public void OptimizersTest()
{
//("Testing optimizers...");
setup();
// Loop over problems (currently there is only 1 problem)
for (int i=0; i<costFunctions_.Count; ++i) {
Problem problem = new Problem(costFunctions_[i], constraints_[i], initialValues_[i]);
Vector initialValues = problem.currentValue();
// Loop over optimizers
for (int j = 0; j < (optimizationMethods_[i]).Count; ++j) {
double rootEpsilon = endCriterias_[i].rootEpsilon();
int endCriteriaTests = 1;
// Loop over rootEpsilon
for(int k=0; k<endCriteriaTests; ++k) {
problem.setCurrentValue(initialValues);
EndCriteria endCriteria = new EndCriteria(endCriterias_[i].maxIterations(),
endCriterias_[i].maxStationaryStateIterations(),
rootEpsilon,
endCriterias_[i].functionEpsilon(),
endCriterias_[i].gradientNormEpsilon());
rootEpsilon *= .1;
EndCriteria.Type endCriteriaResult =
optimizationMethods_[i][j].optimizationMethod.minimize(problem, endCriteria);
Vector xMinCalculated = problem.currentValue();
Vector yMinCalculated = problem.values(xMinCalculated);
// Check optimization results vs known solution
if (endCriteriaResult==EndCriteria.Type.None ||
endCriteriaResult==EndCriteria.Type.MaxIterations ||
endCriteriaResult==EndCriteria.Type.Unknown)
Assert.Fail("function evaluations: " + problem.functionEvaluation() +
" gradient evaluations: " + problem.gradientEvaluation() +
" x expected: " + xMinExpected_[i] +
" x calculated: " + xMinCalculated +
" x difference: " + (xMinExpected_[i]- xMinCalculated) +
" rootEpsilon: " + endCriteria.rootEpsilon() +
" y expected: " + yMinExpected_[i] +
" y calculated: " + yMinCalculated +
" y difference: " + (yMinExpected_[i]- yMinCalculated) +
" functionEpsilon: " + endCriteria.functionEpsilon() +
" endCriteriaResult: " + endCriteriaResult);
}
}
}
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// set up of the problem
//double ftol = endCriteria.functionEpsilon(); // end criteria on f(x) (see Numerical Recipes in C++, p.410)
double xtol = endCriteria.rootEpsilon(); // end criteria on x (see GSL v. 1.9, http://www.gnu.org/software/gsl/)
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
// Initialize vertices of the simplex
bool end = false;
int n = x_.Count;
vertices_ = new InitializedList <Vector>(n + 1, x_);
for (int i = 0; i < n; i++)
{
Vector direction = new Vector(n, 0.0);
Vector vertice = vertices_[i + 1];
direction[i] = 1.0;
P.constraint().update(ref vertice, direction, lambda_);
vertices_[i + 1] = vertice;
}
// Initialize function values at the vertices of the simplex
values_ = new Vector(n + 1, 0.0);
for (int i = 0; i <= n; i++)
{
values_[i] = P.value(vertices_[i]);
}
// Loop looking for minimum
do
{
sum_ = new Vector(n, 0.0);
for (int i = 0; i <= n; i++)
{
sum_ += vertices_[i];
}
// Determine the best (iLowest), worst (iHighest)
// and 2nd worst (iNextHighest) vertices
int iLowest = 0;
int iHighest;
int iNextHighest;
if (values_[0] < values_[1])
{
iHighest = 1;
iNextHighest = 0;
}
else
{
iHighest = 0;
iNextHighest = 1;
}
for (int i = 1; i <= n; i++)
{
if (values_[i] > values_[iHighest])
{
iNextHighest = iHighest;
iHighest = i;
}
else
{
if ((values_[i] > values_[iNextHighest]) && i != iHighest)
{
iNextHighest = i;
}
}
if (values_[i] < values_[iLowest])
{
iLowest = i;
}
}
// Now compute accuracy, update iteration number and check end criteria
//// Numerical Recipes exit strategy on fx (see NR in C++, p.410)
//double low = values_[iLowest];
//double high = values_[iHighest];
//double rtol = 2.0*std::fabs(high - low)/
// (std::fabs(high) + std::fabs(low) + QL_EPSILON);
//++iterationNumber_;
//if (rtol < ftol ||
// endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
// GSL exit strategy on x (see GSL v. 1.9, http://www.gnu.org/software/gsl
double simplexSize = Utils.computeSimplexSize(vertices_);
++iterationNumber_;
if (simplexSize < xtol || endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryPoint(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(ecType);
}
// If end criteria is not met, continue
double factor = -1.0;
double vTry = extrapolate(ref P, iHighest, ref factor);
