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checking if a facet has been analyzed sufficiently precise via smt

main
TimQu 7 years ago
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fbce6a4795
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b696d63953
2 changed files with 143 additions and 21 deletions
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  1. 136
      src/storm/modelchecker/multiobjective/deterministicScheds/DeterministicParetoExplorer.cpp
  2. 28
      src/storm/modelchecker/multiobjective/deterministicScheds/DeterministicParetoExplorer.h

136
src/storm/modelchecker/multiobjective/deterministicScheds/DeterministicParetoExplorer.cpp
View File

@ -12,7 +12,9 @@
#include "storm/environment/modelchecker/MultiObjectiveModelCheckerEnvironment.h" #include "storm/environment/modelchecker/MultiObjectiveModelCheckerEnvironment.h"
#include "storm/utility/export.h" #include "storm/utility/export.h"
#include "storm/utility/solver.h"
#include "storm/exceptions/UnexpectedException.h"
#include "storm/exceptions/InvalidOperationException.h" #include "storm/exceptions/InvalidOperationException.h"
@ -21,12 +23,12 @@ namespace storm {
namespace multiobjective { namespace multiobjective {
template <class SparseModelType, typename GeometryValueType> template <class SparseModelType, typename GeometryValueType>
DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Point::Point(std::vector<GeometryValueType> const& coordinates) : coordinates(coordinates), paretoOptimal(false) {
DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Point::Point(std::vector<GeometryValueType> const& coordinates) : coordinates(coordinates), paretoOptimal(false), onFacet(false) {
STORM_LOG_ASSERT(!this->coordinates.empty(), "Points with dimension 0 are not supported"); STORM_LOG_ASSERT(!this->coordinates.empty(), "Points with dimension 0 are not supported");
} }
template <class SparseModelType, typename GeometryValueType> template <class SparseModelType, typename GeometryValueType>
DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Point::Point(std::vector<GeometryValueType>&& coordinates) : coordinates(std::move(coordinates)), paretoOptimal(false) {
DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Point::Point(std::vector<GeometryValueType>&& coordinates) : coordinates(std::move(coordinates)), paretoOptimal(false), onFacet(false) {
STORM_LOG_ASSERT(!this->coordinates.empty(), "Points with dimension 0 are not supported"); STORM_LOG_ASSERT(!this->coordinates.empty(), "Points with dimension 0 are not supported");
} }
@ -92,6 +94,16 @@ namespace storm {
return paretoOptimal; return paretoOptimal;
} }
template <class SparseModelType, typename GeometryValueType>
void DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Point::setOnFacet(bool value) {
onFacet = value;
}
template <class SparseModelType, typename GeometryValueType>
bool DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Point::liesOnFacet() const {
return onFacet;
}
template <class SparseModelType, typename GeometryValueType> template <class SparseModelType, typename GeometryValueType>
std::string DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Point::toString(bool convertToDouble) const { std::string DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Point::toString(bool convertToDouble) const {
std::stringstream out; std::stringstream out;
@ -147,7 +159,12 @@ namespace storm {
STORM_LOG_WARN("Potential precision issues: Found a point that dominates another point which was flagged as pareto optimal. Distance of points is " << std::sqrt(storm::utility::convertNumber<double>(storm::storage::geometry::squaredEuclideanDistance(pointsIt->second.get(), point.get())))); STORM_LOG_WARN("Potential precision issues: Found a point that dominates another point which was flagged as pareto optimal. Distance of points is " << std::sqrt(storm::utility::convertNumber<double>(storm::storage::geometry::squaredEuclideanDistance(pointsIt->second.get(), point.get()))));
point.setParetoOptimal(true); point.setParetoOptimal(true);
} }
pointsIt = points.erase(pointsIt);
if (pointsIt->second.liesOnFacet()) {
// Do not erase points that lie on a facet
++pointsIt;
} else {
pointsIt = points.erase(pointsIt);
}
break; break;
case Point::DominanceResult::Dominated: case Point::DominanceResult::Dominated:
// The new point is dominated by another point. // The new point is dominated by another point.
