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ortools-clone/ortools/sat/cp_model_loader.cc

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// Copyright 2010-2018 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "ortools/sat/cp_model_loader.h"
#include <algorithm>
#include <map>
#include <memory>
#include <set>
#include <string>
#include <utility>
#include <vector>
#include "absl/container/flat_hash_map.h"
#include "absl/container/flat_hash_set.h"
#include "ortools/base/int_type.h"
#include "ortools/base/int_type_indexed_vector.h"
#include "ortools/base/logging.h"
#include "ortools/base/map_util.h"
#include "ortools/base/stl_util.h"
#include "ortools/sat/all_different.h"
#include "ortools/sat/circuit.h"
#include "ortools/sat/cp_constraints.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_utils.h"
#include "ortools/sat/cumulative.h"
#include "ortools/sat/diffn.h"
#include "ortools/sat/disjunctive.h"
#include "ortools/sat/implied_bounds.h"
#include "ortools/sat/integer.h"
#include "ortools/sat/integer_expr.h"
#include "ortools/sat/intervals.h"
#include "ortools/sat/pb_constraint.h"
#include "ortools/sat/precedences.h"
#include "ortools/sat/sat_base.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/sat/sat_solver.h"
#include "ortools/sat/table.h"
#include "ortools/util/saturated_arithmetic.h"
#include "ortools/util/sorted_interval_list.h"
namespace operations_research {
namespace sat {
namespace {
template <typename Values>
std::vector<int64> ValuesFromProto(const Values& values) {
return std::vector<int64>(values.begin(), values.end());
}
void ComputeLinearBounds(const LinearConstraintProto& proto,
CpModelMapping* mapping, IntegerTrail* integer_trail,
int64* sum_min, int64* sum_max) {
*sum_min = 0;
*sum_max = 0;
for (int i = 0; i < proto.vars_size(); ++i) {
const int64 coeff = proto.coeffs(i);
const IntegerVariable var = mapping->Integer(proto.vars(i));
const int64 lb = integer_trail->LowerBound(var).value();
const int64 ub = integer_trail->UpperBound(var).value();
if (coeff >= 0) {
(*sum_min) += coeff * lb;
(*sum_max) += coeff * ub;
} else {
(*sum_min) += coeff * ub;
(*sum_max) += coeff * lb;
}
}
}
// We check if the constraint is a sum(ax * xi) == value.
bool ConstraintIsEq(const LinearConstraintProto& proto) {
return proto.domain_size() == 2 && proto.domain(0) == proto.domain(1);
}
// We check if the constraint is a sum(ax * xi) != value.
bool ConstraintIsNEq(const LinearConstraintProto& proto,
CpModelMapping* mapping, IntegerTrail* integer_trail,
int64* single_value) {
int64 sum_min = 0;
int64 sum_max = 0;
ComputeLinearBounds(proto, mapping, integer_trail, &sum_min, &sum_max);
const Domain complement =
Domain(sum_min, sum_max)
.IntersectionWith(ReadDomainFromProto(proto).Complement());
if (complement.IsEmpty()) return false;
const int64 value = complement.Min();
if (complement.Size() == 1) {
if (single_value != nullptr) {
*single_value = value;
}
return true;
}
return false;
}
} // namespace
void CpModelMapping::CreateVariables(const CpModelProto& model_proto,
bool view_all_booleans_as_integers,
Model* m) {
const int num_proto_variables = model_proto.variables_size();
// All [0, 1] variables always have a corresponding Boolean, even if it is
// fixed to 0 (domain == [0,0]) or fixed to 1 (domain == [1,1]).
{
auto* sat_solver = m->GetOrCreate<SatSolver>();
CHECK_EQ(sat_solver->NumVariables(), 0);
BooleanVariable new_var(0);
std::vector<BooleanVariable> false_variables;
std::vector<BooleanVariable> true_variables;
booleans_.resize(num_proto_variables, kNoBooleanVariable);
reverse_boolean_map_.resize(num_proto_variables, -1);
for (int i = 0; i < num_proto_variables; ++i) {
const auto& domain = model_proto.variables(i).domain();
if (domain.size() != 2) continue;
if (domain[0] >= 0 && domain[1] <= 1) {
booleans_[i] = new_var;
reverse_boolean_map_[new_var] = i;
if (domain[1] == 0) {
false_variables.push_back(new_var);
} else if (domain[0] == 1) {
true_variables.push_back(new_var);
}
++new_var;
}
}
sat_solver->SetNumVariables(new_var.value());
for (const BooleanVariable var : true_variables) {
m->Add(ClauseConstraint({sat::Literal(var, true)}));
}
for (const BooleanVariable var : false_variables) {
m->Add(ClauseConstraint({sat::Literal(var, false)}));
}
}
// Compute the list of positive variable reference for which we need to
// create an IntegerVariable.
std::vector<int> var_to_instantiate_as_integer;
if (view_all_booleans_as_integers) {
var_to_instantiate_as_integer.resize(num_proto_variables);
for (int i = 0; i < num_proto_variables; ++i) {
var_to_instantiate_as_integer[i] = i;
}
} else {
// Compute the integer variable references used by the model.
absl::flat_hash_set<int> used_variables;
IndexReferences refs;
for (int c = 0; c < model_proto.constraints_size(); ++c) {
const ConstraintProto& ct = model_proto.constraints(c);
refs = GetReferencesUsedByConstraint(ct);
for (const int ref : refs.variables) {
used_variables.insert(PositiveRef(ref));
}
}
// Add the objectives and search heuristics variables that needs to be
// referenceable as integer even if they are only used as Booleans.
if (model_proto.has_objective()) {
for (const int obj_var : model_proto.objective().vars()) {
used_variables.insert(PositiveRef(obj_var));
}
}
for (const DecisionStrategyProto& strategy :
model_proto.search_strategy()) {
for (const int var : strategy.variables()) {
used_variables.insert(PositiveRef(var));
}
}
// Make sure any unused variable, that is not already a Boolean is
// considered "used".
for (int i = 0; i < num_proto_variables; ++i) {
if (booleans_[i] == kNoBooleanVariable) {
used_variables.insert(i);
}
}
// We want the variable in the problem order.
var_to_instantiate_as_integer.assign(used_variables.begin(),
used_variables.end());
gtl::STLSortAndRemoveDuplicates(&var_to_instantiate_as_integer);
}
integers_.resize(num_proto_variables, kNoIntegerVariable);
auto* integer_trail = m->GetOrCreate<IntegerTrail>();
integer_trail->ReserveSpaceForNumVariables(
var_to_instantiate_as_integer.size());
reverse_integer_map_.resize(2 * var_to_instantiate_as_integer.size(), -1);
for (const int i : var_to_instantiate_as_integer) {
const auto& var_proto = model_proto.variables(i);
integers_[i] =
integer_trail->AddIntegerVariable(ReadDomainFromProto(var_proto));
DCHECK_LT(integers_[i], reverse_integer_map_.size());
reverse_integer_map_[integers_[i]] = i;
}
auto* encoder = m->GetOrCreate<IntegerEncoder>();
// Link any variable that has both views.
for (int i = 0; i < num_proto_variables; ++i) {
if (integers_[i] == kNoIntegerVariable) continue;
if (booleans_[i] == kNoBooleanVariable) continue;
// Associate with corresponding integer variable.
encoder->AssociateToIntegerEqualValue(sat::Literal(booleans_[i], true),
integers_[i], IntegerValue(1));
}
// Create the interval variables.
intervals_.resize(model_proto.constraints_size(), kNoIntervalVariable);
for (int c = 0; c < model_proto.constraints_size(); ++c) {
const ConstraintProto& ct = model_proto.constraints(c);
if (ct.constraint_case() != ConstraintProto::ConstraintCase::kInterval) {
continue;
}
if (HasEnforcementLiteral(ct)) {
const sat::Literal enforcement_literal =
Literal(ct.enforcement_literal(0));
// TODO(user): Fix the constant variable situation. An optional interval
// with constant start/end or size cannot share the same constant
// variable if it is used in non-optional situation.
intervals_[c] = m->Add(NewOptionalInterval(
Integer(ct.interval().start()), Integer(ct.interval().end()),
Integer(ct.interval().size()), enforcement_literal));
} else {
intervals_[c] = m->Add(NewInterval(Integer(ct.interval().start()),
Integer(ct.interval().end()),
Integer(ct.interval().size())));
}
already_loaded_ct_.insert(&ct);
}
}
// The logic assumes that the linear constraints have been presolved, so that
// equality with a domain bound have been converted to <= or >= and so that we
// never have any trivial inequalities.
