*compute the indentation for alignment*/
say right('The global minimum for f(-.54719, -1.54719) ───► ', $) fmt(f(-.54719, -1.54719))
say right('The published global minimum is:' , $) fmt( -1.9133 )
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
refine: parse arg xx,yy; h= d * .5
do x=xx-d to xx+d by h
do y=yy-d to yy+d by h; f= f(x, y);
new= fmt(x) fmt(y) fmt(f); if new=old then return 1
#= # + 1; say center(#,13)
end /*y*/
end /*x*/
Line 1,926 ⟶ 2,460:
/*──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
f: procedure: parse arg a,b; return sin(a+b) + (a-b)**2 - 1.5*a + 2.5*b + 1
fmt: ?= format(arg(1), , sDigs);
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=
{{out|output|text= when using the default input:}}
<pre>
Line 1,997 ⟶ 2,531:
Output note: the published global minimum (referenced above, as well as the function's arguments) can be found at:
::::: <u>[http://www.sfu.ca/~ssurjano/mccorm.html http://www.sfu.ca/~ssurjano/mccorm.html]</u>
=={{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>
|