@ -156,6 +173,9 @@ namespace storm {
if (point.isParetoOptimal()) { if (point.isParetoOptimal()) {
pointsIt->second.setParetoOptimal(); pointsIt->second.setParetoOptimal();
} }
if (point.liesOnFacet()) {
pointsIt->second.setOnFacet();
}
return pointsIt->first; return pointsIt->first;
} }
} }
@ -234,8 +254,17 @@ namespace storm {
} }
template <class SparseModelType, typename GeometryValueType> template <class SparseModelType, typename GeometryValueType>
void DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Facet::addPoint(PointId const& pointId) {
void DeterministicParetoExplorer<SparseModelType, GeometryValueType>::Facet::addPoint(PointId const& pointId, Point const& point) {
inducedSimplex = nullptr; inducedSimplex = nullptr;
GeometryValueType product = storm::utility::vector::dotProduct(getHalfspace().normalVector(), point.get());
if (product != getHalfspace().offset()) {
if (product < getHalfspace().offset()) {
STORM_LOG_DEBUG("The point on the facet actually has distance " << storm::utility::convertNumber<double>(getHalfspace().euclideanDistance(point.get())));
} else {
STORM_LOG_DEBUG("Halfspace of facet is shifted by " << storm::utility::convertNumber<double>(getHalfspace().euclideanDistance(point.get())) << " to capture all points that are supposed to lie on the facet.");
halfspace.offset() = product;
}
}
paretoPointsOnFacet.push_back(pointId); paretoPointsOnFacet.push_back(pointId);
} }
@ -282,6 +311,11 @@ namespace storm {
return inducedSimplex; return inducedSimplex;
} }
template <class SparseModelType, typename GeometryValueType>
DeterministicParetoExplorer<SparseModelType, GeometryValueType>::FacetAnalysisContext::FacetAnalysisContext(Facet& f) : facet(f) {
// Intentionally left empty
}
template <class SparseModelType, typename GeometryValueType> template <class SparseModelType, typename GeometryValueType>
DeterministicParetoExplorer<SparseModelType, GeometryValueType>::DeterministicParetoExplorer(preprocessing::SparseMultiObjectivePreprocessorResult<SparseModelType>& preprocessorResult) : model(preprocessorResult.preprocessedModel), objectives(preprocessorResult.objectives) { DeterministicParetoExplorer<SparseModelType, GeometryValueType>::DeterministicParetoExplorer(preprocessing::SparseMultiObjectivePreprocessorResult<SparseModelType>& preprocessorResult) : model(preprocessorResult.preprocessedModel), objectives(preprocessorResult.objectives) {
originalModelInitialState = *preprocessorResult.originalModel.getInitialStates().begin(); originalModelInitialState = *preprocessorResult.originalModel.getInitialStates().begin();
@ -391,7 +425,7 @@ namespace storm {
Point p(storm::utility::vector::convertNumericVector<GeometryValueType>(*pIt)); Point p(storm::utility::vector::convertNumericVector<GeometryValueType>(*pIt));
if (last) { if (last) {
last = false; last = false;
p.setParetoOptimal(true);
p.setOnFacet();
// Adapt the overapproximation // Adapt the overapproximation
std::vector<GeometryValueType> normalVector(objectives.size(), storm::utility::zero<GeometryValueType>()); std::vector<GeometryValueType> normalVector(objectives.size(), storm::utility::zero<GeometryValueType>());
normalVector[objIndex] = storm::utility::one<GeometryValueType>(); normalVector[objIndex] = storm::utility::one<GeometryValueType>();
@ -406,7 +440,7 @@ namespace storm {
Facet f(std::move(h)); Facet f(std::move(h));
for (auto const& p : pointset) { for (auto const& p : pointset) {
if (f.getHalfspace().isPointOnBoundary(p.second.get())) { if (f.getHalfspace().isPointOnBoundary(p.second.get())) {
f.addPoint(p.first);
f.addPoint(p.first, p.second);
} }
} }
STORM_LOG_ASSERT(std::count(f.getHalfspace().normalVector().begin(), f.getHalfspace().normalVector().end(), storm::utility::zero<GeometryValueType>()) + f.getNumberOfPoints() == objectives.size(), "Unexpected number of points on facet."); STORM_LOG_ASSERT(std::count(f.getHalfspace().normalVector().begin(), f.getHalfspace().normalVector().end(), storm::utility::zero<GeometryValueType>()) + f.getNumberOfPoints() == objectives.size(), "Unexpected number of points on facet.");
@ -441,17 +475,18 @@ namespace storm {