//
// TODO(user): Regroup/presolve two encoding like b => x > 2 and the same
// Boolean b => x > 5. These shouldn't happen if we merge linear constraints.
void CpModelMapping::ExtractEncoding(const CpModelProto& model_proto,
Model* m) {
auto* encoder = m->GetOrCreate<IntegerEncoder>();
auto* integer_trail = m->GetOrCreate<IntegerTrail>();
auto* sat_solver = m->GetOrCreate<SatSolver>();
// TODO(user): Debug what makes it unsat at this point.
if (sat_solver->IsModelUnsat()) return;
// Detection of literal equivalent to (i_var == value). We collect all the
// half-reified constraint lit => equality or lit => inequality for a given
// variable, and we will later sort them to detect equivalence.
struct EqualityDetectionHelper {
const ConstraintProto* ct;
sat::Literal literal;
int64 value;
bool is_equality; // false if != instead.
bool operator<(const EqualityDetectionHelper& o) const {
if (literal.Variable() == o.literal.Variable()) {
if (value == o.value) return is_equality && !o.is_equality;
return value < o.value;
}
return literal.Variable() < o.literal.Variable();
}
};
std::vector<std::vector<EqualityDetectionHelper>> var_to_equalities(
model_proto.variables_size());
// TODO(user): We will re-add the same implied bounds during probing, so
// it might not be necessary to do that here. Also, it might be too early
// if some of the literal view used in the LP are created later, but that
// should be fixable via calls to implied_bounds->NotifyNewIntegerView().
auto* implied_bounds = m->GetOrCreate<ImpliedBounds>();
// Detection of literal equivalent to (i_var >= bound). We also collect
// all the half-refied part and we will sort the vector for detection of the
// equivalence.
struct InequalityDetectionHelper {
const ConstraintProto* ct;
sat::Literal literal;
IntegerLiteral i_lit;
bool operator<(const InequalityDetectionHelper& o) const {
if (literal.Variable() == o.literal.Variable()) {
return i_lit.var < o.i_lit.var;
}
return literal.Variable() < o.literal.Variable();
}
};
std::vector<InequalityDetectionHelper> inequalities;
// Loop over all contraints and fill var_to_equalities and inequalities.
for (const ConstraintProto& ct : model_proto.constraints()) {
if (ct.constraint_case() != ConstraintProto::ConstraintCase::kLinear) {
continue;
}
if (ct.enforcement_literal().size() != 1) continue;
if (ct.linear().vars_size() != 1) continue;
// ct is a linear constraint with one term and one enforcement literal.
const sat::Literal enforcement_literal = Literal(ct.enforcement_literal(0));
const int ref = ct.linear().vars(0);
const int var = PositiveRef(ref);
const Domain domain = ReadDomainFromProto(model_proto.variables(var));
const Domain domain_if_enforced =
ReadDomainFromProto(ct.linear())
.InverseMultiplicationBy(ct.linear().coeffs(0) *
(RefIsPositive(ref) ? 1 : -1));
// Detect enforcement_literal => (var >= value or var <= value).
if (domain_if_enforced.NumIntervals() == 1) {
if (domain_if_enforced.Max() >= domain.Max() &&
domain_if_enforced.Min() > domain.Min()) {
inequalities.push_back(
{&ct, enforcement_literal,
IntegerLiteral::GreaterOrEqual(
Integer(var), IntegerValue(domain_if_enforced.Min()))});
implied_bounds->Add(enforcement_literal, inequalities.back().i_lit);
} else if (domain_if_enforced.Min() <= domain.Min() &&
domain_if_enforced.Max() < domain.Max()) {
inequalities.push_back(
{&ct, enforcement_literal,
IntegerLiteral::LowerOrEqual(
Integer(var), IntegerValue(domain_if_enforced.Max()))});
implied_bounds->Add(enforcement_literal, inequalities.back().i_lit);
}
}
// Detect enforcement_literal => (var == value or var != value).
//
// Note that for domain with 2 values like [0, 1], we will detect both ==
// 0 and != 1. Similarly, for a domain in [min, max], we should both
// detect (== min) and (<= min), and both detect (== max) and (>= max).
{
const Domain inter = domain.IntersectionWith(domain_if_enforced);
if (!inter.IsEmpty() && inter.Min() == inter.Max()) {
var_to_equalities[var].push_back(
{&ct, enforcement_literal, inter.Min(), true});
if (domain.Contains(inter.Min())) {
variables_to_encoded_values_[var].insert(inter.Min());
}
}
}
{
const Domain inter =
domain.IntersectionWith(domain_if_enforced.Complement());
if (!inter.IsEmpty() && inter.Min() == inter.Max()) {
var_to_equalities[var].push_back(
{&ct, enforcement_literal, inter.Min(), false});
if (domain.Contains(inter.Min())) {
variables_to_encoded_values_[var].insert(inter.Min());
}
}
}
}
// Detect Literal <=> X >= value
int num_inequalities = 0;
std::sort(inequalities.begin(), inequalities.end());
for (int i = 0; i + 1 < inequalities.size(); i++) {
if (inequalities[i].literal != inequalities[i + 1].literal.Negated()) {
continue;
}
// TODO(user): In these cases, we could fix the enforcement literal right
// away or ignore the constraint. Note that it will be done later anyway
// though.
if (integer_trail->IntegerLiteralIsTrue(inequalities[i].i_lit) ||
integer_trail->IntegerLiteralIsFalse(inequalities[i].i_lit)) {
continue;
}
if (integer_trail->IntegerLiteralIsTrue(inequalities[i + 1].i_lit) ||
integer_trail->IntegerLiteralIsFalse(inequalities[i + 1].i_lit)) {
continue;
}
const auto pair_a = encoder->Canonicalize(inequalities[i].i_lit);
const auto pair_b = encoder->Canonicalize(inequalities[i + 1].i_lit);
if (pair_a.first == pair_b.second) {
++num_inequalities;
encoder->AssociateToIntegerLiteral(inequalities[i].literal,
inequalities[i].i_lit);
already_loaded_ct_.insert(inequalities[i].ct);
already_loaded_ct_.insert(inequalities[i + 1].ct);
}
}
// Encode the half-inequalities.
int num_half_inequalities = 0;
for (const auto inequality : inequalities) {
if (ConstraintIsAlreadyLoaded(inequality.ct)) continue;
m->Add(
Implication(inequality.literal,
encoder->GetOrCreateAssociatedLiteral(inequality.i_lit)));
if (sat_solver->IsModelUnsat()) return;
++num_half_inequalities;
already_loaded_ct_.insert(inequality.ct);
is_half_encoding_ct_.insert(inequality.ct);
}
if (!inequalities.empty()) {
VLOG(1) << num_inequalities << " literals associated to VAR >= value, and "
<< num_half_inequalities << " half-associations.";
}
// Detect Literal <=> X == value and associate them in the IntegerEncoder.
//
// TODO(user): Fully encode variable that are almost fully encoded?
int num_constraints = 0;
int num_equalities = 0;
int num_half_equalities = 0;
int num_fully_encoded = 0;
int num_partially_encoded = 0;
for (int i = 0; i < var_to_equalities.size(); ++i) {
std::vector<EqualityDetectionHelper>& encoding = var_to_equalities[i];
std::sort(encoding.begin(), encoding.end());
if (encoding.empty()) continue;
num_constraints += encoding.size();
absl::flat_hash_set<int64> values;
for (int j = 0; j + 1 < encoding.size(); j++) {
if ((encoding[j].value != encoding[j + 1].value) ||
(encoding[j].literal != encoding[j + 1].literal.Negated()) ||
(encoding[j].is_equality != true) ||
(encoding[j + 1].is_equality != false)) {
continue;
}
++num_equalities;
encoder->AssociateToIntegerEqualValue(encoding[j].literal, integers_[i],
IntegerValue(encoding[j].value));
already_loaded_ct_.insert(encoding[j].ct);
already_loaded_ct_.insert(encoding[j + 1].ct);
values.insert(encoding[j].value);
}
// TODO(user): Try to remove it. Normally we caught UNSAT above, but
// tests are very flaky (it only happens in parallel). Keeping it there for
// the time being.
if (sat_solver->IsModelUnsat()) return;
// Encode the half-equalities.
