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tempest/src/counterexamples/MILPMinimalLabelSetGenerator.h

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/*
* MILPMinimalLabelSetGenerator.h
*
* Created on: 15.09.2013
* Author: Christian Dehnert
*/
#ifndef STORM_COUNTEREXAMPLES_MILPMINIMALLABELSETGENERATOR_MDP_H_
#define STORM_COUNTEREXAMPLES_MILPMINIMALLABELSETGENERATOR_MDP_H_
// To detect whether the usage of Gurobi is possible, this include is neccessary.
#include "storm-config.h"
#ifdef STORM_HAVE_GUROBI
extern "C" {
#include "gurobi_c.h"
int __stdcall GRBislp(GRBenv **, const char *, const char *, const char *, const char *);
}
#endif
#include "src/models/Mdp.h"
#include "src/ir/Program.h"
#include "src/exceptions/NotImplementedException.h"
#include "src/exceptions/InvalidArgumentException.h"
#include "src/exceptions/InvalidStateException.h"
#include "src/utility/counterexamples.h"
namespace storm {
namespace counterexamples {
/*!
* This class provides functionality to generate a minimal counterexample to a probabilistic reachability
* property in terms of used labels.
*/
template <class T>
class MILPMinimalLabelSetGenerator {
#ifdef STORM_HAVE_GUROBI
private:
/*!
* A helper class that provides the functionality to compute a hash value for pairs of state indices.
*/
class PairHash {
public:
std::size_t operator()(std::pair<uint_fast64_t, uint_fast64_t> const& pair) const {
size_t seed = 0;
boost::hash_combine(seed, pair.first);
boost::hash_combine(seed, pair.second);
return seed;
}
};
/*!
* A helper struct storing which states are relevant or problematic.
*/
struct StateInformation {
storm::storage::BitVector relevantStates;
storm::storage::BitVector problematicStates;
};
/*!
* A helper struct capturing information about relevant and problematic choices of states and which labels
* are relevant.
*/
struct ChoiceInformation {
std::unordered_map<uint_fast64_t, std::list<uint_fast64_t>> relevantChoicesForRelevantStates;
std::unordered_map<uint_fast64_t, std::list<uint_fast64_t>> problematicChoicesForProblematicStates;
storm::storage::VectorSet<uint_fast64_t> allRelevantLabels;
storm::storage::VectorSet<uint_fast64_t> knownLabels;
};
/*!
* A helper struct capturing information about the variables of the MILP formulation.
*/
struct VariableInformation {
std::unordered_map<uint_fast64_t, uint_fast64_t> labelToVariableIndexMap;
std::unordered_map<uint_fast64_t, std::list<uint_fast64_t>> stateToChoiceVariablesIndexMap;
std::unordered_map<uint_fast64_t, uint_fast64_t> initialStateToChoiceVariableIndexMap;
std::unordered_map<uint_fast64_t, uint_fast64_t> stateToProbabilityVariableIndexMap;
uint_fast64_t virtualInitialStateVariableIndex;
std::unordered_map<uint_fast64_t, uint_fast64_t> problematicStateToVariableIndexMap;
std::unordered_map<std::pair<uint_fast64_t, uint_fast64_t>, uint_fast64_t, PairHash> problematicTransitionToVariableIndexMap;
uint_fast64_t nextFreeVariableIndex;
VariableInformation() : nextFreeVariableIndex(0) {}
};
/*!
* Determines the relevant and the problematic states of the given MDP with respect to the given phi and psi
* state sets. The relevant states are those for which there exists at least one scheduler that attains a
* non-zero probability of satisfying phi until psi. Problematic states are relevant states that have at
* least one scheduler such that the probability of satisfying phi until psi is zero.
*
* @param labeledMdp The MDP whose states to search.
* @param phiStates A bit vector characterizing all states satisfying phi.
* @param psiStates A bit vector characterizing all states satisfying psi.
* @return A structure that stores the relevant and problematic states.
*/
static struct StateInformation determineRelevantAndProblematicStates(storm::models::Mdp<T> const& labeledMdp, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) {
StateInformation result;
storm::storage::SparseMatrix<bool> backwardTransitions = labeledMdp.getBackwardTransitions();
result.relevantStates = storm::utility::graph::performProbGreater0E(labeledMdp, backwardTransitions, phiStates, psiStates);
result.relevantStates &= ~psiStates;
result.problematicStates = storm::utility::graph::performProbGreater0E(labeledMdp, backwardTransitions, phiStates, psiStates);
result.problematicStates.complement();
result.problematicStates &= result.relevantStates;
LOG4CPLUS_DEBUG(logger, "Found " << phiStates.getNumberOfSetBits() << " filter states.");
LOG4CPLUS_DEBUG(logger, "Found " << psiStates.getNumberOfSetBits() << " target states.");
LOG4CPLUS_DEBUG(logger, "Found " << result.relevantStates.getNumberOfSetBits() << " relevant states .");
LOG4CPLUS_DEBUG(logger, "Found " << result.problematicStates.getNumberOfSetBits() << " problematic states.");
return result;
}
/*!
* Determines the relevant and problematic choices of the given MDP with respect to the given parameters.
*
* @param labeledMdp The MDP whose choices to search.
* @param stateInformation The relevant and problematic states of the model.
* @param psiStates A bit vector characterizing the psi states in the model.
* @return A structure that stores the relevant and problematic choices in the model as well as the set
* of relevant labels.
*/
static struct ChoiceInformation determineRelevantAndProblematicChoices(storm::models::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, storm::storage::BitVector const& psiStates) {
// Create result and shortcuts to needed data for convenience.
ChoiceInformation result;
storm::storage::SparseMatrix<T> const& transitionMatrix = labeledMdp.getTransitionMatrix();
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = labeledMdp.getNondeterministicChoiceIndices();
std::vector<storm::storage::VectorSet<uint_fast64_t>> const& choiceLabeling = labeledMdp.getChoiceLabeling();
// Now traverse all choices of all relevant states and check whether there is a relevant target state.
// If so, the associated labels become relevant. Also, if a choice of relevant state has at least one
// relevant successor, the choice is considered to be relevant.
for (auto state : stateInformation.relevantStates) {
result.relevantChoicesForRelevantStates.emplace(state, std::list<uint_fast64_t>());
if (stateInformation.problematicStates.get(state)) {
result.problematicChoicesForProblematicStates.emplace(state, std::list<uint_fast64_t>());
}
for (uint_fast64_t row = nondeterministicChoiceIndices[state]; row < nondeterministicChoiceIndices[state + 1]; ++row) {
bool currentChoiceRelevant = false;
bool allSuccessorsProblematic = true;
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = transitionMatrix.constColumnIteratorBegin(row); successorIt != transitionMatrix.constColumnIteratorEnd(row); ++successorIt) {
// If there is a relevant successor, we need to add the labels of the current choice.
if (stateInformation.relevantStates.get(*successorIt) || psiStates.get(*successorIt)) {
for (auto const& label : choiceLabeling[row]) {
result.allRelevantLabels.insert(label);
}
if (!currentChoiceRelevant) {
currentChoiceRelevant = true;
result.relevantChoicesForRelevantStates[state].push_back(row);
}
}
if (!stateInformation.problematicStates.get(*successorIt)) {
allSuccessorsProblematic = false;
}
}
// If all successors of a problematic state are problematic themselves, we record this choice
// as being problematic.
if (stateInformation.problematicStates.get(state) && allSuccessorsProblematic) {
result.problematicChoicesForProblematicStates[state].push_back(row);
}
}
}
// Finally, determine the set of labels that are known to be taken.
result.knownLabels = storm::utility::counterexamples::getGuaranteedLabelSet(labeledMdp, psiStates, result.allRelevantLabels);
std::cout << "Found " << result.allRelevantLabels.size() << " relevant labels and " << result.knownLabels.size() << " known labels." << std::endl;
LOG4CPLUS_DEBUG(logger, "Found " << result.allRelevantLabels.size() << " relevant labels and " << result.knownLabels.size() << " known labels.");
return result;
}
/*!
