public static double normL(Velocity v, double L)
{
// L-norm of a vector
int d;
double n;
n = 0;
for (d = 0; d < v.size; d++)
n = n + Math.Pow(Math.Abs(v.v[d]), L);
n = Math.Pow(n, 1 / L);
return n;
}
public Swarm(int maxSwarmSize)
{
P = new Position[maxSwarmSize];
X = new Position[maxSwarmSize];
V = new Velocity[maxSwarmSize];
for (int i = 0; i < maxSwarmSize; i++)
{
P[i] = new Position();
X[i] = new Position();
V[i] = new Velocity();
}
//P = Enumerable.Repeat(new Position(), maxSwarmSize).ToArray();
//X = Enumerable.Repeat(new Position(), maxSwarmSize).ToArray();
//V = Enumerable.Repeat(new Velocity(), maxSwarmSize).ToArray();
}
public static Velocity NextVector(this Random rand,int dimensions, double coeff)
{
Velocity velocity = new Velocity();
int K = 2; // 1 => uniform distribution in a hypercube
// 2 => "triangle" distribution
velocity.size = dimensions;
for (int d = 0; d < dimensions; d++)
{
double rnd = 0.0;
for (int i = 0; i < K; i++)
{
rnd += rand.NextDouble();
}
velocity.v[d] = rnd * coeff / K;
}
return velocity;
}
public int NextIteration()
{
double lAve = 0.0;
int vNum = 0;
int numClamped = 0;
iter++;
if (initLinks == 1) // Random topology
{
// Who informs who, at random
for (s = 0; s < PSOResult.SW.S; s++)
{
for (m = 0; m < PSOResult.SW.S; m++)
{
if (rand.NextDouble() < p) LINKS[m, s] = 1; // Probabilistic method
else LINKS[m, s] = 0;
}
LINKS[s, s] = 1;
}
}
// The swarm MOVES
//Utils.Logger.Log("\nIteration %i",iter);
for (int i = 0; i < PSOResult.SW.S; i++)
index[i] = i;
//Permutate the index order
if (param.randOrder == 1)
{
index.Shuffle(7, PSOResult.SW.S);
}
Velocity GX = new Velocity(pb.SS.D);
for (s0 = 0; s0 < PSOResult.SW.S; s0++) // For each particle ...
{
s = index[s0];
// ... find the first informant
s1 = 0;
while (LINKS[s1, s] == 0) s1++;
if (s1 >= PSOResult.SW.S) s1 = s;
// Find the best informant
g = s1;
for (m = s1; m < PSOResult.SW.S; m++)
{
if (LINKS[m, s] == 1 && PSOResult.SW.P[m].f < PSOResult.SW.P[g].f)
g = m;
}
//.. compute the new velocity, and move
// Exploration tendency
for (d = 0; d < pb.SS.D; d++)
{
PSOResult.SW.V[s].v[d] = param.w * PSOResult.SW.V[s].v[d];
// Prepare Exploitation tendency p-x
PX.v[d] = PSOResult.SW.P[s].x[d] - PSOResult.SW.X[s].x[d];
if (g != s)
GX.v[d] = PSOResult.SW.P[g].x[d] - PSOResult.SW.X[s].x[d];// g-x
}
PX.size = pb.SS.D;
GX.size = pb.SS.D;
// Option "non sentivity to rotation"
if (param.rotation > 0)
{
normPX = Velocity.normL(PX, 2);
if (g != s) normGX = Velocity.normL(GX, 2);
if (normPX > 0)
{
RotatePX = Matrix.MatrixRotation(PX);
}
if (g != s && normGX > 0)
{
RotateGX = Matrix.MatrixRotation(GX);
}
}
// Exploitation tendencies
switch (param.rotation)
{
default:
for (d = 0; d < pb.SS.D; d++)
{
PSOResult.SW.V[s].v[d] = PSOResult.SW.V[s].v[d] + rand.NextDouble(0.0, param.c) * PX.v[d];
if (g != s)
PSOResult.SW.V[s].v[d] = PSOResult.SW.V[s].v[d] + rand.NextDouble(0.0, param.c) * GX.v[d];
}
break;
case 1:
// First exploitation tendency