//
// TODO(user): delay this after PropagateEncodingFromEquivalenceRelations()?
// Otherwise we might create new Boolean variables for no reason. Note
// however, that in the presolve, we should only use the "representative" in
// linear constraints, so we should be fine.
for (const auto equality : encoding) {
if (ConstraintIsAlreadyLoaded(equality.ct)) continue;
const class Literal eq = encoder->GetOrCreateLiteralAssociatedToEquality(
integers_[i], IntegerValue(equality.value));
if (equality.is_equality) {
m->Add(Implication(equality.literal, eq));
} else {
m->Add(Implication(equality.literal, eq.Negated()));
}
++num_half_equalities;
already_loaded_ct_.insert(equality.ct);
is_half_encoding_ct_.insert(equality.ct);
}
// Update stats.
if (VLOG_IS_ON(1)) {
if (encoder->VariableIsFullyEncoded(integers_[i])) {
++num_fully_encoded;
} else {
++num_partially_encoded;
}
}
}
if (num_constraints > 0) {
VLOG(1) << num_equalities << " literals associated to VAR == value, and "
<< num_half_equalities << " half-associations.";
}
if (num_fully_encoded > 0) {
VLOG(1) << "num_fully_encoded_variables: " << num_fully_encoded;
}
if (num_partially_encoded > 0) {
VLOG(1) << "num_partially_encoded_variables: " << num_partially_encoded;
}
}
void CpModelMapping::PropagateEncodingFromEquivalenceRelations(
const CpModelProto& model_proto, Model* m) {
auto* encoder = m->GetOrCreate<IntegerEncoder>();
auto* sat_solver = m->GetOrCreate<SatSolver>();
// Loop over all contraints and find affine ones.
int64 num_associations = 0;
int64 num_set_to_false = 0;
for (const ConstraintProto& ct : model_proto.constraints()) {
if (!ct.enforcement_literal().empty()) continue;
if (ct.constraint_case() != ConstraintProto::kLinear) continue;
if (ct.linear().vars_size() != 2) continue;
if (!ConstraintIsEq(ct.linear())) continue;
const IntegerValue rhs(ct.linear().domain(0));
// Make sure the coefficient are positive.
IntegerVariable var1 = Integer(ct.linear().vars(0));
IntegerVariable var2 = Integer(ct.linear().vars(1));
IntegerValue coeff1(ct.linear().coeffs(0));
IntegerValue coeff2(ct.linear().coeffs(1));
if (coeff1 < 0) {
var1 = NegationOf(var1);
coeff1 = -coeff1;
}
if (coeff2 < 0) {
var2 = NegationOf(var2);
coeff2 = -coeff2;
}
// TODO(user): This is not supposed to happen, but apparently it did on
// once on routing_GCM_0001_sat.fzn. Investigate and fix.
if (coeff1 == 0 || coeff2 == 0) continue;
// We first map the >= literals.
// It is important to do that first, since otherwise mapping a == literal
// might creates the underlying >= and <= literals.
for (int i = 0; i < 2; ++i) {
for (const auto value_literal :
encoder->PartialGreaterThanEncoding(var1)) {
const IntegerValue value1 = value_literal.first;
const IntegerValue bound2 = FloorRatio(rhs - value1 * coeff1, coeff2);
++num_associations;
encoder->AssociateToIntegerLiteral(
value_literal.second, IntegerLiteral::LowerOrEqual(var2, bound2));
}
std::swap(var1, var2);
std::swap(coeff1, coeff2);
}
// Same for the == literals.
//
// TODO(user): This is similar to LoadEquivalenceAC() for unreified
// constraints, but when the later is called, more encoding might have taken
// place.
for (int i = 0; i < 2; ++i) {
for (const auto value_literal : encoder->PartialDomainEncoding(var1)) {
const IntegerValue value1 = value_literal.value;
const IntegerValue intermediate = rhs - value1 * coeff1;
if (intermediate % coeff2 != 0) {
// Using this function deals properly with UNSAT.
++num_set_to_false;
sat_solver->AddUnitClause(value_literal.literal.Negated());
continue;
}
++num_associations;
encoder->AssociateToIntegerEqualValue(value_literal.literal, var2,
intermediate / coeff2);
}
std::swap(var1, var2);
std::swap(coeff1, coeff2);
}
}
if (num_associations > 0) {
VLOG(1) << "Num associations from equivalences = " << num_associations;
}
if (num_set_to_false > 0) {
VLOG(1) << "Num literals set to false from equivalences = "
<< num_set_to_false;
}
}
void CpModelMapping::DetectOptionalVariables(const CpModelProto& model_proto,
Model* m) {
const SatParameters& parameters = *(m->GetOrCreate<SatParameters>());
if (!parameters.use_optional_variables()) return;
if (parameters.enumerate_all_solutions()) return;
// The variables from the objective cannot be marked as optional!
const int num_proto_variables = model_proto.variables_size();
std::vector<bool> already_seen(num_proto_variables, false);
if (model_proto.has_objective()) {
for (const int ref : model_proto.objective().vars()) {
already_seen[PositiveRef(ref)] = true;
}
}
// Compute for each variables the intersection of the enforcement literals
// of the constraints in which they appear.
//
// TODO(user): This deals with the simplest cases, but we could try to
// detect literals that implies all the constaints in which a variable
// appear to false. This can be done with a LCA computation in the tree of
// Boolean implication (once the presolve remove cycles). Not sure if we can
// properly exploit that afterwards though. Do some research!
std::vector<std::vector<int>> enforcement_intersection(num_proto_variables);
std::set<int> literals_set;
for (int c = 0; c < model_proto.constraints_size(); ++c) {
const ConstraintProto& ct = model_proto.constraints(c);
if (ct.enforcement_literal().empty()) {
for (const int var : UsedVariables(ct)) {
already_seen[var] = true;
enforcement_intersection[var].clear();
}
} else {
literals_set.clear();
literals_set.insert(ct.enforcement_literal().begin(),
ct.enforcement_literal().end());
for (const int var : UsedVariables(ct)) {
if (!already_seen[var]) {
enforcement_intersection[var].assign(ct.enforcement_literal().begin(),
ct.enforcement_literal().end());
} else {
// Take the intersection.
std::vector<int>& vector_ref = enforcement_intersection[var];
int new_size = 0;
for (const int literal : vector_ref) {
if (gtl::ContainsKey(literals_set, literal)) {
vector_ref[new_size++] = literal;
}
}
vector_ref.resize(new_size);
}
already_seen[var] = true;
}
}
}
// Auto-detect optional variables.
int num_optionals = 0;
auto* integer_trail = m->GetOrCreate<IntegerTrail>();
for (int var = 0; var < num_proto_variables; ++var) {
const IntegerVariableProto& var_proto = model_proto.variables(var);
const int64 min = var_proto.domain(0);
const int64 max = var_proto.domain(var_proto.domain().size() - 1);
if (min == max) continue;
if (min == 0 && max == 1) continue;
if (enforcement_intersection[var].empty()) continue;
++num_optionals;
integer_trail->MarkIntegerVariableAsOptional(
Integer(var), Literal(enforcement_intersection[var].front()));
}
VLOG(2) << "Auto-detected " << num_optionals << " optional variables.";
}
// ============================================================================
// A class that detects when variables should be fully encoded by computing a
// fixed point. It also fully encodes such variables.