* Sets the desired properties for the given Gurobi environment.
*
* @param env The Gurobi environment to modify.
*/
static void setGurobiEnvironmentProperties(GRBenv* env) {
// Enable the following line to only print the output of Gurobi if the debug flag is set.
// int error = error = GRBsetintparam(env, "OutputFlag", storm::settings::Settings::getInstance()->isSet("debug") ? 1 : 0);
int error = error = GRBsetintparam(env, "OutputFlag", 1);
// Enable the following line to restrict Gurobi to one thread only.
error = error = GRBsetintparam(env, "Threads", 1);
// Enable the following line to force Gurobi to be as precise about the binary variables as required by the given precision option.
error = GRBsetdblparam(env, "IntFeasTol", storm::settings::Settings::getInstance()->getOptionByLongName("precision").getArgument(0).getValueAsDouble());
}
/*!
* Creates a Gurobi environment and model and returns pointers to them.
*
* @return A pair of two pointers to a Gurobi environment and model, respectively.
*/
static std::pair<GRBenv*, GRBmodel*> createGurobiEnvironmentAndModel() {
GRBenv* env = nullptr;
int error = GRBloadenv(&env, "");
if (error || env == NULL) {
LOG4CPLUS_ERROR(logger, "Could not initialize Gurobi (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not initialize Gurobi (" << GRBgeterrormsg(env) << ").";
}
setGurobiEnvironmentProperties(env);
GRBmodel* model = nullptr;
error = GRBnewmodel(env, &model, "minimal_label_milp", 0, nullptr, nullptr, nullptr, nullptr, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Could not initialize Gurobi model (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not initialize Gurobi model (" << GRBgeterrormsg(env) << ").";
}
return std::make_pair(env, model);
}
/*!
* Retrieves whether the given Gurobi model was optimized.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @return True if the model was optimized. Otherwise an exception is thrown.
*/
static bool checkGurobiModelIsOptimized(GRBenv* env, GRBmodel* model) {
int optimalityStatus = 0;
int error = GRBgetintattr(model, GRB_INT_ATTR_STATUS, &optimalityStatus);
if (optimalityStatus == GRB_INF_OR_UNBD) {
LOG4CPLUS_ERROR(logger, "Unable to get Gurobi solution from infeasible or unbounded model (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to get Gurobi solution from infeasible or unbounded MILP (" << GRBgeterrormsg(env) << ").";
} else if (optimalityStatus != GRB_OPTIMAL) {
LOG4CPLUS_ERROR(logger, "Unable to get Gurobi solution from unoptimized model (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to get Gurobi solution from unoptimized model (" << GRBgeterrormsg(env) << ").";
}
return true;
}
/*!
* Writes the given Gurobi model to a file.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param filename The name of the file in which to write the model.
*/
static void writeModelToFile(GRBenv* env, GRBmodel* model, std::string const& filename) {
int error = GRBwrite(model, filename.c_str());
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to write Gurobi model (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to write Gurobi model (" << GRBgeterrormsg(env) << ").";
}
}
/*!
* Updates the Gurobi model to incorporate any prior changes.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
*/
static void updateModel(GRBenv* env, GRBmodel* model) {
int error = GRBupdatemodel(model);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to update Gurobi model (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to update Gurobi model (" << GRBgeterrormsg(env) << ").";
}
}
/*!
* Calls Gurobi to optimize the given model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
*/
static void optimizeModel(GRBenv* env, GRBmodel* model) {
int error = GRBoptimize(model);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to optimize Gurobi model (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to optimize Gurobi model (" << GRBgeterrormsg(env) << ").";
}
}
/*!
* Destroys the given Gurobi model and environment to free ressources.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
*/
static void destroyGurobiModelAndEnvironment(GRBenv* env, GRBmodel* model) {
GRBfreemodel(model);
GRBfreeenv(env);
}
/*!
* Creates the variables for the labels of the model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param relevantLabels The set of relevant labels of the model.
* @param nextFreeVariableIndex A reference to the next free variable index. Note: when creating new
* variables, this value is increased.
* @return A mapping from labels to variable indices.
*/
static std::unordered_map<uint_fast64_t, uint_fast64_t> createLabelVariables(GRBenv* env, GRBmodel* model, storm::storage::VectorSet<uint_fast64_t> const& relevantLabels, uint_fast64_t& nextFreeVariableIndex) {
int error = 0;
std::stringstream variableNameBuffer;
std::unordered_map<uint_fast64_t, uint_fast64_t> resultingMap;
for (auto const& label : relevantLabels) {
variableNameBuffer.str("");
variableNameBuffer.clear();
variableNameBuffer << "label" << label;
error = GRBaddvar(model, 0, nullptr, nullptr, 1.0, 0.0, 1.0, GRB_BINARY, variableNameBuffer.str().c_str());
if (error) {
LOG4CPLUS_ERROR(logger, "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").";
}
resultingMap[label] = nextFreeVariableIndex;
++nextFreeVariableIndex;
}
return resultingMap;
}
/*!
* Creates the variables for the relevant choices in the model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param stateInformation The information about the states of the model.
* @param choiceInformation The information about the choices of the model.
* @param nextFreeVariableIndex A reference to the next free variable index. Note: when creating new
* variables, this value is increased.
* @return A mapping from states to a list of choice variable indices.
*/
static std::unordered_map<uint_fast64_t, std::list<uint_fast64_t>> createSchedulerVariables(GRBenv* env, GRBmodel* model, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, uint_fast64_t& nextFreeVariableIndex) {
int error = 0;
std::stringstream variableNameBuffer;
std::unordered_map<uint_fast64_t, std::list<uint_fast64_t>> resultingMap;
for (auto state : stateInformation.relevantStates) {
resultingMap.emplace(state, std::list<uint_fast64_t>());
std::list<uint_fast64_t> const& relevantChoicesForState = choiceInformation.relevantChoicesForRelevantStates.at(state);
for (uint_fast64_t row : relevantChoicesForState) {
variableNameBuffer.str("");
variableNameBuffer.clear();
variableNameBuffer << "choice" << row << "in" << state;
error = GRBaddvar(model, 0, nullptr, nullptr, 0.0, 0.0, 1.0, GRB_BINARY, variableNameBuffer.str().c_str());
if (error) {
LOG4CPLUS_ERROR(logger, "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").";
}
resultingMap[state].push_back(nextFreeVariableIndex);
++nextFreeVariableIndex;
}
}
return resultingMap;
}
/*!
* Creates the variables needed for encoding the nondeterministic selection of one of the initial states
* in the model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param stateInformation The information about the states of the model.
* @param nextFreeVariableIndex A reference to the next free variable index. Note: when creating new
* variables, this value is increased.
* @return A mapping from initial states to choice variable indices.
