Task: Particle swarm optimization



C#: 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++) {
                
                v[j] = fn.Invoke(y.pos[j]);
                
                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++) {
                
                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 }));
        }
    }
}





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):
        
        v[j] = fn(y.pos[j])
        
        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):
        
        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()