if (normPX > 0)
{
zz = param.c * normPX / sqrtD;
aleaV = rand.NextVector(pb.SS.D, zz);
Velocity expt1 = RotatePX.VectorProduct(aleaV);
for (d = 0; d < pb.SS.D; d++)
{
PSOResult.SW.V[s].v[d] = PSOResult.SW.V[s].v[d] + expt1.v[d];
}
}
// Second exploitation tendency
if (g != s && normGX > 0)
{
zz = param.c * normGX / sqrtD;
aleaV = rand.NextVector(pb.SS.D, zz);
Velocity expt2 = RotateGX.VectorProduct(aleaV);
for (d = 0; d < pb.SS.D; d++)
{
PSOResult.SW.V[s].v[d] = PSOResult.SW.V[s].v[d] + expt2.v[d];
}
}
break;
}
// Update the position
for (d = 0; d < pb.SS.D; d++)
{
lAve += Math.Abs(PSOResult.SW.V[s].v[d]);
vNum++;
if (iter > 1)
{
if (PSOResult.SW.V[s].v[d] > vMax)
{
PSOResult.SW.V[s].v[d] = vAve;
}
else if (PSOResult.SW.V[s].v[d] < -vMax)
{
PSOResult.SW.V[s].v[d] = -vAve;
}
}
PSOResult.SW.X[s].x[d] = PSOResult.SW.X[s].x[d] + (PSOResult.SW.V[s].v[d]);
}
// --------------------------
//noEval = 1;
// Quantisation
//Position.quantis(PSOResult.SW.X[s], pb.SS);
switch (param.clamping)
{
case 0: // No clamping AND no evaluation
outside = 0;
for (d = 0; d < pb.SS.D; d++)
{
if (PSOResult.SW.X[s].x[d] < pb.SS.min[d] || PSOResult.SW.X[s].x[d] > pb.SS.max[d])
outside++;
}
//if (outside == 0) // If inside, the position is evaluated
{
PSOResult.SW.X[s].f =
pb.perf(PSOResult.SW.X[s], pb.function, pb.objective);
PSOResult.nEval = PSOResult.nEval + 1;
}
break;
case 1: // Set to the bounds, and v to zero
for (d = 0; d < pb.SS.D; d++)
{
if (PSOResult.SW.X[s].x[d] < pb.SS.min[d])
{
PSOResult.SW.X[s].x[d] = pb.SS.min[d];
PSOResult.SW.V[s].v[d] = 0;
numClamped++;
}
if (PSOResult.SW.X[s].x[d] > pb.SS.max[d])
{
PSOResult.SW.X[s].x[d] = pb.SS.max[d];
PSOResult.SW.V[s].v[d] = 0;
numClamped++;
}
}
PSOResult.SW.X[s].f = pb.perf(PSOResult.SW.X[s], pb.function, pb.objective);
PSOResult.nEval = PSOResult.nEval + 1;
break;
}
// ... update the best previous position
if (PSOResult.SW.X[s].f < PSOResult.SW.P[s].f) // Improvement
{
PSOResult.SW.P[s] = PSOResult.SW.X[s].Clone();
// ... update the best of the bests
if (PSOResult.SW.P[s].f < PSOResult.SW.P[PSOResult.SW.best].f)
{
PSOResult.SW.best = s;
}
}
} // End of "for (s0=0 ... "
vAve = lAve / (double)vNum;
// Check if finished
switch (param.stop)
{
default:
Error = PSOResult.SW.P[PSOResult.SW.best].f;
break;
case 2:
Error = Position.distanceL(PSOResult.SW.P[PSOResult.SW.best], pb.solution, 2);
break;
}
//error= fabs(error - pb.epsilon);
if (Error < errorPrev) // Improvement
{
initLinks = 0;
}
else // No improvement
{
initLinks = 1; // Information links will be reinitialized
}
if (param.initLink == 1) initLinks = 1 - initLinks;
errorPrev = Error;
//return (int)PSOResult.nEval;
return numClamped;
}
// =================================================
public Algorithm(Problem pb, Parameters param)
{
this.pb = pb;
bestBest = new Position(pb.SS.D);
PX = new Velocity(pb.SS.D);
R = new SPSO_2007.Result(pb.SS.D);
//f_run = File.OpenWrite("f_run.txt");
//f_synth = File.OpenWrite("f_synth.txt");