// ============================================================================
class FullEncodingFixedPointComputer {
public:
FullEncodingFixedPointComputer(const CpModelProto& model_proto, Model* model)
: model_proto_(model_proto),
parameters_(*(model->GetOrCreate<SatParameters>())),
model_(model),
mapping_(model->GetOrCreate<CpModelMapping>()),
integer_encoder_(model->GetOrCreate<IntegerEncoder>()),
integer_trail_(model->GetOrCreate<IntegerTrail>()) {}
void ComputeFixedPoint();
private:
DEFINE_INT_TYPE(ConstraintIndex, int32);
// Constraint ct is interested by (full-encoding) state of variable.
void Register(ConstraintIndex ct_index, int variable) {
variable = PositiveRef(variable);
constraint_is_registered_[ct_index] = true;
if (variable_watchers_.size() <= variable) {
variable_watchers_.resize(variable + 1);
variable_was_added_in_to_propagate_.resize(variable + 1);
}
variable_watchers_[variable].push_back(ct_index);
}
void AddVariableToPropagationQueue(int variable) {
variable = PositiveRef(variable);
if (variable_was_added_in_to_propagate_.size() <= variable) {
variable_watchers_.resize(variable + 1);
variable_was_added_in_to_propagate_.resize(variable + 1);
}
if (!variable_was_added_in_to_propagate_[variable]) {
variable_was_added_in_to_propagate_[variable] = true;
variables_to_propagate_.push_back(variable);
}
}
// Note that we always consider a fixed variable to be fully encoded here.
const bool IsFullyEncoded(int v) {
const IntegerVariable variable = mapping_->Integer(v);
if (v == kNoIntegerVariable) return false;
return integer_trail_->IsFixed(variable) ||
integer_encoder_->VariableIsFullyEncoded(variable);
}
const bool VariableIsFixed(int v) {
const IntegerVariable variable = mapping_->Integer(v);
if (v == kNoIntegerVariable) return false;
return integer_trail_->IsFixed(variable);
}
void FullyEncode(int v) {
v = PositiveRef(v);
const IntegerVariable variable = mapping_->Integer(v);
if (v == kNoIntegerVariable) return;
if (!integer_trail_->IsFixed(variable)) {
model_->Add(FullyEncodeVariable(variable));
}
AddVariableToPropagationQueue(v);
}
bool ProcessConstraint(ConstraintIndex ct_index);
bool ProcessElement(ConstraintIndex ct_index);
bool ProcessTable(ConstraintIndex ct_index);
bool ProcessAutomaton(ConstraintIndex ct_index);
bool ProcessLinear(ConstraintIndex ct_index);
const CpModelProto& model_proto_;
const SatParameters& parameters_;
Model* model_;
CpModelMapping* mapping_;
IntegerEncoder* integer_encoder_;
IntegerTrail* integer_trail_;
std::vector<bool> variable_was_added_in_to_propagate_;
std::vector<int> variables_to_propagate_;
std::vector<std::vector<ConstraintIndex>> variable_watchers_;
gtl::ITIVector<ConstraintIndex, bool> constraint_is_finished_;
gtl::ITIVector<ConstraintIndex, bool> constraint_is_registered_;
absl::flat_hash_map<int, absl::flat_hash_set<int>>
variables_to_equal_or_diff_variables_;
};
// We only add to the propagation queue variable that are fully encoded.
// Note that if a variable was already added once, we never add it again.
void FullEncodingFixedPointComputer::ComputeFixedPoint() {
const int num_constraints = model_proto_.constraints_size();
const int num_vars = model_proto_.variables_size();
constraint_is_finished_.assign(num_constraints, false);
constraint_is_registered_.assign(num_constraints, false);
// Process all constraint once.
for (ConstraintIndex ct_index(0); ct_index < num_constraints; ++ct_index) {
constraint_is_finished_[ct_index] = ProcessConstraint(ct_index);
}
// We run a heuristics to decide if we want to fully encode a variable or not.
// We decide to fully encode a variable if:
// - a variable appears in enough a1 * x1 + a2 + x2 ==/!= value and the
// domain is small.
// - the number of values that appears in b => x ==/!= value that are not
// the bounds of the variables is more that half the size of the domain.
// . - the size of the domain is > 2
int num_variables_fully_encoded_by_heuristics = 0;
for (int var = 0; var < num_vars; ++var) {
if (!mapping_->IsInteger(var) || IsFullyEncoded(var)) continue;
const IntegerVariableProto& int_var_proto = model_proto_.variables(var);
const Domain domain = ReadDomainFromProto(int_var_proto);
int64 domain_size = domain.Size();
int64 num_diff_or_equal_var_constraints = 0;
int64 num_potential_encoded_values_without_bounds = 0;
if (domain_size <= 2) continue;
const absl::flat_hash_set<int64>& value_set =
mapping_->PotentialEncodedValues(var);
for (const int value : value_set) {
if (value > domain.Min() && value < domain.Max() &&
domain.Contains(value)) {
num_potential_encoded_values_without_bounds++;
}
}
const auto& it = variables_to_equal_or_diff_variables_.find(var);
if (it != variables_to_equal_or_diff_variables_.end()) {
num_diff_or_equal_var_constraints = it->second.size();
}
if (num_potential_encoded_values_without_bounds >= domain_size / 2 ||
(num_diff_or_equal_var_constraints >= domain_size / 2 &&
domain_size < 16)) {
VLOG(3) << model_proto_.variables(var).ShortDebugString()
<< " is encoded with "
<< num_potential_encoded_values_without_bounds
<< " unary constraints, and " << num_diff_or_equal_var_constraints
<< " binary constraints on a domain of size " << domain_size;
FullyEncode(var);
num_variables_fully_encoded_by_heuristics++;
}
}
if (num_variables_fully_encoded_by_heuristics > 0) {
VLOG(2) << num_variables_fully_encoded_by_heuristics
<< " variables fully encoded after model introspection.";
}
// Make sure all fully encoded variables of interest are in the queue.
for (int v = 0; v < variable_watchers_.size(); v++) {
if (!variable_watchers_[v].empty() && IsFullyEncoded(v)) {
AddVariableToPropagationQueue(v);
}
}
// Loop until no additional variable can be fully encoded.
while (!variables_to_propagate_.empty()) {
const int variable = variables_to_propagate_.back();
variables_to_propagate_.pop_back();
for (const ConstraintIndex ct_index : variable_watchers_[variable]) {
if (constraint_is_finished_[ct_index]) continue;
constraint_is_finished_[ct_index] = ProcessConstraint(ct_index);
}
}
}
// Returns true if the constraint has finished encoding what it wants.
bool FullEncodingFixedPointComputer::ProcessConstraint(
ConstraintIndex ct_index) {
const ConstraintProto& ct = model_proto_.constraints(ct_index.value());
switch (ct.constraint_case()) {
case ConstraintProto::ConstraintProto::kElement:
return ProcessElement(ct_index);
case ConstraintProto::ConstraintProto::kTable:
return ProcessTable(ct_index);
case ConstraintProto::ConstraintProto::kAutomaton:
return ProcessAutomaton(ct_index);
case ConstraintProto::ConstraintProto::kLinear:
return ProcessLinear(ct_index);
default:
return true;
}
}
bool FullEncodingFixedPointComputer::ProcessElement(ConstraintIndex ct_index) {
const ConstraintProto& ct = model_proto_.constraints(ct_index.value());
// Index must always be full encoded.
FullyEncode(ct.element().index());
const int target = ct.element().target();
// If target is fixed, do not encode variables.
if (VariableIsFixed(target)) return true;
// If target is a constant or fully encoded, variables must be fully encoded.
if (IsFullyEncoded(target)) {
for (const int v : ct.element().vars()) FullyEncode(v);
}
// If all non-target variables are fully encoded, target must be too.
bool all_variables_are_fully_encoded = true;
for (const int v : ct.element().vars()) {
if (v == target) continue;
if (!IsFullyEncoded(v)) {
all_variables_are_fully_encoded = false;
break;
}
}
if (all_variables_are_fully_encoded) {
if (!IsFullyEncoded(target)) FullyEncode(target);
return true;
}
// If some variables are not fully encoded, register on those.
if (constraint_is_registered_[ct_index]) {
for (const int v : ct.element().vars()) Register(ct_index, v);
Register(ct_index, target);
}
return false;
}
bool FullEncodingFixedPointComputer::ProcessTable(ConstraintIndex ct_index) {
const ConstraintProto& ct = model_proto_.constraints(ct_index.value());
if (ct.table().negated()) return true;
for (const int variable : ct.table().vars()) {
FullyEncode(variable);
}
return true;
}
bool FullEncodingFixedPointComputer::ProcessAutomaton(
ConstraintIndex ct_index) {
const ConstraintProto& ct = model_proto_.constraints(ct_index.value());
for (const int variable : ct.automaton().vars()) {
FullyEncode(variable);
}
return true;
}
bool FullEncodingFixedPointComputer::ProcessLinear(ConstraintIndex ct_index) {
// We are only interested in linear equations of the form:
// [b =>] a1 * x1 + a2 * x2 ==|!= value
const ConstraintProto& ct = model_proto_.constraints(ct_index.value());
if (parameters_.boolean_encoding_level() == 0 ||
ct.linear().vars_size() != 2) {
return true;
}
if (!ConstraintIsEq(ct.linear()) &&
!ConstraintIsNEq(ct.linear(), mapping_, integer_trail_, nullptr)) {
return true;
}
const int var0 = ct.linear().vars(0);
const int var1 = ct.linear().vars(1);
if (!IsFullyEncoded(var0)) {
variables_to_equal_or_diff_variables_[var0].insert(var1);
}
if (!IsFullyEncoded(var1)) {
variables_to_equal_or_diff_variables_[var1].insert(var0);
}
return true;
}
void MaybeFullyEncodeMoreVariables(const CpModelProto& model_proto, Model* m) {
FullEncodingFixedPointComputer fixpoint(model_proto, m);
fixpoint.ComputeFixedPoint();
}
// ============================================================================
// Constraint loading functions.