*/
static std::unordered_map<uint_fast64_t, uint_fast64_t> createInitialChoiceVariables(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, uint_fast64_t& nextFreeVariableIndex) {
int error = 0;
std::stringstream variableNameBuffer;
std::unordered_map<uint_fast64_t, uint_fast64_t> resultingMap;
for (auto initialState : labeledMdp.getLabeledStates("init")) {
// Only consider this initial state if it is relevant.
if (stateInformation.relevantStates.get(initialState)) {
variableNameBuffer.str("");
variableNameBuffer.clear();
variableNameBuffer << "init" << initialState;
error = GRBaddvar(model, 0, nullptr, nullptr, 0.0, 0.0, 1.0, GRB_BINARY, variableNameBuffer.str().c_str());
if (error) {
LOG4CPLUS_ERROR(logger, "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").";
}
resultingMap[initialState] = nextFreeVariableIndex;
++nextFreeVariableIndex;
}
}
return resultingMap;
}
/*!
* Creates the variables for the probabilities in the model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param stateInformation The information about the states in the model.
* @param nextFreeVariableIndex A reference to the next free variable index. Note: when creating new
* variables, this value is increased.
* @param maximizeProbability If set to true, the objective function is constructed in a way that a
* label-minimal subsystem of maximal probability is computed.
* @return A mapping from states to the index of the corresponding probability variables.
*/
static std::unordered_map<uint_fast64_t, uint_fast64_t> createProbabilityVariables(GRBenv* env, GRBmodel* model, StateInformation const& stateInformation, uint_fast64_t& nextFreeVariableIndex) {
int error = 0;
std::stringstream variableNameBuffer;
std::unordered_map<uint_fast64_t, uint_fast64_t> resultingMap;
for (auto state : stateInformation.relevantStates) {
variableNameBuffer.str("");
variableNameBuffer.clear();
variableNameBuffer << "p" << state;
error = GRBaddvar(model, 0, nullptr, nullptr, 0.0, 0.0, 1.0, GRB_CONTINUOUS, variableNameBuffer.str().c_str());
if (error) {
LOG4CPLUS_ERROR(logger, "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").";
}
resultingMap[state] = nextFreeVariableIndex;
++nextFreeVariableIndex;
}
return resultingMap;
}
/*!
* Creates the variables for the probabilities in the model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param nextFreeVariableIndex A reference to the next free variable index. Note: when creating new
* variables, this value is increased.
* @param maximizeProbability If set to true, the objective function is constructed in a way that a
* label-minimal subsystem of maximal probability is computed.
* @return The index of the variable for the probability of the virtual initial state.
*/
static uint_fast64_t createVirtualInitialStateVariable(GRBenv* env, GRBmodel* model, uint_fast64_t& nextFreeVariableIndex, bool maximizeProbability = false) {
int error = 0;
std::stringstream variableNameBuffer;
variableNameBuffer << "pinit";
error = GRBaddvar(model, 0, nullptr, nullptr, maximizeProbability ? -0.5 : 0.0, 0.0, 1.0, GRB_CONTINUOUS, variableNameBuffer.str().c_str());
if (error) {
LOG4CPLUS_ERROR(logger, "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").";
}
uint_fast64_t variableIndex = nextFreeVariableIndex;
++nextFreeVariableIndex;
return variableIndex;
}
/*!
* Creates the variables for the problematic states in the model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param stateInformation The information about the states in the model.
* @param nextFreeVariableIndex A reference to the next free variable index. Note: when creating new
* variables, this value is increased.
* @return A mapping from problematic states to the index of the corresponding variables.
*/
static std::unordered_map<uint_fast64_t, uint_fast64_t> createProblematicStateVariables(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, uint_fast64_t& nextFreeVariableIndex) {
int error = 0;
std::stringstream variableNameBuffer;
std::unordered_map<uint_fast64_t, uint_fast64_t> resultingMap;
for (auto state : stateInformation.problematicStates) {
// First check whether there is not already a variable for this state and advance to the next state
// in this case.
if (resultingMap.find(state) == resultingMap.end()) {
variableNameBuffer.str("");
variableNameBuffer.clear();
variableNameBuffer << "r" << state;
error = GRBaddvar(model, 0, nullptr, nullptr, 0.0, 0.0, 1.0, GRB_CONTINUOUS, variableNameBuffer.str().c_str());
if (error) {
LOG4CPLUS_ERROR(logger, "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").";
}
resultingMap[state] = nextFreeVariableIndex;
++nextFreeVariableIndex;
}
std::list<uint_fast64_t> const& relevantChoicesForState = choiceInformation.relevantChoicesForRelevantStates.at(state);
for (uint_fast64_t row : relevantChoicesForState) {
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = labeledMdp.getTransitionMatrix().constColumnIteratorBegin(row); successorIt != labeledMdp.getTransitionMatrix().constColumnIteratorEnd(row); ++successorIt) {
if (stateInformation.relevantStates.get(*successorIt)) {
if (resultingMap.find(*successorIt) == resultingMap.end()) {
variableNameBuffer.str("");
variableNameBuffer.clear();
variableNameBuffer << "r" << *successorIt;
error = GRBaddvar(model, 0, nullptr, nullptr, 0.0, 0.0, 1.0, GRB_CONTINUOUS, variableNameBuffer.str().c_str());
if (error) {
LOG4CPLUS_ERROR(logger, "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").";
}
resultingMap[state] = nextFreeVariableIndex;
++nextFreeVariableIndex;
}
}
}
}
}
return resultingMap;
}
/*!
* Creates the variables for the problematic choices in the model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param stateInformation The information about the states in the model.
* @param choiceInformation The information about the choices in the model.
* @param nextFreeVariableIndex A reference to the next free variable index. Note: when creating new
* variables, this value is increased.
* @return A mapping from problematic choices to the index of the corresponding variables.
*/
static std::unordered_map<std::pair<uint_fast64_t, uint_fast64_t>, uint_fast64_t, PairHash> createProblematicChoiceVariables(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, uint_fast64_t& nextFreeVariableIndex) {
int error = 0;
std::stringstream variableNameBuffer;
std::unordered_map<std::pair<uint_fast64_t, uint_fast64_t>, uint_fast64_t, PairHash> resultingMap;
for (auto state : stateInformation.problematicStates) {
std::list<uint_fast64_t> const& relevantChoicesForState = choiceInformation.relevantChoicesForRelevantStates.at(state);
for (uint_fast64_t row : relevantChoicesForState) {
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = labeledMdp.getTransitionMatrix().constColumnIteratorBegin(row); successorIt != labeledMdp.getTransitionMatrix().constColumnIteratorEnd(row); ++successorIt) {
if (stateInformation.relevantStates.get(*successorIt)) {
variableNameBuffer.str("");
variableNameBuffer.clear();
variableNameBuffer << "t" << state << "to" << *successorIt;
error = GRBaddvar(model, 0, nullptr, nullptr, 0.0, 0.0, 1.0, GRB_BINARY, variableNameBuffer.str().c_str());
if (error) {
LOG4CPLUS_ERROR(logger, "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Could not create Gurobi variable (" << GRBgeterrormsg(env) << ").";
}
resultingMap[std::make_pair(state, *successorIt)] = nextFreeVariableIndex;
++nextFreeVariableIndex;
}
}
}
}
return resultingMap;
}
/*!
* Creates all variables needed to encode the problem as an MILP problem and returns a struct containing
* information about the variables that were created. This implicitly establishes the objective function
* passed to the solver.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param stateInformation The information about the states in the model.
* @param choiceInformation The information about the choices in the model.
*/
static VariableInformation createVariables(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation) {
// Create a struct that stores all information about variables.