// ----------------------------------------------- PROBLEM
this.param = param;
runMax = 100;
if (runMax > R_max) runMax = R_max;
this.vMax = param.vMax;
Utils.Logger.Log("\n c = {0}, w = {1}", param.c, param.w);
//---------------
sqrtD = Math.Sqrt(pb.SS.D);
//------------------------------------- RUNS
/*
for (run = 0; run < runMax; run++)
{
} // End loop on "run"
*/
// ---------------------END
// Save
//TODO: Fix up writing out to files
/*fUtils.Logger.Log(f_synth, "%f %f %.0f%% %f ",
errorMean, variance, successRate, evalMean);
for (d = 0; d < pb.SS.D; d++) fUtils.Logger.Log(f_synth, " %f", bestBest.x[d]);
fUtils.Logger.Log(f_synth, "\n");
* */
return; // End of main program
}
public static Matrix MatrixRotation(Velocity V)
{
/*
Define the matrice of the rotation V' => V
where V'=(1,1,...1)*normV/Math.Sqrt(D) (i.e. norm(V') = norm(V) )
*/
int D = V.size;
//matrix reflex1; // Global variable
double normV = Velocity.normL(V, 2);
var reflex2 = new Matrix { size = D };
var reflex1 = new Matrix {size = D};
// Reflection relatively to the vector V'=(1,1, ...1)/Math.Sqrt(D)
// norm(V')=1
for (int i = 0; i < D; i++)
{
for (int j = 0; j < D; j++)
{
reflex1.v[i, j] = -2.0 /D;
}
}
for (int d = 0; d < D; d++)
{
reflex1.v[d, d] = 1 + reflex1.v[d, d];
}
//Define the "bisectrix" B of (V',V) as an unit vector
var B = new Velocity { size = D };
for (int d = 0; d < D; d++)
{
B.v[d] = V.v[d] + normV / Math.Sqrt(D);
}
double normB = Velocity.normL(B, 2);
if (normB > 0)
{
for (int d = 0; d < D; d++)
{
B.v[d] = B.v[d] / normB;
}
}
// Reflection relatively to B
for (int i = 0; i < D; i++)
{
for (int j = 0; j < D; j++)
{
reflex2.v[i, j] = -2 * B.v[i] * B.v[j];
}
}
for (int d = 0; d < D; d++)
{
reflex2.v[d, d] = 1 + reflex2.v[d, d];
}
// Multiply the two reflections
// => rotation
return MatrixProduct(reflex2, reflex1);
}
public Velocity VectorProduct(Velocity V)
{
var velocity = new Velocity();
for (int d = 0; d < V.size; d++)
{
double sum = 0;
for (int j = 0; j < V.size; j++)
{
sum = sum + this.v[d, j] * V.v[j];
}
velocity.v[d] = sum;
}
velocity.size = V.size;
return velocity;
}
// ===============================================================
// PSO
static Result PSO(Parameters param, Problem pb)
{
Velocity aleaV = new Velocity();
int d;
int g;
int[] index = new int[S_max];
int[] indexTemp = new int[S_max];
// Iteration number (time step)
int iterBegin;
int[,] LINKS = new int[S_max, S_max]; // Information links
int m;
int noEval;
double normPX = 0.0, normGX = 0.0;
int noStop;
int outside;
double p;
Velocity PX = new Velocity();
Result R = new Result();
Matrix RotatePX = new Matrix();
Matrix RotateGX = new Matrix();
int s0, s, s1;
double zz;
aleaV.size = pb.SS.D;
RotatePX.size = pb.SS.D;
RotateGX.size = pb.SS.D;
// -----------------------------------------------------
// INITIALISATION
p = param.p; // Probability threshold for random topology
R.SW.S = param.S; // Size of the current swarm
// Position and velocity
for (s = 0; s < R.SW.S; s++)