// ============================================================================
void LoadBoolOrConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
std::vector<Literal> literals = mapping->Literals(ct.bool_or().literals());
for (const int ref : ct.enforcement_literal()) {
literals.push_back(mapping->Literal(ref).Negated());
}
m->Add(ClauseConstraint(literals));
}
void LoadBoolAndConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
std::vector<Literal> literals;
for (const int ref : ct.enforcement_literal()) {
literals.push_back(mapping->Literal(ref).Negated());
}
auto* sat_solver = m->GetOrCreate<SatSolver>();
for (const Literal literal : mapping->Literals(ct.bool_and().literals())) {
literals.push_back(literal);
sat_solver->AddProblemClause(literals);
literals.pop_back();
}
}
void LoadAtMostOneConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
CHECK(!HasEnforcementLiteral(ct)) << "Not supported.";
m->Add(AtMostOneConstraint(mapping->Literals(ct.at_most_one().literals())));
}
void LoadBoolXorConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
CHECK(!HasEnforcementLiteral(ct)) << "Not supported.";
m->Add(LiteralXorIs(mapping->Literals(ct.bool_xor().literals()), true));
}
namespace {
// Boolean encoding of:
// enforcement_literal => coeff1 * var1 + coeff2 * var2 == rhs;
void LoadEquivalenceAC(const std::vector<Literal> enforcement_literal,
IntegerValue coeff1, IntegerVariable var1,
IntegerValue coeff2, IntegerVariable var2,
const IntegerValue rhs, Model* m) {
auto* encoder = m->GetOrCreate<IntegerEncoder>();
CHECK(encoder->VariableIsFullyEncoded(var1));
CHECK(encoder->VariableIsFullyEncoded(var2));
absl::flat_hash_map<IntegerValue, Literal> term1_value_to_literal;
for (const auto value_literal : encoder->FullDomainEncoding(var1)) {
term1_value_to_literal[coeff1 * value_literal.value] =
value_literal.literal;
}
for (const auto value_literal : encoder->FullDomainEncoding(var2)) {
const IntegerValue target = rhs - value_literal.value * coeff2;
if (!gtl::ContainsKey(term1_value_to_literal, target)) {
m->Add(EnforcedClause(enforcement_literal,
{value_literal.literal.Negated()}));
} else {
const Literal target_literal = term1_value_to_literal[target];
m->Add(EnforcedClause(enforcement_literal,
{value_literal.literal.Negated(), target_literal}));
m->Add(EnforcedClause(enforcement_literal,
{value_literal.literal, target_literal.Negated()}));
// This "target" can never be reached again, so it is safe to remove it.
// We do that so we know the term1 values that are never reached.
term1_value_to_literal.erase(target);
}
}
// Exclude the values that can never be "matched" by coeff2 * var2.
// We need the std::sort() to be deterministic!
std::vector<Literal> implied_false;
for (const auto entry : term1_value_to_literal) {
implied_false.push_back(entry.second);
}
std::sort(implied_false.begin(), implied_false.end());
for (const Literal l : implied_false) {
m->Add(EnforcedClause(enforcement_literal, {l.Negated()}));
}
}
// Boolean encoding of:
// enforcement_literal => coeff1 * var1 + coeff2 * var2 != rhs;
void LoadEquivalenceNeqAC(const std::vector<Literal> enforcement_literal,
IntegerValue coeff1, IntegerVariable var1,
IntegerValue coeff2, IntegerVariable var2,
const IntegerValue rhs, Model* m) {
auto* encoder = m->GetOrCreate<IntegerEncoder>();
CHECK(encoder->VariableIsFullyEncoded(var1));
CHECK(encoder->VariableIsFullyEncoded(var2));
absl::flat_hash_map<IntegerValue, Literal> term1_value_to_literal;
for (const auto value_literal : encoder->FullDomainEncoding(var1)) {
term1_value_to_literal[coeff1 * value_literal.value] =
value_literal.literal;
}
for (const auto value_literal : encoder->FullDomainEncoding(var2)) {
const IntegerValue target_value = rhs - value_literal.value * coeff2;
const auto& it = term1_value_to_literal.find(target_value);
if (it != term1_value_to_literal.end()) {
const Literal target_literal = it->second;
m->Add(EnforcedClause(
enforcement_literal,
{value_literal.literal.Negated(), target_literal.Negated()}));
}
}
}
} // namespace
void LoadLinearConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
if (ct.linear().vars().empty()) {
const Domain rhs = ReadDomainFromProto(ct.linear());
if (rhs.Contains(0)) return;
if (HasEnforcementLiteral(ct)) {
std::vector<Literal> clause;
for (const int ref : ct.enforcement_literal()) {
clause.push_back(mapping->Literal(ref).Negated());
}
m->Add(ClauseConstraint(clause));
} else {
VLOG(1) << "Trivially UNSAT constraint: " << ct.DebugString();
m->GetOrCreate<SatSolver>()->NotifyThatModelIsUnsat();
}
return;
}
auto* integer_trail = m->GetOrCreate<IntegerTrail>();
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.linear().vars());
const std::vector<int64> coeffs = ValuesFromProto(ct.linear().coeffs());
// Compute the min/max to relax the bounds if needed.
//
// TODO(user): Reuse ComputeLinearBounds()? but then we need another loop
// to detect if we only have Booleans.
IntegerValue min_sum(0);
IntegerValue max_sum(0);
IntegerValue max_domain_size(0);
bool all_booleans = true;
for (int i = 0; i < vars.size(); ++i) {
if (all_booleans && !mapping->IsBoolean(ct.linear().vars(i))) {
all_booleans = false;
}
const IntegerValue lb = integer_trail->LowerBound(vars[i]);
const IntegerValue ub = integer_trail->UpperBound(vars[i]);
max_domain_size = std::max(max_domain_size, ub - lb + 1);
const IntegerValue term_a = coeffs[i] * lb;
const IntegerValue term_b = coeffs[i] * ub;
min_sum += std::min(term_a, term_b);
max_sum += std::max(term_a, term_b);
}
if (ct.linear().vars_size() == 2 && !integer_trail->IsFixed(vars[0]) &&
!integer_trail->IsFixed(vars[1]) && max_domain_size < 16) {
const SatParameters& params = *m->GetOrCreate<SatParameters>();
auto* encoder = m->GetOrCreate<IntegerEncoder>();
if (params.boolean_encoding_level() > 0 && ConstraintIsEq(ct.linear()) &&
ct.linear().domain(0) != min_sum && ct.linear().domain(0) != max_sum &&
encoder->VariableIsFullyEncoded(vars[0]) &&
encoder->VariableIsFullyEncoded(vars[1])) {
VLOG(3) << "Load AC version of " << ct.DebugString() << ", var0 domain = "
<< integer_trail->InitialVariableDomain(vars[0])
<< ", var1 domain = "
<< integer_trail->InitialVariableDomain(vars[1]);
return LoadEquivalenceAC(mapping->Literals(ct.enforcement_literal()),
IntegerValue(coeffs[0]), vars[0],
IntegerValue(coeffs[1]), vars[1],
IntegerValue(ct.linear().domain(0)), m);
}
int64 single_value = 0;
if (params.boolean_encoding_level() > 0 &&
ConstraintIsNEq(ct.linear(), mapping, integer_trail, &single_value) &&
single_value != min_sum && single_value != max_sum &&
encoder->VariableIsFullyEncoded(vars[0]) &&
encoder->VariableIsFullyEncoded(vars[1])) {
VLOG(3) << "Load NAC version of " << ct.DebugString()
<< ", var0 domain = "
<< integer_trail->InitialVariableDomain(vars[0])
<< ", var1 domain = "
<< integer_trail->InitialVariableDomain(vars[1])
<< ", value = " << single_value;
return LoadEquivalenceNeqAC(mapping->Literals(ct.enforcement_literal()),
IntegerValue(coeffs[0]), vars[0],
IntegerValue(coeffs[1]), vars[1],
IntegerValue(single_value), m);
}
}
if (ct.linear().domain_size() == 2) {
int64 lb = ct.linear().domain(0);
int64 ub = ct.linear().domain(1);
if (min_sum >= lb) lb = kint64min;
if (max_sum <= ub) ub = kint64max;
if (!HasEnforcementLiteral(ct)) {
if (all_booleans) {
// TODO(user): we should probably also implement an
// half-reified version of this constraint.