VariableInformation result;
// Create variables for involved labels.
result.labelToVariableIndexMap = createLabelVariables(env, model, choiceInformation.allRelevantLabels, result.nextFreeVariableIndex);
LOG4CPLUS_DEBUG(logger, "Created variables for labels.");
// Create scheduler variables for relevant states and their actions.
result.stateToChoiceVariablesIndexMap = createSchedulerVariables(env, model, stateInformation, choiceInformation, result.nextFreeVariableIndex);
LOG4CPLUS_DEBUG(logger, "Created variables for nondeterministic choices.");
// Create scheduler variables for nondeterministically choosing an initial state.
result.initialStateToChoiceVariableIndexMap = createInitialChoiceVariables(env, model, labeledMdp, stateInformation, result.nextFreeVariableIndex);
LOG4CPLUS_DEBUG(logger, "Created variables for the nondeterministic choice of the initial state.");
// Create variables for probabilities for all relevant states.
result.stateToProbabilityVariableIndexMap = createProbabilityVariables(env, model, stateInformation, result.nextFreeVariableIndex);
LOG4CPLUS_DEBUG(logger, "Created variables for the reachability probabilities.");
// Create a probability variable for a virtual initial state that nondeterministically chooses one of the system's real initial states as its target state.
result.virtualInitialStateVariableIndex = createVirtualInitialStateVariable(env, model, result.nextFreeVariableIndex);
LOG4CPLUS_DEBUG(logger, "Created variables for the virtual initial state.");
// Create variables for problematic states.
result.problematicStateToVariableIndexMap = createProblematicStateVariables(env, model, labeledMdp, stateInformation, choiceInformation, result.nextFreeVariableIndex);
LOG4CPLUS_DEBUG(logger, "Created variables for the problematic states.");
// Create variables for problematic choices.
result.problematicTransitionToVariableIndexMap = createProblematicChoiceVariables(env, model, labeledMdp, stateInformation, choiceInformation, result.nextFreeVariableIndex);
LOG4CPLUS_DEBUG(logger, "Created variables for the problematic choices.");
LOG4CPLUS_INFO(logger, "Successfully created " << result.nextFreeVariableIndex << " Gurobi variables.");
// Finally, return variable information struct.
return result;
}
/*!
* Asserts a constraint in the MILP problem that makes sure the reachability probability in the subsystem
* exceeds the given threshold.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param variableInformation A struct with information about the variables of the model.
* @param probabilityThreshold The probability that the subsystem must exceed.
* @param strictBound A flag indicating whether the threshold must be exceeded or only matched.
* @return The total number of constraints that were created.
*/
static uint_fast64_t assertProbabilityGreaterThanThreshold(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, VariableInformation const& variableInformation, double probabilityThreshold, bool strictBound) {
uint_fast64_t numberOfConstraintsCreated = 0;
int error = 0;
int variableIndex = static_cast<int>(variableInformation.virtualInitialStateVariableIndex);
double coefficient = 1.0;
error = GRBaddconstr(model, 1, &variableIndex, &coefficient, GRB_GREATER_EQUAL, strictBound ? probabilityThreshold : probabilityThreshold + 1e-6, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
return numberOfConstraintsCreated;
}
/*!
* Asserts constraints that make sure the selected policy is valid, i.e. chooses at most one action in each state.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param stateInformation The information about the states in the model.
* @param variableInformation A struct with information about the variables of the model.
* @return The total number of constraints that were created.
*/
static uint_fast64_t assertValidPolicy(GRBenv* env, GRBmodel* model, StateInformation const& stateInformation, VariableInformation const& variableInformation) {
// Assert that the policy chooses at most one action in each state of the system.
uint_fast64_t numberOfConstraintsCreated = 0;
int error = 0;
for (auto state : stateInformation.relevantStates) {
std::list<uint_fast64_t> const& choiceVariableIndices = variableInformation.stateToChoiceVariablesIndexMap.at(state);
std::vector<int> variables;
std::vector<double> coefficients(choiceVariableIndices.size(), 1);
variables.reserve(choiceVariableIndices.size());
for (auto choiceVariableIndex : choiceVariableIndices) {
variables.push_back(static_cast<int>(choiceVariableIndex));
}
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_LESS_EQUAL, 1, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
}
// Now assert that the virtual initial state picks exactly one initial state from the system as its
// successor state.
std::vector<int> variables;
variables.reserve(variableInformation.initialStateToChoiceVariableIndexMap.size());
std::vector<double> coefficients(variableInformation.initialStateToChoiceVariableIndexMap.size(), 1);
for (auto initialStateVariableIndexPair : variableInformation.initialStateToChoiceVariableIndexMap) {
variables.push_back(static_cast<int>(initialStateVariableIndexPair.second));
}
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_EQUAL, 1, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
return numberOfConstraintsCreated;
}
/*!
* Asserts constraints that make sure the labels are included in the solution set if the policy selects a
* choice that is labeled with the label in question.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param stateInformation The information about the states in the model.
* @param choiceInformation The information about the choices in the model.
* @param variableInformation A struct with information about the variables of the model.
* @return The total number of constraints that were created.
*/
static uint_fast64_t assertChoicesImplyLabels(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
uint_fast64_t numberOfConstraintsCreated = 0;
int error = 0;
std::vector<storm::storage::VectorSet<uint_fast64_t>> const& choiceLabeling = labeledMdp.getChoiceLabeling();
for (auto state : stateInformation.relevantStates) {
std::list<uint_fast64_t>::const_iterator choiceVariableIndicesIterator = variableInformation.stateToChoiceVariablesIndexMap.at(state).begin();
for (auto choice : choiceInformation.relevantChoicesForRelevantStates.at(state)) {
int indices[2]; indices[0] = 0; indices[1] = *choiceVariableIndicesIterator;
double coefficients[2]; coefficients[0] = 1; coefficients[1] = -1;
for (auto label : choiceLabeling[choice]) {
indices[0] = variableInformation.labelToVariableIndexMap.at(label);
error = GRBaddconstr(model, 2, indices, coefficients, GRB_GREATER_EQUAL, 0, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
}
++choiceVariableIndicesIterator;
}
}
return numberOfConstraintsCreated;
}
/*!
* Asserts constraints that make sure the reachability probability is zero for states in which the policy
* does not pick any outgoing action.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param stateInformation The information about the states in the model.
* @param choiceInformation The information about the choices in the model.
* @param variableInformation A struct with information about the variables of the model.
* @return The total number of constraints that were created.
*/
static uint_fast64_t assertZeroProbabilityWithoutChoice(GRBenv* env, GRBmodel* model, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
uint_fast64_t numberOfConstraintsCreated = 0;
int error = 0;
for (auto state : stateInformation.relevantStates) {
std::list<uint_fast64_t> const& choiceVariableIndices = variableInformation.stateToChoiceVariablesIndexMap.at(state);
std::vector<double> coefficients(choiceVariableIndices.size() + 1, -1);
coefficients[0] = 1;
std::vector<int> variables;
variables.reserve(variableInformation.stateToChoiceVariablesIndexMap.at(state).size() + 1);
variables.push_back(static_cast<int>(variableInformation.stateToProbabilityVariableIndexMap.at(state)));
variables.insert(variables.end(), choiceVariableIndices.begin(), choiceVariableIndices.end());
error = GRBaddconstr(model, choiceVariableIndices.size() + 1, &variables[0], &coefficients[0], GRB_LESS_EQUAL, 0, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
}
return numberOfConstraintsCreated;
}
/*!
* Asserts constraints that encode the correct reachability probabilties for all states.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param psiStates A bit vector characterizing the psi states in the model.
* @param stateInformation The information about the states in the model.
* @param choiceInformation The information about the choices in the model.
* @param variableInformation A struct with information about the variables of the model.
* @return The total number of constraints that were created.