if (optimizeAndSplitFacet(env,f)) { if (optimizeAndSplitFacet(env,f)) {
return; return;
} }
std::set<PointId> collectedPoints;
if (findAndCheckCachedPoints(env, f, collectedPoints)) {
FacetAnalysisContext context = createAnalysisContext(env, f);
if (findAndCheckCachedPoints(env, context)) {
return; return;
} }
if (analyzePointsOnFacet(env, f, collectedPoints)) {
if (analyzePointsOnFacet(env, context)) {
return; return;
} }
if (analyzePointsInSimplex(env, f, collectedPoints)) {
if (analyzePointsInSimplex(env, context)) {
return; return;
} }
@ -459,10 +494,47 @@ namespace storm {
STORM_LOG_ERROR("Facet " << f.getHalfspace().toString(true) << " could not be analyzed completely."); STORM_LOG_ERROR("Facet " << f.getHalfspace().toString(true) << " could not be analyzed completely.");
} }
template <class SparseModelType, typename GeometryValueType>
typename DeterministicParetoExplorer<SparseModelType, GeometryValueType>::FacetAnalysisContext DeterministicParetoExplorer<SparseModelType, GeometryValueType>::createAnalysisContext(Environment const& env, Facet& f) {
FacetAnalysisContext res(f);
res.expressionManager = std::make_shared<storm::expressions::ExpressionManager>();
res.smtSolver = storm::utility::solver::SmtSolverFactory().create(*res.expressionManager);
Polytope const& inducedPoly = res.facet.getInducedSimplex(pointset);
res.x = inducedPoly->declareVariables(*res.expressionManager, "x");
for (auto const& c : inducedPoly->getConstraints(*res.expressionManager, res.x)) {
res.smtSolver->add(c);
}
res.xMinusEps = inducedPoly->declareVariables(*res.expressionManager, "y");
for (auto const& c : inducedPoly->getConstraints(*res.expressionManager, res.xMinusEps)) {
res.smtSolver->add(c);
}
auto eps = res.expressionManager->rational(env.modelchecker().multi().getPrecision());
storm::expressions::Expression xme;
for (uint64_t i = 0; i < res.x.size(); ++i) {
storm::expressions::Expression subExpr = (res.xMinusEps[i].getExpression() == res.x[i].getExpression() - eps);
if (i == 0) {
xme = subExpr;
} else {
xme = xme && subExpr;
}
}
res.smtSolver->add(xme);
res.smtSolver->push();
return res;
}
template <class SparseModelType, typename GeometryValueType> template <class SparseModelType, typename GeometryValueType>
bool DeterministicParetoExplorer<SparseModelType, GeometryValueType>::optimizeAndSplitFacet(Environment const& env, Facet& f) { bool DeterministicParetoExplorer<SparseModelType, GeometryValueType>::optimizeAndSplitFacet(Environment const& env, Facet& f) {
// Obtain the correct weight vector // Obtain the correct weight vector
auto weightVector = storm::utility::vector::convertNumericVector<ModelValueType>(f.getHalfspace().normalVector()); auto weightVector = storm::utility::vector::convertNumericVector<ModelValueType>(f.getHalfspace().normalVector());
bool weightVectorYieldsParetoOptimalPoint = !storm::utility::vector::hasZeroEntry(weightVector);
for (uint_fast64_t objIndex = 0; objIndex < this->objectives.size(); ++objIndex) { for (uint_fast64_t objIndex = 0; objIndex < this->objectives.size(); ++objIndex) {
if (storm::solver::minimize(objectives[objIndex].formula->getOptimalityType())) { if (storm::solver::minimize(objectives[objIndex].formula->getOptimalityType())) {
weightVector[objIndex] *= -storm::utility::one<ModelValueType>(); weightVector[objIndex] *= -storm::utility::one<ModelValueType>();
@ -482,7 +554,8 @@ namespace storm {
Point p(storm::utility::vector::convertNumericVector<GeometryValueType>(*pIt)); Point p(storm::utility::vector::convertNumericVector<GeometryValueType>(*pIt));
if (last) { if (last) {
last = false; last = false;
p.setParetoOptimal(true);
p.setParetoOptimal(weightVectorYieldsParetoOptimalPoint);
p.setOnFacet();
addHalfspaceToOverApproximation(env, f.getHalfspace().normalVector(), p); addHalfspaceToOverApproximation(env, f.getHalfspace().normalVector(), p);
optPointId = pointset.addPoint(env, std::move(p)); optPointId = pointset.addPoint(env, std::move(p));
} else { } else {
@ -508,13 +581,13 @@ namespace storm {
if (!storm::utility::vector::hasNegativeEntry(h.normalVector())) { if (!storm::utility::vector::hasNegativeEntry(h.normalVector())) {