std::vector<LiteralWithCoeff> cst;
for (int i = 0; i < vars.size(); ++i) {
const int ref = ct.linear().vars(i);
cst.push_back({mapping->Literal(ref), coeffs[i]});
}
m->Add(BooleanLinearConstraint(lb, ub, &cst));
} else {
if (lb != kint64min) {
m->Add(WeightedSumGreaterOrEqual(vars, coeffs, lb));
}
if (ub != kint64max) {
m->Add(WeightedSumLowerOrEqual(vars, coeffs, ub));
}
}
} else {
const std::vector<Literal> enforcement_literals =
mapping->Literals(ct.enforcement_literal());
if (lb != kint64min) {
m->Add(ConditionalWeightedSumGreaterOrEqual(enforcement_literals, vars,
coeffs, lb));
}
if (ub != kint64max) {
m->Add(ConditionalWeightedSumLowerOrEqual(enforcement_literals, vars,
coeffs, ub));
}
}
} else {
std::vector<Literal> clause;
for (int i = 0; i < ct.linear().domain_size(); i += 2) {
int64 lb = ct.linear().domain(i);
int64 ub = ct.linear().domain(i + 1);
if (min_sum >= lb) lb = kint64min;
if (max_sum <= ub) ub = kint64max;
const Literal subdomain_literal(m->Add(NewBooleanVariable()), true);
clause.push_back(subdomain_literal);
if (lb != kint64min) {
m->Add(ConditionalWeightedSumGreaterOrEqual({subdomain_literal}, vars,
coeffs, lb));
}
if (ub != kint64max) {
m->Add(ConditionalWeightedSumLowerOrEqual({subdomain_literal}, vars,
coeffs, ub));
}
}
for (const int ref : ct.enforcement_literal()) {
clause.push_back(mapping->Literal(ref).Negated());
}
// TODO(user): In the cases where this clause only contains two literals,
// then we could have only used one literal and its negation above.
m->Add(ClauseConstraint(clause));
}
}
void LoadAllDiffConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.all_diff().vars());
// If all variables are fully encoded and domains are not too large, use
// arc-consistent reasoning. Otherwise, use bounds-consistent reasoning.
IntegerTrail* integer_trail = m->GetOrCreate<IntegerTrail>();
IntegerEncoder* encoder = m->GetOrCreate<IntegerEncoder>();
int num_fully_encoded = 0;
int64 max_domain_size = 0;
for (const IntegerVariable variable : vars) {
if (encoder->VariableIsFullyEncoded(variable)) num_fully_encoded++;
IntegerValue lb = integer_trail->LowerBound(variable);
IntegerValue ub = integer_trail->UpperBound(variable);
const int64 domain_size = ub.value() - lb.value() + 1;
max_domain_size = std::max(max_domain_size, domain_size);
}
if (num_fully_encoded == vars.size() && max_domain_size < 1024) {
m->Add(AllDifferentBinary(vars));
m->Add(AllDifferentAC(vars));
} else {
m->Add(AllDifferentOnBounds(vars));
}
}
void LoadIntProdConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const IntegerVariable prod = mapping->Integer(ct.int_prod().target());
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.int_prod().vars());
CHECK_EQ(vars.size(), 2) << "General int_prod not supported yet.";
m->Add(ProductConstraint(vars[0], vars[1], prod));
}
void LoadIntDivConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const IntegerVariable div = mapping->Integer(ct.int_div().target());
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.int_div().vars());
if (m->Get(IsFixed(vars[1]))) {
const IntegerValue denom(m->Get(Value(vars[1])));
if (denom == 1) {
m->Add(Equality(vars[0], div));
} else {
m->Add(FixedDivisionConstraint(vars[0], denom, div));
}
} else {
m->Add(DivisionConstraint(vars[0], vars[1], div));
}
}
void LoadIntMinConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const IntegerVariable min = mapping->Integer(ct.int_min().target());
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.int_min().vars());
m->Add(IsEqualToMinOf(min, vars));
}
LinearExpression GetExprFromProto(const LinearExpressionProto& expr_proto,
const CpModelMapping& mapping) {
LinearExpression expr;
expr.vars = mapping.Integers(expr_proto.vars());
for (int j = 0; j < expr_proto.coeffs_size(); ++j) {
expr.coeffs.push_back(IntegerValue(expr_proto.coeffs(j)));
}
expr.offset = IntegerValue(expr_proto.offset());
return CanonicalizeExpr(expr);
}
void LoadLinMinConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const LinearExpression min =
GetExprFromProto(ct.lin_min().target(), *mapping);
std::vector<LinearExpression> exprs;
exprs.reserve(ct.lin_min().exprs_size());
for (int i = 0; i < ct.lin_min().exprs_size(); ++i) {
exprs.push_back(GetExprFromProto(ct.lin_min().exprs(i), *mapping));
}
m->Add(IsEqualToMinOf(min, exprs));
}
void LoadIntMaxConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const IntegerVariable max = mapping->Integer(ct.int_max().target());
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.int_max().vars());
m->Add(IsEqualToMaxOf(max, vars));
}
void LoadNoOverlapConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
m->Add(Disjunctive(mapping->Intervals(ct.no_overlap().intervals())));
}
void LoadNoOverlap2dConstraint(const ConstraintProto& ct, Model* m) {
if (ct.no_overlap_2d().x_intervals().empty()) return;
auto* mapping = m->GetOrCreate<CpModelMapping>();
const std::vector<IntervalVariable> x_intervals =
mapping->Intervals(ct.no_overlap_2d().x_intervals());
const std::vector<IntervalVariable> y_intervals =
mapping->Intervals(ct.no_overlap_2d().y_intervals());
m->Add(NonOverlappingRectangles(
x_intervals, y_intervals,
!ct.no_overlap_2d().boxes_with_null_area_can_overlap()));
}
void LoadCumulativeConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const std::vector<IntervalVariable> intervals =
mapping->Intervals(ct.cumulative().intervals());
const IntegerVariable capacity = mapping->Integer(ct.cumulative().capacity());
const std::vector<IntegerVariable> demands =
mapping->Integers(ct.cumulative().demands());
m->Add(Cumulative(intervals, demands, capacity));
}
// If a variable is constant and its value appear in no other variable domains,
// then the literal encoding the index and the one encoding the target at this
// value are equivalent.
bool DetectEquivalencesInElementConstraint(const ConstraintProto& ct,
Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
IntegerEncoder* encoder = m->GetOrCreate<IntegerEncoder>();
IntegerTrail* integer_trail = m->GetOrCreate<IntegerTrail>();
const IntegerVariable index = mapping->Integer(ct.element().index());
const IntegerVariable target = mapping->Integer(ct.element().target());
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.element().vars());
CHECK(!m->Get(IsFixed(index)));
CHECK(!m->Get(IsFixed(target)));
Domain union_of_non_constant_domains;
std::map<IntegerValue, int> constant_to_num;
for (const auto literal_value : m->Add(FullyEncodeVariable(index))) {
const int i = literal_value.value.value();
if (m->Get(IsFixed(vars[i]))) {
const IntegerValue value(m->Get(Value(vars[i])));
constant_to_num[value]++;
} else {
union_of_non_constant_domains = union_of_non_constant_domains.UnionWith(
integer_trail->InitialVariableDomain(vars[i]));
}
}
// Bump the number if the constant appear in union_of_non_constant_domains.