*/
static uint_fast64_t assertReachabilityProbabilities(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, storm::storage::BitVector const& psiStates, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
uint_fast64_t numberOfConstraintsCreated = 0;
int error = 0;
for (auto state : stateInformation.relevantStates) {
std::vector<double> coefficients;
std::vector<int> variables;
std::list<uint_fast64_t>::const_iterator choiceVariableIndicesIterator = variableInformation.stateToChoiceVariablesIndexMap.at(state).begin();
for (auto choice : choiceInformation.relevantChoicesForRelevantStates.at(state)) {
variables.clear();
coefficients.clear();
variables.push_back(static_cast<int>(variableInformation.stateToProbabilityVariableIndexMap.at(state)));
coefficients.push_back(1.0);
double rightHandSide = 1;
typename storm::storage::SparseMatrix<T>::Rows rows = labeledMdp.getTransitionMatrix().getRows(choice, choice);
for (typename storm::storage::SparseMatrix<T>::ConstIterator successorIt = rows.begin(), successorIte = rows.end(); successorIt != successorIte; ++successorIt) {
if (stateInformation.relevantStates.get(successorIt.column())) {
variables.push_back(static_cast<int>(variableInformation.stateToProbabilityVariableIndexMap.at(successorIt.column())));
coefficients.push_back(-successorIt.value());
} else if (psiStates.get(successorIt.column())) {
rightHandSide += successorIt.value();
}
}
coefficients.push_back(1);
variables.push_back(static_cast<int>(*choiceVariableIndicesIterator));
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_LESS_EQUAL, rightHandSide, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
++choiceVariableIndicesIterator;
}
}
// Make sure that the virtual initial state is being assigned the probability from the initial state
// that it selected as a successor state.
std::vector<double> coefficients(3);
coefficients[0] = 1;
coefficients[1] = -1;
coefficients[2] = 1;
std::vector<int> variables(3);
variables[0] = static_cast<int>(variableInformation.virtualInitialStateVariableIndex);
for (auto initialStateVariableIndexPair : variableInformation.initialStateToChoiceVariableIndexMap) {
variables[1] = static_cast<int>(variableInformation.stateToProbabilityVariableIndexMap.at(initialStateVariableIndexPair.first));
variables[2] = static_cast<int>(initialStateVariableIndexPair.second);
}
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_LESS_EQUAL, 1, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
return numberOfConstraintsCreated;
}
/*!
* Asserts constraints that make sure an unproblematic state is reachable from each problematic state.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param stateInformation The information about the states in the model.
* @param choiceInformation The information about the choices in the model.
* @param variableInformation A struct with information about the variables of the model.
* @return The total number of constraints that were created.
*/
static uint_fast64_t assertUnproblematicStateReachable(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
uint_fast64_t numberOfConstraintsCreated = 0;
int error = 0;
for (auto stateListPair : choiceInformation.problematicChoicesForProblematicStates) {
for (auto problematicChoice : stateListPair.second) {
std::list<uint_fast64_t>::const_iterator choiceVariableIndicesIterator = variableInformation.stateToChoiceVariablesIndexMap.at(stateListPair.first).begin();
for (auto relevantChoice : choiceInformation.relevantChoicesForRelevantStates.at(stateListPair.first)) {
if (relevantChoice == problematicChoice) {
break;
}
++choiceVariableIndicesIterator;
}
std::vector<int> variables;
std::vector<double> coefficients;
variables.push_back(static_cast<int>(*choiceVariableIndicesIterator));
coefficients.push_back(1);
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = labeledMdp.getTransitionMatrix().constColumnIteratorBegin(problematicChoice); successorIt != labeledMdp.getTransitionMatrix().constColumnIteratorEnd(problematicChoice); ++successorIt) {
variables.push_back(static_cast<int>(variableInformation.problematicTransitionToVariableIndexMap.at(std::make_pair(stateListPair.first, *successorIt))));
coefficients.push_back(-1);
}
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_LESS_EQUAL, 0, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
}
}
for (auto state : stateInformation.problematicStates) {
for (auto problematicChoice : choiceInformation.problematicChoicesForProblematicStates.at(state)) {
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = labeledMdp.getTransitionMatrix().constColumnIteratorBegin(problematicChoice); successorIt != labeledMdp.getTransitionMatrix().constColumnIteratorEnd(problematicChoice); ++successorIt) {
std::vector<int> variables;
std::vector<double> coefficients;
variables.push_back(static_cast<int>(variableInformation.problematicStateToVariableIndexMap.at(state)));
coefficients.push_back(1);
variables.push_back(static_cast<int>(variableInformation.problematicStateToVariableIndexMap.at(*successorIt)));
coefficients.push_back(-1);
variables.push_back(static_cast<int>(variableInformation.problematicTransitionToVariableIndexMap.at(std::make_pair(state, *successorIt))));
coefficients.push_back(1);
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_LESS_EQUAL, 1 - 1e-6, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
}
}
}
return numberOfConstraintsCreated;
}
/*
* Asserts that labels that are on all paths from initial to target states are definitely taken.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param psiStates A bit vector characterizing the psi states in the model.
* @param choiceInformation The information about the choices in the model.
* @param variableInformation A struct with information about the variables of the model.
* @return The total number of constraints that were created.
*/
static uint_fast64_t assertKnownLabels(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, storm::storage::BitVector const& psiStates, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
uint_fast64_t numberOfConstraintsCreated = 0;
int error = 0;
for (auto label : choiceInformation.knownLabels) {
double coefficient = 1;
int variableIndex = variableInformation.labelToVariableIndexMap.at(label);
error = GRBaddconstr(model, 1, &variableIndex, &coefficient, GRB_LESS_EQUAL, 1, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
}
return numberOfConstraintsCreated;
}
/*!
* Asserts constraints that rule out many suboptimal policies.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param psiStates A bit vector characterizing the psi states in the model.
* @param stateInformation The information about the states in the model.
* @param choiceInformation The information about the choices in the model.
* @param variableInformation A struct with information about the variables of the model.
* @return The total number of constraints that were created.
*/
static uint_fast64_t assertSchedulerCuts(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, storm::storage::BitVector const& psiStates, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
storm::storage::SparseMatrix<bool> backwardTransitions = labeledMdp.getBackwardTransitions();
uint_fast64_t numberOfConstraintsCreated = 0;
int error = 0;
std::vector<int> variables;
std::vector<double> coefficients;
for (auto state : stateInformation.relevantStates) {
// Assert that all states, that select an action, this action either has a non-zero probability to
// go to a psi state directly, or in the successor states, at least one action is selected as well.
std::list<uint_fast64_t>::const_iterator choiceVariableIndicesIterator = variableInformation.stateToChoiceVariablesIndexMap.at(state).begin();
for (auto choice : choiceInformation.relevantChoicesForRelevantStates.at(state)) {
bool psiStateReachableInOneStep = false;
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = labeledMdp.getTransitionMatrix().constColumnIteratorBegin(choice); successorIt != labeledMdp.getTransitionMatrix().constColumnIteratorEnd(choice); ++successorIt) {
if (psiStates.get(*successorIt)) {
psiStateReachableInOneStep = true;
}
}
if (!psiStateReachableInOneStep) {
variables.clear();
coefficients.clear();
variables.push_back(static_cast<int>(*choiceVariableIndicesIterator));
coefficients.push_back(1);
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = labeledMdp.getTransitionMatrix().constColumnIteratorBegin(choice); successorIt != labeledMdp.getTransitionMatrix().constColumnIteratorEnd(choice); ++successorIt) {
if (state != *successorIt && stateInformation.relevantStates.get(*successorIt)) {
std::list<uint_fast64_t> const& successorChoiceVariableIndices = variableInformation.stateToChoiceVariablesIndexMap.at(*successorIt);
for (auto choiceVariableIndex : successorChoiceVariableIndices) {
variables.push_back(static_cast<int>(choiceVariableIndex));
coefficients.push_back(-1);
}
}
}
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_LESS_EQUAL, 0, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
}
++choiceVariableIndicesIterator;
}
// For all states assert that there is either a selected incoming transition in the subsystem or the
// state is the chosen initial state if there is one selected action in the current state.