{
R.SW.X[s].size = pb.SS.D;
R.SW.V[s].size = pb.SS.D;
for (d = 0; d < pb.SS.D; d++)
{
R.SW.X[s].x[d] = rand.NextDouble(pb.SS.minInit[d], pb.SS.maxInit[d]);
R.SW.V[s].v[d] = (rand.NextDouble(pb.SS.min[d], pb.SS.max[d]) - R.SW.X[s].x[d]) / 2;
}
// Take quantisation into account
Position.quantis(R.SW.X[s], pb.SS);
// First evaluations
R.SW.X[s].f =
Problem.perf(R.SW.X[s], pb.function, pb.objective);
R.SW.P[s] = R.SW.X[s].Clone(); // Best position = current one
R.SW.P[s].improved = 0; // No improvement
}
// If the number max of evaluations is smaller than
// the swarm size, just keep evalMax particles, and finish
if (R.SW.S > pb.evalMax) R.SW.S = pb.evalMax;
R.nEval = R.SW.S;
// Find the best
R.SW.best = 0;
double errorPrev;
switch (param.stop)
{
default:
errorPrev = R.SW.P[R.SW.best].f; // "distance" to the wanted f value (objective)
break;
case 2:
errorPrev = Position.distanceL(R.SW.P[R.SW.best], pb.solution, 2); // Distance to the wanted solution
break;
}
for (s = 1; s < R.SW.S; s++)
{
switch (param.stop)
{
default:
zz = R.SW.P[s].f;
if (zz < errorPrev)
{
R.SW.best = s;
errorPrev = zz;
}
break;
case 2:
zz = Position.distanceL(R.SW.P[R.SW.best], pb.solution, 2);
if (zz < errorPrev)
{
R.SW.best = s;
errorPrev = zz;
}
break;
}
}
// Display the best
Console.Write(" Best value after init. {0} ", errorPrev);
// Console.Write( "\n Position :\n" );
// for ( d = 0; d < SS.D; d++ ) Console.Write( " %f", R.SW.P[R.SW.best].x[d] );
int initLinks = 1; // So that information links will beinitialized
// Note: It is also a flag saying "No improvement"
noStop = 0;
double error = errorPrev;
// ---------------------------------------------- ITERATIONS
int iter = 0;
while (noStop == 0)
{
iter++;
if (initLinks == 1) // Random topology
{
// Who informs who, at random
for (s = 0; s < R.SW.S; s++)
{
for (m = 0; m < R.SW.S; m++)
{
if (rand.NextDouble() < p) LINKS[m, s] = 1; // Probabilistic method
else LINKS[m, s] = 0;
}
LINKS[s, s] = 1;
}
}
// The swarm MOVES
//Console.Write("\nIteration %i",iter);
for (int i = 0; i < R.SW.S; i++)
index[i] = i;
//Permutate the index order
if (param.randOrder == 1)
{
index.Shuffle(7, R.SW.S);
}
Velocity GX = new Velocity();
for (s0 = 0; s0 < R.SW.S; s0++) // For each particle ...
{
s = index[s0];
// ... find the first informant
s1 = 0;
while (LINKS[s1, s] == 0) s1++;
if (s1 >= R.SW.S) s1 = s;
// Find the best informant
g = s1;
for (m = s1; m < R.SW.S; m++)
{
if (LINKS[m, s] == 1 && R.SW.P[m].f < R.SW.P[g].f)
g = m;
}
//.. compute the new velocity, and move
// Exploration tendency
for (d = 0; d < pb.SS.D; d++)
{
R.SW.V[s].v[d] = param.w * R.SW.V[s].v[d];
// Prepare Exploitation tendency p-x
PX.v[d] = R.SW.P[s].x[d] - R.SW.X[s].x[d];
if (g != s)
GX.v[d] = R.SW.P[g].x[d] - R.SW.X[s].x[d];// g-x
}
PX.size = pb.SS.D;
GX.size = pb.SS.D;
// Option "non sentivity to rotation"
if (param.rotation > 0)
{
normPX = Velocity.normL(PX, 2);
if (g != s) normGX = Velocity.normL(GX, 2);
if (normPX > 0)
{