STORM_LOG_ASSERT(h.isPointOnBoundary(optPoint.get()), "Unexpected facet found while splitting."); STORM_LOG_ASSERT(h.isPointOnBoundary(optPoint.get()), "Unexpected facet found while splitting.");
Facet fNew(std::move(h)); Facet fNew(std::move(h));
fNew.addPoint(optPointId.get());
fNew.addPoint(optPointId.get(), optPoint);
auto vertexIt = vertices.begin(); auto vertexIt = vertices.begin();
++vertexIt; ++vertexIt;
for (auto const& pId : f.getPoints()) { for (auto const& pId : f.getPoints()) {
assert(pointset.getPoint(pId).get() == *vertexIt); assert(pointset.getPoint(pId).get() == *vertexIt);
if (fNew.getHalfspace().isPointOnBoundary(*vertexIt)) { if (fNew.getHalfspace().isPointOnBoundary(*vertexIt)) {
fNew.addPoint(pId);
fNew.addPoint(pId, pointset.getPoint(pId));
} }
++vertexIt; ++vertexIt;
} }
@ -533,20 +606,49 @@ namespace storm {
} }
template <class SparseModelType, typename GeometryValueType> template <class SparseModelType, typename GeometryValueType>
bool DeterministicParetoExplorer<SparseModelType, GeometryValueType>::findAndCheckCachedPoints(Environment const& env, Facet& f, std::set<PointId>& collectedPoints) {
// TODO
bool DeterministicParetoExplorer<SparseModelType, GeometryValueType>::findAndCheckCachedPoints(Environment const& env, FacetAnalysisContext& context) {
Polytope inducedPoly = context.facet.getInducedSimplex(pointset);
pointset.collectPointsInPolytope(context.collectedPoints, inducedPoly);
if (context.collectedPoints.size() != context.facet.getNumberOfPoints()) {
STORM_LOG_ASSERT(context.collectedPoints.size() > context.facet.getNumberOfPoints(), "Did not find all points on the facet");
// formulate SMT constraints to assert that xMinusEps is not dominated by one of the cached points
for (auto const& pId : context.collectedPoints) {
auto const& coordinates = pointset.getPoint(pId).get();
storm::expressions::Expression pointAchievesXMinusEps;
for (uint64_t i = 0; i < coordinates.size(); ++i) {
storm::expressions::Expression subExpr = context.xMinusEps[i] <= context.expressionManager->rational(coordinates[i]);
if (i == 0) {
pointAchievesXMinusEps = subExpr;
} else {
pointAchievesXMinusEps = pointAchievesXMinusEps && subExpr;
}
}
context.smtSolver->add(!pointAchievesXMinusEps);
}
context.smtSolver->push();
auto smtCheckResult = context.smtSolver->check();
if (smtCheckResult == storm::solver::SmtSolver::CheckResult::Unsat) {
// There is no point x that violates the 'precision criterion' for this facet
return true;
} else {
STORM_LOG_THROW(smtCheckResult == storm::solver::SmtSolver::CheckResult::Sat, storm::exceptions::UnexpectedException, "The smt solver did not yield sat or unsat.");
return false;
}
}
return false; return false;
} }
template <class SparseModelType, typename GeometryValueType> template <class SparseModelType, typename GeometryValueType>
bool DeterministicParetoExplorer<SparseModelType, GeometryValueType>::analyzePointsOnFacet(Environment const& env, Facet& f, std::set<PointId>& collectedPoints) {
bool DeterministicParetoExplorer<SparseModelType, GeometryValueType>::analyzePointsOnFacet(Environment const& env, FacetAnalysisContext& context) {
// TODO // TODO
return false; return false;
} }
template <class SparseModelType, typename GeometryValueType> template <class SparseModelType, typename GeometryValueType>
bool DeterministicParetoExplorer<SparseModelType, GeometryValueType>::analyzePointsInSimplex(Environment const& env, Facet& f, std::set<PointId>& collectedPoints) {
bool DeterministicParetoExplorer<SparseModelType, GeometryValueType>::analyzePointsInSimplex(Environment const& env, FacetAnalysisContext& context) {
// TODO // TODO
return false; return false;
} }

28
src/storm/modelchecker/multiobjective/deterministicScheds/DeterministicParetoExplorer.h
View File

@ -9,6 +9,8 @@
#include "storm/storage/geometry/Polytope.h" #include "storm/storage/geometry/Polytope.h"
#include "storm/storage/geometry/Halfspace.h" #include "storm/storage/geometry/Halfspace.h"
#include "storm/modelchecker/results/CheckResult.h" #include "storm/modelchecker/results/CheckResult.h"
#include "storm/storage/expressions/ExpressionManager.h"
#include "storm/solver/SmtSolver.h"