variables.clear();
coefficients.clear();
for (auto choiceVariableIndex : variableInformation.stateToChoiceVariablesIndexMap.at(state)) {
variables.push_back(static_cast<int>(choiceVariableIndex));
coefficients.push_back(1);
}
// Compute the set of predecessors.
std::unordered_set<uint_fast64_t> predecessors;
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator predecessorIt = backwardTransitions.constColumnIteratorBegin(state); predecessorIt != backwardTransitions.constColumnIteratorEnd(state); ++predecessorIt) {
if (state != *predecessorIt) {
predecessors.insert(*predecessorIt);
}
}
for (auto predecessor : predecessors) {
// If the predecessor is not a relevant state, we need to skip it.
if (!stateInformation.relevantStates.get(predecessor)) {
continue;
}
std::list<uint_fast64_t>::const_iterator choiceVariableIndicesIterator = variableInformation.stateToChoiceVariablesIndexMap.at(predecessor).begin();
for (auto relevantChoice : choiceInformation.relevantChoicesForRelevantStates.at(predecessor)) {
bool choiceTargetsCurrentState = false;
// Check if the current choice targets the current state.
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = labeledMdp.getTransitionMatrix().constColumnIteratorBegin(relevantChoice); successorIt != labeledMdp.getTransitionMatrix().constColumnIteratorEnd(relevantChoice); ++successorIt) {
if (state == *successorIt) {
choiceTargetsCurrentState = true;
break;
}
}
// If it does, we can add the choice to the sum.
if (choiceTargetsCurrentState) {
variables.push_back(static_cast<int>(*choiceVariableIndicesIterator));
coefficients.push_back(-1);
}
++choiceVariableIndicesIterator;
}
}
// If the current state is an initial state and is selected as a successor state by the virtual
// initial state, then this also justifies making a choice in the current state.
if (labeledMdp.getLabeledStates("init").get(state)) {
variables.push_back(static_cast<int>(variableInformation.initialStateToChoiceVariableIndexMap.at(state)));
coefficients.push_back(-1);
}
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_LESS_EQUAL, 0, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
}
// Assert that at least one initial state selects at least one action.
variables.clear();
coefficients.clear();
for (auto initialState : labeledMdp.getLabeledStates("init")) {
for (auto choiceVariableIndex : variableInformation.stateToChoiceVariablesIndexMap.at(initialState)) {
variables.push_back(static_cast<int>(choiceVariableIndex));
coefficients.push_back(1);
}
}
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_GREATER_EQUAL, 1, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
// Add constraints that ensure at least one choice is selected that targets a psi state.
variables.clear();
coefficients.clear();
std::unordered_set<uint_fast64_t> predecessors;
for (auto psiState : psiStates) {
// Compute the set of predecessors.
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator predecessorIt = backwardTransitions.constColumnIteratorBegin(psiState); predecessorIt != backwardTransitions.constColumnIteratorEnd(psiState); ++predecessorIt) {
if (psiState != *predecessorIt) {
predecessors.insert(*predecessorIt);
}
}
}
for (auto predecessor : predecessors) {
// If the predecessor is not a relevant state, we need to skip it.
if (!stateInformation.relevantStates.get(predecessor)) {
continue;
}
std::list<uint_fast64_t>::const_iterator choiceVariableIndicesIterator = variableInformation.stateToChoiceVariablesIndexMap.at(predecessor).begin();
for (auto relevantChoice : choiceInformation.relevantChoicesForRelevantStates.at(predecessor)) {
bool choiceTargetsPsiState = false;
// Check if the current choice targets the current state.
for (typename storm::storage::SparseMatrix<T>::ConstIndexIterator successorIt = labeledMdp.getTransitionMatrix().constColumnIteratorBegin(relevantChoice); successorIt != labeledMdp.getTransitionMatrix().constColumnIteratorEnd(relevantChoice); ++successorIt) {
if (psiStates.get(*successorIt)) {
choiceTargetsPsiState = true;
break;
}
}
// If it does, we can add the choice to the sum.
if (choiceTargetsPsiState) {
variables.push_back(static_cast<int>(*choiceVariableIndicesIterator));
coefficients.push_back(1);
}
++choiceVariableIndicesIterator;
}
}
error = GRBaddconstr(model, variables.size(), &variables[0], &coefficients[0], GRB_GREATER_EQUAL, 1, nullptr);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to assert constraint (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to assert constraint (" << GRBgeterrormsg(env) << ").";
}
++numberOfConstraintsCreated;
return numberOfConstraintsCreated;
}
/*!
* Builds a system of constraints that express that the reachability probability in the subsystem exceeeds
* the given threshold.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param psiStates A bit vector characterizing all psi states in the model.
* @param stateInformation The information about the states in the model.
* @param choiceInformation The information about the choices in the model.
* @param variableInformation A struct with information about the variables of the model.
* @param probabilityThreshold The probability threshold the subsystem is required to exceed.
* @param strictBound A flag indicating whether the threshold must be exceeded or only matched.
* @param includeSchedulerCuts If set to true, additional constraints are asserted that reduce the set of
* possible choices.
*/
static void buildConstraintSystem(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, storm::storage::BitVector const& psiStates, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation, double probabilityThreshold, bool strictBound, bool includeSchedulerCuts = false) {
// Assert that the reachability probability in the subsystem exceeds the given threshold.
uint_fast64_t numberOfConstraints = assertProbabilityGreaterThanThreshold(env, model, labeledMdp, variableInformation, probabilityThreshold, strictBound);
LOG4CPLUS_DEBUG(logger, "Asserted that reachability probability exceeds threshold.");
// Add constraints that assert the policy takes at most one action in each state.
numberOfConstraints += assertValidPolicy(env, model, stateInformation, variableInformation);
LOG4CPLUS_DEBUG(logger, "Asserted that policy is valid.");
// Add constraints that assert the labels that belong to some taken choices are taken as well.
numberOfConstraints += assertChoicesImplyLabels(env, model, labeledMdp, stateInformation, choiceInformation, variableInformation);
LOG4CPLUS_DEBUG(logger, "Asserted that labels implied by choices are taken.");
// Add constraints that encode that the reachability probability from states which do not pick any action
// is zero.
numberOfConstraints += assertZeroProbabilityWithoutChoice(env, model, stateInformation, choiceInformation, variableInformation);
LOG4CPLUS_DEBUG(logger, "Asserted that reachability probability is zero if no choice is taken.");
// Add constraints that encode the reachability probabilities for states.
numberOfConstraints += assertReachabilityProbabilities(env, model, labeledMdp, psiStates, stateInformation, choiceInformation, variableInformation);
LOG4CPLUS_DEBUG(logger, "Asserted constraints for reachability probabilities.");
// Add constraints that ensure the reachability of an unproblematic state from each problematic state.
numberOfConstraints += assertUnproblematicStateReachable(env, model, labeledMdp, stateInformation, choiceInformation, variableInformation);
LOG4CPLUS_DEBUG(logger, "Asserted that unproblematic state reachable from problematic states.");
// Add constraints that express that certain labels are already known to be taken.
numberOfConstraints += assertKnownLabels(env, model, labeledMdp, psiStates, choiceInformation, variableInformation);
LOG4CPLUS_DEBUG(logger, "Asserted known labels are taken.");
// If required, assert additional constraints that reduce the number of possible policies.
if (includeSchedulerCuts) {
numberOfConstraints += assertSchedulerCuts(env, model, labeledMdp, psiStates, stateInformation, choiceInformation, variableInformation);
LOG4CPLUS_DEBUG(logger, "Asserted scheduler cuts.");
}
LOG4CPLUS_INFO(logger, "Successfully created " << numberOfConstraints << " Gurobi constraints.");
}
/*!