if ((vTry <= values_[iLowest]) && (factor == -1.0))
{
factor = 2.0;
extrapolate(ref P, iHighest, ref factor);
}
else if (Math.Abs(factor) > Const.QL_EPSILON)
{
if (vTry >= values_[iNextHighest])
{
double vSave = values_[iHighest];
factor = 0.5;
vTry = extrapolate(ref P, iHighest, ref factor);
if (vTry >= vSave && Math.Abs(factor) > Const.QL_EPSILON)
{
for (int i = 0; i <= n; i++)
{
if (i != iLowest)
{
#if QL_ARRAY_EXPRESSIONS
vertices_[i] = 0.5 * (vertices_[i] + vertices_[iLowest]);
#else
vertices_[i] += vertices_[iLowest];
vertices_[i] *= 0.5;
#endif
values_[i] = P.value(vertices_[i]);
}
}
}
}
}
// If can't extrapolate given the constraints, exit
if (Math.Abs(factor) <= Const.QL_EPSILON)
{
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(EndCriteria.Type.StationaryFunctionValue);
}
} while (end == false);
throw new Exception("optimization failed: unexpected behaviour");
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// set up of the problem
//double ftol = endCriteria.functionEpsilon(); // end criteria on f(x) (see Numerical Recipes in C++, p.410)
double xtol = endCriteria.rootEpsilon(); // end criteria on x (see GSL v. 1.9, http://www.gnu.org/software/gsl/)
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
// Initialize vertices of the simplex
bool end = false;
int n = x_.Count;
vertices_ = new InitializedList<Vector>(n + 1, x_);
for (int i = 0; i < n; i++)
{
Vector direction = new Vector(n, 0.0);
direction[i] = 1.0;
P.constraint().update(vertices_[i + 1], direction, lambda_);
}
// Initialize function values at the vertices of the simplex
values_ = new Vector(n + 1, 0.0);
for (int i = 0; i <= n; i++)
values_[i] = P.value(vertices_[i]);
// Loop looking for minimum
do
{
sum_ = new Vector(n, 0.0);
for (int i = 0; i <= n; i++)
sum_ += vertices_[i];
// Determine the best (iLowest), worst (iHighest)
// and 2nd worst (iNextHighest) vertices
int iLowest = 0;
int iHighest;
int iNextHighest;
if (values_[0] < values_[1])
{
iHighest = 1;
iNextHighest = 0;
}
else
{
iHighest = 0;
iNextHighest = 1;
}
for (int i = 1; i <= n; i++)
{
if (values_[i] > values_[iHighest])
{
iNextHighest = iHighest;
iHighest = i;
}
else
{
if ((values_[i] > values_[iNextHighest]) && i != iHighest)
iNextHighest = i;
}
if (values_[i] < values_[iLowest])
iLowest = i;
}
// Now compute accuracy, update iteration number and check end criteria
//// Numerical Recipes exit strategy on fx (see NR in C++, p.410)
//double low = values_[iLowest];
//double high = values_[iHighest];
//double rtol = 2.0*std::fabs(high - low)/
// (std::fabs(high) + std::fabs(low) + QL_EPSILON);
//++iterationNumber_;
//if (rtol < ftol ||
// endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
// GSL exit strategy on x (see GSL v. 1.9, http://www.gnu.org/software/gsl
double simplexSize = Utils.computeSimplexSize(vertices_);
++iterationNumber_;
if (simplexSize < xtol || endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryPoint(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return ecType;
}
// If end criteria is not met, continue
double factor = -1.0;
double vTry = extrapolate(ref P, iHighest, ref factor);
if ((vTry <= values_[iLowest]) && (factor == -1.0))
{
factor = 2.0;
extrapolate(ref P, iHighest, ref factor);
}
else if (Math.Abs(factor) > Const.QL_Epsilon)
{
if (vTry >= values_[iNextHighest])
{
double vSave = values_[iHighest];
factor = 0.5;
vTry = extrapolate(ref P, iHighest, ref factor);
if (vTry >= vSave && Math.Abs(factor) > Const.QL_Epsilon)
{
for (int i = 0; i <= n; i++)
{
if (i != iLowest)
{
#if QL_ARRAY_EXPRESSIONS
vertices_[i] = 0.5 * (vertices_[i] + vertices_[iLowest]);
#else
vertices_[i] += vertices_[iLowest];
vertices_[i] *= 0.5;
#endif
values_[i] = P.value(vertices_[i]);
}
}
}
}
}
// If can't extrapolate given the constraints, exit
if (Math.Abs(factor) <= Const.QL_Epsilon)
{
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return EndCriteria.Type.StationaryFunctionValue;
}
} while (end == false);
throw new ApplicationException("optimization failed: unexpected behaviour");
}