namespace storm { namespace storm {
@ -44,12 +46,15 @@ namespace storm {
void setParetoOptimal(bool value = true); void setParetoOptimal(bool value = true);
bool isParetoOptimal() const; bool isParetoOptimal() const;
void setOnFacet(bool value = true);
bool liesOnFacet() const;
std::string toString(bool convertToDouble = false) const; std::string toString(bool convertToDouble = false) const;
private: private:
std::vector<GeometryValueType> coordinates; std::vector<GeometryValueType> coordinates;
bool paretoOptimal; bool paretoOptimal;
bool onFacet;
}; };
@ -102,7 +107,7 @@ namespace storm {
Facet(storm::storage::geometry::Halfspace<GeometryValueType> const& halfspace); Facet(storm::storage::geometry::Halfspace<GeometryValueType> const& halfspace);
Facet(storm::storage::geometry::Halfspace<GeometryValueType>&& halfspace); Facet(storm::storage::geometry::Halfspace<GeometryValueType>&& halfspace);
storm::storage::geometry::Halfspace<GeometryValueType> const& getHalfspace() const; storm::storage::geometry::Halfspace<GeometryValueType> const& getHalfspace() const;
void addPoint(PointId const& pointId);
void addPoint(PointId const& pointId, Point const& point);
std::vector<PointId> const& getPoints() const; std::vector<PointId> const& getPoints() const;
uint64_t getNumberOfPoints() const; uint64_t getNumberOfPoints() const;
@ -121,6 +126,19 @@ namespace storm {
Polytope inducedSimplex; Polytope inducedSimplex;
}; };
struct FacetAnalysisContext {
FacetAnalysisContext(Facet& f);
Facet& facet;
std::set<PointId> collectedPoints;
std::unique_ptr<storm::solver::SmtSolver> smtSolver;
std::shared_ptr<storm::expressions::ExpressionManager> expressionManager;
// Variables that encode two points that lie in the induced simplex of the analyzed facet
// xMinusEps = (x_1-eps, x_m-eps)
std::vector<storm::expressions::Variable> x, xMinusEps;
};
DeterministicParetoExplorer(preprocessing::SparseMultiObjectivePreprocessorResult<SparseModelType>& preprocessorResult); DeterministicParetoExplorer(preprocessing::SparseMultiObjectivePreprocessorResult<SparseModelType>& preprocessorResult);
@ -170,6 +188,8 @@ namespace storm {
*/ */
void processFacet(Environment const& env, Facet& f); void processFacet(Environment const& env, Facet& f);
FacetAnalysisContext createAnalysisContext(Environment const& env, Facet& f);
/*! /*!
* Optimizes in the facet direction. If this results in a point that does not lie on the facet, * Optimizes in the facet direction. If this results in a point that does not lie on the facet,
* 1. The new Pareto optimal point is added * 1. The new Pareto optimal point is added
@ -182,7 +202,7 @@ namespace storm {
* Finds all points that lie within the induced Simplex of the given facet. * Finds all points that lie within the induced Simplex of the given facet.
* Returns true if the facet is sufficiently precise when considering all added points * Returns true if the facet is sufficiently precise when considering all added points
*/ */
bool findAndCheckCachedPoints(Environment const& env, Facet& f, std::set<PointId>& collectedPoints);
bool findAndCheckCachedPoints(Environment const& env, FacetAnalysisContext& context);
/*! /*!
* Finds points that lie on the facet * Finds points that lie on the facet
@ -192,9 +212,9 @@ namespace storm {
* use smt to find an eps-box in the simplex that does not contain a point. Add new points until one in the box is found. repeat. * use smt to find an eps-box in the simplex that does not contain a point. Add new points until one in the box is found. repeat.
* stop when no more points or boxes can be found. * stop when no more points or boxes can be found.
*/ */
bool analyzePointsOnFacet(Environment const& env, Facet& f, std::set<PointId>& collectedPoints);
bool analyzePointsOnFacet(Environment const& env, FacetAnalysisContext& context);
bool analyzePointsInSimplex(Environment const& env, Facet& f, std::set<PointId>& collectedPoints);
bool analyzePointsInSimplex(Environment const& env, FacetAnalysisContext& context);
Pointset pointset; Pointset pointset;
std::queue<Facet> unprocessedFacets; std::queue<Facet> unprocessedFacets;

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