* Computes the set of labels that was used in the given optimized model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param variableInformation A struct with information about the variables of the model.
*/
static storm::storage::VectorSet<uint_fast64_t> getUsedLabelsInSolution(GRBenv* env, GRBmodel* model, VariableInformation const& variableInformation) {
int error = 0;
// Check whether the model was optimized, so we can read off the solution.
if (checkGurobiModelIsOptimized(env, model)) {
storm::storage::VectorSet<uint_fast64_t> result;
double value = 0;
for (auto labelVariablePair : variableInformation.labelToVariableIndexMap) {
error = GRBgetdblattrelement(model, GRB_DBL_ATTR_X, labelVariablePair.second, &value);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to get Gurobi solution (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to get Gurobi solution (" << GRBgeterrormsg(env) << ").";
}
if (std::abs(value - 1) <= storm::settings::Settings::getInstance()->getOptionByLongName("precision").getArgument(0).getValueAsDouble()) {
result.insert(labelVariablePair.first);
} else if (std::abs(value) > storm::settings::Settings::getInstance()->getOptionByLongName("precision").getArgument(0).getValueAsDouble()) {
LOG4CPLUS_ERROR(logger, "Illegal value for binary variable in Gurobi solution (" << value << ").");
throw storm::exceptions::InvalidStateException() << "Illegal value for binary variable in Gurobi solution (" << value << ").";
}
}
return result;
}
LOG4CPLUS_ERROR(logger, "Unable to get Gurobi solution from unoptimized model.");
throw storm::exceptions::InvalidStateException() << "Unable to get Gurobi solution from unoptimized model.";
}
/*!
* Computes a mapping from relevant states to choices such that a state is mapped to one of its choices if
* it is selected by the subsystem computed by the solver.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param stateInformation The information about the states in the model.
* @param choiceInformation The information about the choices in the model.
* @param variableInformation A struct with information about the variables of the model.
*/
static std::map<uint_fast64_t, uint_fast64_t> getChoices(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, StateInformation const& stateInformation, ChoiceInformation const& choiceInformation, VariableInformation const& variableInformation) {
int error = 0;
if (checkGurobiModelIsOptimized(env, model)) {
std::map<uint_fast64_t, uint_fast64_t> result;
double value = 0;
for (auto state : stateInformation.relevantStates) {
std::list<uint_fast64_t>::const_iterator choiceVariableIndicesIterator = variableInformation.stateToChoiceVariablesIndexMap.at(state).begin();
for (auto choice : choiceInformation.relevantChoicesForRelevantStates.at(state)) {
error = GRBgetdblattrelement(model, GRB_DBL_ATTR_X, *choiceVariableIndicesIterator, &value);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to get Gurobi solution (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to get Gurobi solution (" << GRBgeterrormsg(env) << ").";
}
++choiceVariableIndicesIterator;
if (std::abs(value - 1) <= storm::settings::Settings::getInstance()->getOptionByLongName("precision").getArgument(0).getValueAsDouble()) {
result.emplace_hint(result.end(), state, choice);
} else if (std::abs(value) > storm::settings::Settings::getInstance()->getOptionByLongName("precision").getArgument(0).getValueAsDouble()) {
LOG4CPLUS_ERROR(logger, "Illegal value for binary variable in Gurobi solution (" << value << ").");
throw storm::exceptions::InvalidStateException() << "Illegal value for binary variable in Gurobi solution (" << value << ").";
}
}
}
return result;
}
LOG4CPLUS_ERROR(logger, "Unable to get Gurobi solution from unoptimized model.");
throw storm::exceptions::InvalidStateException() << "Unable to get Gurobi solution from unoptimized model.";
}
/*!
* Computes the reachability probability and the selected initial state in the given optimized Gurobi model.
*
* @param env The Gurobi environment.
* @param model The Gurobi model.
* @param labeledMdp The labeled MDP.
* @param variableInformation A struct with information about the variables of the model.
*/
static std::pair<uint_fast64_t, double> getReachabilityProbability(GRBenv* env, GRBmodel* model, storm::models::Mdp<T> const& labeledMdp, VariableInformation const& variableInformation) {
int error = 0;
// Check whether the model was optimized, so we can read off the solution.
if (checkGurobiModelIsOptimized(env, model)) {
uint_fast64_t selectedInitialState = 0;
double value = 0;
for (auto initialStateVariableIndexPair : variableInformation.initialStateToChoiceVariableIndexMap) {
error = GRBgetdblattrelement(model, GRB_DBL_ATTR_X, initialStateVariableIndexPair.second, &value);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to get Gurobi solution (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to get Gurobi solution (" << GRBgeterrormsg(env) << ").";
}
if (std::abs(value - 1) <= storm::settings::Settings::getInstance()->getOptionByLongName("precision").getArgument(0).getValueAsDouble()) {
selectedInitialState = initialStateVariableIndexPair.first;
break;
} else if (std::abs(value) > storm::settings::Settings::getInstance()->getOptionByLongName("precision").getArgument(0).getValueAsDouble()) {
LOG4CPLUS_ERROR(logger, "Illegal value for binary variable in Gurobi solution (" << value << ").");
throw storm::exceptions::InvalidStateException() << "Illegal value for binary variable in Gurobi solution (" << value << ").";
}
}
double reachabilityProbability = 0;
error = GRBgetdblattrelement(model, GRB_DBL_ATTR_X, variableInformation.virtualInitialStateVariableIndex, &reachabilityProbability);
if (error) {
LOG4CPLUS_ERROR(logger, "Unable to get Gurobi solution (" << GRBgeterrormsg(env) << ").");
throw storm::exceptions::InvalidStateException() << "Unable to get Gurobi solution (" << GRBgeterrormsg(env) << ").";
}
return std::make_pair(selectedInitialState, reachabilityProbability);
}
LOG4CPLUS_ERROR(logger, "Unable to get Gurobi solution from unoptimized model.");
throw storm::exceptions::InvalidStateException() << "Unable to get Gurobi solution from unoptimized model.";
}
#endif
public:
static storm::storage::VectorSet<uint_fast64_t> getMinimalLabelSet(storm::models::Mdp<T> const& labeledMdp, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, double probabilityThreshold, bool strictBound, bool checkThresholdFeasible = false, bool includeSchedulerCuts = false) {
#ifdef STORM_HAVE_GUROBI
// (0) Check whether the MDP is indeed labeled.
if (!labeledMdp.hasChoiceLabeling()) {
throw storm::exceptions::InvalidArgumentException() << "Minimal label set generation is impossible for unlabeled model.";
}
// (1) Check whether its possible to exceed the threshold if checkThresholdFeasible is set.
double maximalReachabilityProbability = 0;
storm::modelchecker::prctl::SparseMdpPrctlModelChecker<T> modelchecker(labeledMdp, new storm::solver::GmmxxNondeterministicLinearEquationSolver<T>());
std::vector<T> result = modelchecker.checkUntil(false, phiStates, psiStates, false).first;
for (auto state : labeledMdp.getInitialStates()) {
maximalReachabilityProbability = std::max(maximalReachabilityProbability, result[state]);
}
if ((strictBound && maximalReachabilityProbability < probabilityThreshold) || (!strictBound && maximalReachabilityProbability <= probabilityThreshold)) {
throw storm::exceptions::InvalidArgumentException() << "Given probability threshold " << probabilityThreshold << " can not be " << (strictBound ? "achieved" : "exceeded") << " in model with maximal reachability probability of " << maximalReachabilityProbability << ".";
}
// (2) Identify relevant and problematic states.