for (const auto entry : constant_to_num) {
if (union_of_non_constant_domains.Contains(entry.first.value())) {
constant_to_num[entry.first]++;
}
}
// Use the literal from the index encoding to encode the target at the
// "unique" values.
bool is_one_to_one_mapping = true;
for (const auto literal_value : m->Add(FullyEncodeVariable(index))) {
const int i = literal_value.value.value();
if (!m->Get(IsFixed(vars[i]))) {
is_one_to_one_mapping = false;
continue;
}
const IntegerValue value(m->Get(Value(vars[i])));
if (constant_to_num[value] == 1) {
const Literal r = literal_value.literal;
encoder->AssociateToIntegerEqualValue(r, target, value);
} else {
is_one_to_one_mapping = false;
}
}
return is_one_to_one_mapping;
}
// TODO(user): Be more efficient when the element().vars() are constants.
// Ideally we should avoid creating them as integer variable since we don't
// use them.
void LoadElementConstraintBounds(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const IntegerVariable index = mapping->Integer(ct.element().index());
const IntegerVariable target = mapping->Integer(ct.element().target());
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.element().vars());
CHECK(!m->Get(IsFixed(index)));
// We always fully encode the index on an element constraint.
const auto encoding = m->Add(FullyEncodeVariable((index)));
std::vector<Literal> selectors;
std::vector<IntegerVariable> possible_vars;
for (const auto literal_value : encoding) {
const int i = literal_value.value.value();
CHECK_GE(i, 0);
CHECK_LT(i, vars.size());
possible_vars.push_back(vars[i]);
selectors.push_back(literal_value.literal);
const Literal r = literal_value.literal;
if (vars[i] == target) continue;
if (m->Get(IsFixed(target))) {
const int64 value = m->Get(Value(target));
m->Add(ImpliesInInterval(r, vars[i], value, value));
} else if (m->Get(IsFixed(vars[i]))) {
const int64 value = m->Get(Value(vars[i]));
m->Add(ImpliesInInterval(r, target, value, value));
} else {
m->Add(ConditionalLowerOrEqualWithOffset(vars[i], target, 0, r));
m->Add(ConditionalLowerOrEqualWithOffset(target, vars[i], 0, r));
}
}
if (!m->Get(IsFixed(target))) {
m->Add(PartialIsOneOfVar(target, possible_vars, selectors));
}
}
// Arc-Consistent encoding of the element constraint as SAT clauses.
// The constraint enforces vars[index] == target.
//
// The AC propagation can be decomposed in three rules:
// Rule 1: dom(index) == i => dom(vars[i]) == dom(target).
// Rule 2: dom(target) \subseteq \Union_{i \in dom(index)} dom(vars[i]).
// Rule 3: dom(index) \subseteq { i | |dom(vars[i]) \inter dom(target)| > 0 }.
//
// We encode this in a way similar to the table constraint, except that the
// set of admissible tuples is not explicit.
// First, we add Booleans selected[i][value] <=> (index == i /\ vars[i] ==
// value). Rules 1 and 2 are enforced by target == value <=> \Or_{i}
// selected[i][value]. Rule 3 is enforced by index == i <=> \Or_{value}
// selected[i][value].
void LoadElementConstraintAC(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const IntegerVariable index = mapping->Integer(ct.element().index());
const IntegerVariable target = mapping->Integer(ct.element().target());
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.element().vars());
CHECK(!m->Get(IsFixed(index)));
CHECK(!m->Get(IsFixed(target)));
absl::flat_hash_map<IntegerValue, Literal> target_map;
const auto target_encoding = m->Add(FullyEncodeVariable(target));
for (const auto literal_value : target_encoding) {
target_map[literal_value.value] = literal_value.literal;
}
// For i \in index and value in vars[i], make (index == i /\ vars[i] == value)
// literals and store them by value in vectors.
absl::flat_hash_map<IntegerValue, std::vector<Literal>> value_to_literals;
const auto index_encoding = m->Add(FullyEncodeVariable(index));
IntegerTrail* integer_trail = m->GetOrCreate<IntegerTrail>();
for (const auto literal_value : index_encoding) {
const int i = literal_value.value.value();
const Literal i_lit = literal_value.literal;
// Special case where vars[i] == value /\ i_lit is actually i_lit.
if (m->Get(IsFixed(vars[i]))) {
value_to_literals[integer_trail->LowerBound(vars[i])].push_back(i_lit);
continue;
}
const auto var_encoding = m->Add(FullyEncodeVariable(vars[i]));
std::vector<Literal> var_selected_literals;
for (const auto var_literal_value : var_encoding) {
const IntegerValue value = var_literal_value.value;
const Literal var_is_value = var_literal_value.literal;
if (!gtl::ContainsKey(target_map, value)) {
// No need to add to value_to_literals, selected[i][value] is always
// false.
m->Add(Implication(i_lit, var_is_value.Negated()));
continue;
}
const Literal var_is_value_and_selected =
Literal(m->Add(NewBooleanVariable()), true);
m->Add(ReifiedBoolAnd({i_lit, var_is_value}, var_is_value_and_selected));
value_to_literals[value].push_back(var_is_value_and_selected);
var_selected_literals.push_back(var_is_value_and_selected);
}
// index == i <=> \Or_{value} selected[i][value].
m->Add(ReifiedBoolOr(var_selected_literals, i_lit));
}
// target == value <=> \Or_{i \in index} (vars[i] == value /\ index == i).
for (const auto& entry : target_map) {
const IntegerValue value = entry.first;
const Literal target_is_value = entry.second;
if (!gtl::ContainsKey(value_to_literals, value)) {
m->Add(ClauseConstraint({target_is_value.Negated()}));
} else {
m->Add(ReifiedBoolOr(value_to_literals[value], target_is_value));
}
}
}
namespace {
// This Boolean encoding is enough for consistency, but does not propagate as
// much as LoadElementConstraintAC(). However, setting any of the non-propagated
// Booleans to its "wrong" value will result directly in a conflict, so the
// solver will easily learn an AC encoding...
//
// The advantage is that this does not introduce extra BooleanVariables.
void LoadElementConstraintHalfAC(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const IntegerVariable index = mapping->Integer(ct.element().index());
const IntegerVariable target = mapping->Integer(ct.element().target());
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.element().vars());
CHECK(!m->Get(IsFixed(index)));
CHECK(!m->Get(IsFixed(target)));
m->Add(FullyEncodeVariable(target));
for (const auto value_literal : m->Add(FullyEncodeVariable(index))) {
const int i = value_literal.value.value();
m->Add(FullyEncodeVariable(vars[i]));
LoadEquivalenceAC({value_literal.literal}, IntegerValue(1), vars[i],
IntegerValue(-1), target, IntegerValue(0), m);
}
}
void LoadBooleanElement(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const IntegerVariable index = mapping->Integer(ct.element().index());
const std::vector<Literal> literals = mapping->Literals(ct.element().vars());
const Literal target = mapping->Literal(ct.element().target());
if (m->Get(IsFixed(index))) {
m->Add(Equality(target, literals[m->Get(Value(index))]));
return;
}
std::vector<Literal> all_true;
std::vector<Literal> all_false;
for (const auto value_literal : m->Add(FullyEncodeVariable(index))) {
const Literal a_lit = literals[value_literal.value.value()];
const Literal i_lit = value_literal.literal;
m->Add(ClauseConstraint({i_lit.Negated(), a_lit.Negated(), target}));
m->Add(ClauseConstraint({i_lit.Negated(), a_lit, target.Negated()}));
all_true.push_back(a_lit.Negated());
all_false.push_back(a_lit);
}
all_true.push_back(target);
all_false.push_back(target.Negated());
m->Add(ClauseConstraint(all_true));
m->Add(ClauseConstraint(all_false));
// TODO(user): Investigate filtering this with active literals.