RotatePX = Matrix.MatrixRotation(PX);
}
if (g != s && normGX > 0)
{
RotateGX = Matrix.MatrixRotation(GX);
}
}
// Exploitation tendencies
switch (param.rotation)
{
default:
for (d = 0; d < pb.SS.D; d++)
{
R.SW.V[s].v[d] = R.SW.V[s].v[d] + rand.NextDouble(0.0, param.c) * PX.v[d];
if(g!=s)
R.SW.V[s].v[d] = R.SW.V[s].v[d] + rand.NextDouble(0.0, param.c) * GX.v[d];
}
break;
case 1:
// First exploitation tendency
if (normPX > 0)
{
zz = param.c * normPX / sqrtD;
aleaV = rand.NextVector(pb.SS.D, zz);
Velocity expt1 = RotatePX.VectorProduct(aleaV);
for (d = 0; d < pb.SS.D; d++)
{
R.SW.V[s].v[d] = R.SW.V[s].v[d] + expt1.v[d];
}
}
// Second exploitation tendency
if (g != s && normGX > 0)
{
zz = param.c * normGX / sqrtD;
aleaV = rand.NextVector(pb.SS.D, zz);
Velocity expt2 = RotateGX.VectorProduct(aleaV);
for (d = 0; d < pb.SS.D; d++)
{
R.SW.V[s].v[d] = R.SW.V[s].v[d] + expt2.v[d];
}
}
break;
}
// Update the position
for (d = 0; d < pb.SS.D; d++)
{
R.SW.X[s].x[d] = R.SW.X[s].x[d] + R.SW.V[s].v[d];
}
if (R.nEval >= pb.evalMax)
{
//error= fabs(error - pb.objective);
goto end;
}
// --------------------------
noEval = 1;
// Quantisation
Position.quantis(R.SW.X[s], pb.SS);
switch (param.clamping)
{
case 0: // No clamping AND no evaluation
outside = 0;
for (d = 0; d < pb.SS.D; d++)
{
if (R.SW.X[s].x[d] < pb.SS.min[d] || R.SW.X[s].x[d] > pb.SS.max[d])
outside++;
}
if (outside == 0) // If inside, the position is evaluated
{
R.SW.X[s].f =
Problem.perf(R.SW.X[s], pb.function, pb.objective);
R.nEval = R.nEval + 1;
}
break;
case 1: // Set to the bounds, and v to zero
for (d = 0; d < pb.SS.D; d++)
{
if (R.SW.X[s].x[d] < pb.SS.min[d])
{
R.SW.X[s].x[d] = pb.SS.min[d];
R.SW.V[s].v[d] = 0;
}
if (R.SW.X[s].x[d] > pb.SS.max[d])
{
R.SW.X[s].x[d] = pb.SS.max[d];
R.SW.V[s].v[d] = 0;
}
}
R.SW.X[s].f = Problem.perf(R.SW.X[s], pb.function, pb.objective);
R.nEval = R.nEval + 1;
break;
}
// ... update the best previous position
if (R.SW.X[s].f < R.SW.P[s].f) // Improvement
{
R.SW.P[s] = R.SW.X[s].Clone();
// ... update the best of the bests
if (R.SW.P[s].f < R.SW.P[R.SW.best].f)
{
R.SW.best = s;
}
}
} // End of "for (s0=0 ... "
// Check if finished
switch (param.stop)
{
default:
error = R.SW.P[R.SW.best].f;
break;
case 2:
error = Position.distanceL(R.SW.P[R.SW.best], pb.solution, 2);
break;
}
//error= fabs(error - pb.epsilon);
if (error < errorPrev) // Improvement
{
initLinks = 0;
}
else // No improvement
{
initLinks = 1; // Information links will be reinitialized
}
if (param.initLink == 1) initLinks = 1 - initLinks;
errorPrev = error;
end:
switch (param.stop)
{
case 0:
case 2:
if (error > pb.epsilon && R.nEval < pb.evalMax)
{
noStop = 0; // Won't stop
}
else
{
noStop = 1; // Will stop
}
break;
case 1:
if (R.nEval < pb.evalMax)
noStop = 0; // Won't stop
else
noStop = 1; // Will stop
break;
}
} // End of "while nostop ...
// Console.Write( "\n and the winner is ... %i", R.SW.best );
// fConsole.Write( f_stag, "\nEND" );
R.error = error;
return R;
}