StateInformation stateInformation = determineRelevantAndProblematicStates(labeledMdp, phiStates, psiStates);
// (3) Determine sets of relevant labels and problematic choices.
ChoiceInformation choiceInformation = determineRelevantAndProblematicChoices(labeledMdp, stateInformation, psiStates);
// (4) Encode resulting system as MILP problem.
// (4.1) Initialize Gurobi environment and model.
std::pair<GRBenv*, GRBmodel*> environmentModelPair = createGurobiEnvironmentAndModel();
// (4.2) Create variables.
VariableInformation variableInformation = createVariables(environmentModelPair.first, environmentModelPair.second, labeledMdp, stateInformation, choiceInformation);
// Update model.
updateModel(environmentModelPair.first, environmentModelPair.second);
// (4.3) Construct constraint system.
buildConstraintSystem(environmentModelPair.first, environmentModelPair.second, labeledMdp, psiStates, stateInformation, choiceInformation, variableInformation, probabilityThreshold, strictBound, includeSchedulerCuts);
// Update model.
updateModel(environmentModelPair.first, environmentModelPair.second);
// writeModelToFile(environmentModelPair.first, environmentModelPair.second, "storm.lp");
// (4.4) Optimize the model.
optimizeModel(environmentModelPair.first, environmentModelPair.second);
// (4.5) Read off result from variables.
storm::storage::VectorSet<uint_fast64_t> usedLabelSet = getUsedLabelsInSolution(environmentModelPair.first, environmentModelPair.second, variableInformation);
usedLabelSet.insert(choiceInformation.knownLabels);
// Display achieved probability.
std::pair<uint_fast64_t, double> initialStateProbabilityPair = getReachabilityProbability(environmentModelPair.first, environmentModelPair.second, labeledMdp, variableInformation);
// (4.6) Shutdown Gurobi.
destroyGurobiModelAndEnvironment(environmentModelPair.first, environmentModelPair.second);
// (5) Return result.
return usedLabelSet;
#else
throw storm::exceptions::NotImplementedException() << "This functionality is unavailable since StoRM has been compiled without support for Gurobi.";
#endif
}
/*!
* Computes a (minimally labeled) counterexample for the given model and (safety) formula. If the model satisfies the property, an exception is thrown.
*
* @param labeledMdp A labeled MDP that is the model in which to generate the counterexample.
* @param formulaPtr A pointer to a safety formula. The outermost operator must be a probabilistic bound operator with a strict upper bound. The nested
* formula can be either an unbounded until formula or an eventually formula.
*/
static void computeCounterexample(storm::ir::Program const& program, storm::models::Mdp<T> const& labeledMdp, storm::property::prctl::AbstractPrctlFormula<double> const* formulaPtr) {
#ifdef STORM_HAVE_GUROBI
std::cout << std::endl << "Generating minimal label counterexample for formula " << formulaPtr->toString() << std::endl;
// First, we need to check whether the current formula is an Until-Formula.
storm::property::prctl::ProbabilisticBoundOperator<double> const* probBoundFormula = dynamic_cast<storm::property::prctl::ProbabilisticBoundOperator<double> const*>(formulaPtr);
if (probBoundFormula == nullptr) {
LOG4CPLUS_ERROR(logger, "Illegal formula " << probBoundFormula->toString() << " for counterexample generation.");
throw storm::exceptions::InvalidPropertyException() << "Illegal formula " << probBoundFormula->toString() << " for counterexample generation.";
}
if (probBoundFormula->getComparisonOperator() != storm::property::ComparisonType::LESS && probBoundFormula->getComparisonOperator() != storm::property::ComparisonType::LESS_EQUAL) {
LOG4CPLUS_ERROR(logger, "Illegal comparison operator in formula " << probBoundFormula->toString() << ". Only upper bounds are supported for counterexample generation.");
throw storm::exceptions::InvalidPropertyException() << "Illegal comparison operator in formula " << probBoundFormula->toString() << ". Only upper bounds are supported for counterexample generation.";
}
bool strictBound = probBoundFormula->getComparisonOperator() == storm::property::ComparisonType::LESS;
// Now derive the probability threshold we need to exceed as well as the phi and psi states. Simultaneously, check whether the formula is of a valid shape.
double bound = probBoundFormula->getBound();
storm::property::prctl::AbstractPathFormula<double> const& pathFormula = probBoundFormula->getPathFormula();
storm::storage::BitVector phiStates;
storm::storage::BitVector psiStates;
storm::modelchecker::prctl::SparseMdpPrctlModelChecker<T> modelchecker(labeledMdp, new storm::solver::GmmxxNondeterministicLinearEquationSolver<T>());
try {
storm::property::prctl::Until<double> const& untilFormula = dynamic_cast<storm::property::prctl::Until<double> const&>(pathFormula);
phiStates = untilFormula.getLeft().check(modelchecker);
psiStates = untilFormula.getRight().check(modelchecker);
} catch (std::bad_cast const& e) {
// If the nested formula was not an until formula, it remains to check whether it's an eventually formula.
try {
storm::property::prctl::Eventually<double> const& eventuallyFormula = dynamic_cast<storm::property::prctl::Eventually<double> const&>(pathFormula);
phiStates = storm::storage::BitVector(labeledMdp.getNumberOfStates(), true);
psiStates = eventuallyFormula.getChild().check(modelchecker);
} catch (std::bad_cast const& e) {
// If the nested formula is neither an until nor a finally formula, we throw an exception.
throw storm::exceptions::InvalidPropertyException() << "Formula nested inside probability bound operator must be an until or eventually formula for counterexample generation.";
}
}
// Delegate the actual computation work to the function of equal name.
auto startTime = std::chrono::high_resolution_clock::now();
storm::storage::VectorSet<uint_fast64_t> usedLabelSet = getMinimalLabelSet(labeledMdp, phiStates, psiStates, bound, strictBound, true, true);
auto endTime = std::chrono::high_resolution_clock::now();
std::cout << std::endl << "Computed minimal label set of size " << usedLabelSet.size() << " in " << std::chrono::duration_cast<std::chrono::milliseconds>(endTime - startTime).count() << "ms." << std::endl;
std::cout << "Resulting program:" << std::endl;
storm::ir::Program restrictedProgram(program);
restrictedProgram.restrictCommands(usedLabelSet);
std::cout << restrictedProgram.toString() << std::endl;
std::cout << std::endl << "-------------------------------------------" << std::endl;
// FIXME: Return the DTMC that results from applying the max scheduler in the MDP restricted to the computed label set.
#else
throw storm::exceptions::NotImplementedException() << "This functionality is unavailable since StoRM has been compiled without support for Gurobi.";
#endif
}
};
} // namespace counterexamples
} // namespace storm
#endif /* STORM_COUNTEREXAMPLES_MILPMINIMALLABELSETGENERATOR_MDP_H_ */