}
} // namespace
void LoadElementConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const IntegerVariable index = mapping->Integer(ct.element().index());
bool boolean_array = true;
for (const int ref : ct.element().vars()) {
if (!mapping->IsBoolean(ref)) {
boolean_array = false;
break;
}
}
if (boolean_array && !mapping->IsBoolean(ct.element().target())) {
// Should have been reduced but presolve.
VLOG(1) << "Fix boolean_element not propagated on target";
boolean_array = false;
}
// TODO(user): Move this to presolve. Leads to a larger discussion on
// adding full encoding to model during presolve.
if (boolean_array) {
LoadBooleanElement(ct, m);
return;
}
const IntegerVariable target = mapping->Integer(ct.element().target());
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.element().vars());
// Retrict the domain of index in case there was no presolve.
if (!m->GetOrCreate<IntegerTrail>()->UpdateInitialDomain(
index, Domain(0, vars.size() - 1))) {
return;
}
// This returns true if there is nothing else to do after the equivalences
// of the form (index literal <=> target_literal) have been added.
if (!m->Get(IsFixed(index)) && !m->Get(IsFixed(target)) &&
DetectEquivalencesInElementConstraint(ct, m)) {
return;
}
// Special case when index is fixed.
if (m->Get(IsFixed(index))) {
m->Add(Equality(target, vars[m->Get(Value(index))]));
return;
}
// Special case when target is fixed.
if (m->Get(IsFixed(target))) {
return LoadElementConstraintBounds(ct, m);
}
IntegerEncoder* encoder = m->GetOrCreate<IntegerEncoder>();
const bool target_is_AC = encoder->VariableIsFullyEncoded(target);
int num_AC_variables = 0;
const int num_vars = ct.element().vars().size();
for (const int v : ct.element().vars()) {
IntegerVariable variable = mapping->Integer(v);
const bool is_full =
m->Get(IsFixed(variable)) || encoder->VariableIsFullyEncoded(variable);
if (is_full) num_AC_variables++;
}
const SatParameters& params = *m->GetOrCreate<SatParameters>();
if (params.boolean_encoding_level() > 0 &&
(target_is_AC || num_AC_variables >= num_vars - 1)) {
if (params.boolean_encoding_level() > 1) {
LoadElementConstraintAC(ct, m);
} else {
LoadElementConstraintHalfAC(ct, m);
}
} else {
LoadElementConstraintBounds(ct, m);
}
}
void LoadTableConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.table().vars());
const std::vector<int64> values = ValuesFromProto(ct.table().values());
const int num_vars = vars.size();
const int num_tuples = values.size() / num_vars;
std::vector<std::vector<int64>> tuples(num_tuples);
int count = 0;
for (int i = 0; i < num_tuples; ++i) {
for (int j = 0; j < num_vars; ++j) {
tuples[i].push_back(values[count++]);
}
}
if (ct.table().negated()) {
AddNegatedTableConstraint(vars, std::move(tuples), m);
} else {
AddTableConstraint(vars, std::move(tuples), m);
}
}
void LoadAutomatonConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const std::vector<IntegerVariable> vars =
mapping->Integers(ct.automaton().vars());
const int num_transitions = ct.automaton().transition_tail_size();
std::vector<std::vector<int64>> transitions;
transitions.reserve(num_transitions);
for (int i = 0; i < num_transitions; ++i) {
transitions.push_back({ct.automaton().transition_tail(i),
ct.automaton().transition_label(i),
ct.automaton().transition_head(i)});
}
const int64 starting_state = ct.automaton().starting_state();
const std::vector<int64> final_states =
ValuesFromProto(ct.automaton().final_states());
m->Add(TransitionConstraint(vars, transitions, starting_state, final_states));
}
// From vector of n IntegerVariables, returns an n x n matrix of Literal
// such that matrix[i][j] is the Literal corresponding to vars[i] == j.
std::vector<std::vector<Literal>> GetSquareMatrixFromIntegerVariables(
const std::vector<IntegerVariable>& vars, Model* m) {
const int n = vars.size();
const Literal kTrueLiteral =
m->GetOrCreate<IntegerEncoder>()->GetTrueLiteral();
const Literal kFalseLiteral =
m->GetOrCreate<IntegerEncoder>()->GetFalseLiteral();
std::vector<std::vector<Literal>> matrix(
n, std::vector<Literal>(n, kFalseLiteral));
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (m->Get(IsFixed(vars[i]))) {
const int value = m->Get(Value(vars[i]));
DCHECK_LE(0, value);
DCHECK_LT(value, n);
matrix[i][value] = kTrueLiteral;
} else {
const auto encoding = m->Add(FullyEncodeVariable(vars[i]));
for (const auto& entry : encoding) {
const int value = entry.value.value();
DCHECK_LE(0, value);
DCHECK_LT(value, n);
matrix[i][value] = entry.literal;
}
}
}
}
return matrix;
}
void LoadCircuitConstraint(const ConstraintProto& ct, Model* m) {
const auto& circuit = ct.circuit();
if (circuit.tails().empty()) return;
std::vector<int> tails(circuit.tails().begin(), circuit.tails().end());
std::vector<int> heads(circuit.heads().begin(), circuit.heads().end());
std::vector<Literal> literals =
m->GetOrCreate<CpModelMapping>()->Literals(circuit.literals());
const int num_nodes = ReindexArcs(&tails, &heads, &literals);
m->Add(SubcircuitConstraint(num_nodes, tails, heads, literals));
}
void LoadRoutesConstraint(const ConstraintProto& ct, Model* m) {
const auto& routes = ct.routes();
if (routes.tails().empty()) return;
std::vector<int> tails(routes.tails().begin(), routes.tails().end());
std::vector<int> heads(routes.heads().begin(), routes.heads().end());
std::vector<Literal> literals =
m->GetOrCreate<CpModelMapping>()->Literals(routes.literals());
const int num_nodes = ReindexArcs(&tails, &heads, &literals);
m->Add(SubcircuitConstraint(num_nodes, tails, heads, literals,
/*multiple_subcircuit_through_zero=*/true));
}
void LoadCircuitCoveringConstraint(const ConstraintProto& ct, Model* m) {
auto* mapping = m->GetOrCreate<CpModelMapping>();
const std::vector<IntegerVariable> nexts =
mapping->Integers(ct.circuit_covering().nexts());
const std::vector<std::vector<Literal>> graph =
GetSquareMatrixFromIntegerVariables(nexts, m);
const std::vector<int> distinguished(
ct.circuit_covering().distinguished_nodes().begin(),
ct.circuit_covering().distinguished_nodes().end());
m->Add(ExactlyOnePerRowAndPerColumn(graph));
m->Add(CircuitCovering(graph, distinguished));
}
bool LoadConstraint(const ConstraintProto& ct, Model* m) {
switch (ct.constraint_case()) {
case ConstraintProto::ConstraintCase::CONSTRAINT_NOT_SET:
return true;
case ConstraintProto::ConstraintCase::kBoolOr:
LoadBoolOrConstraint(ct, m);
return true;
case ConstraintProto::ConstraintCase::kBoolAnd:
LoadBoolAndConstraint(ct, m);
return true;
case ConstraintProto::ConstraintCase::kAtMostOne:
LoadAtMostOneConstraint(ct, m);
return true;
case ConstraintProto::ConstraintCase::kBoolXor:
LoadBoolXorConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kLinear:
LoadLinearConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kAllDiff:
LoadAllDiffConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kIntProd:
LoadIntProdConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kIntDiv:
LoadIntDivConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kIntMin:
LoadIntMinConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kLinMin:
LoadLinMinConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kIntMax:
LoadIntMaxConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kInterval:
// Already dealt with.
return true;
case ConstraintProto::ConstraintProto::kNoOverlap:
LoadNoOverlapConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kNoOverlap2D:
LoadNoOverlap2dConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kCumulative:
LoadCumulativeConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kElement:
LoadElementConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kTable:
LoadTableConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kAutomaton:
LoadAutomatonConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kCircuit:
LoadCircuitConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kRoutes:
LoadRoutesConstraint(ct, m);
return true;
case ConstraintProto::ConstraintProto::kCircuitCovering:
LoadCircuitCoveringConstraint(ct, m);
return true;
default:
return false;
}
}
} // namespace sat
} // namespace operations_research
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