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cp_model_expand.cc
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cp_model_expand.cc
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// Copyright 2010-2024 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_expand.h"
#include <algorithm>
#include <cstdint>
#include <deque>
#include <limits>
#include <optional>
#include <string>
#include <utility>
#include <vector>
#include "absl/container/btree_map.h"
#include "absl/container/flat_hash_map.h"
#include "absl/container/flat_hash_set.h"
#include "absl/container/inlined_vector.h"
#include "absl/log/check.h"
#include "absl/meta/type_traits.h"
#include "absl/strings/str_cat.h"
#include "google/protobuf/message.h"
#include "ortools/base/logging.h"
#include "ortools/base/stl_util.h"
#include "ortools/port/proto_utils.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_checker.h"
#include "ortools/sat/cp_model_utils.h"
#include "ortools/sat/presolve_context.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/sat/util.h"
#include "ortools/util/logging.h"
#include "ortools/util/sorted_interval_list.h"
namespace operations_research {
namespace sat {
// TODO(user): Note that if we have duplicate variables controlling different
// time point, this might not reach the fixed point. Fix? it is not that
// important as the expansion take care of this case anyway.
void PropagateAutomaton(const AutomatonConstraintProto& proto,
const PresolveContext& context,
std::vector<absl::flat_hash_set<int64_t>>* states,
std::vector<absl::flat_hash_set<int64_t>>* labels) {
const int n = proto.vars_size();
const absl::flat_hash_set<int64_t> final_states(
{proto.final_states().begin(), proto.final_states().end()});
labels->clear();
labels->resize(n);
states->clear();
states->resize(n + 1);
(*states)[0].insert(proto.starting_state());
// Forward pass.
for (int time = 0; time < n; ++time) {
for (int t = 0; t < proto.transition_tail_size(); ++t) {
const int64_t tail = proto.transition_tail(t);
const int64_t label = proto.transition_label(t);
const int64_t head = proto.transition_head(t);
if (!(*states)[time].contains(tail)) continue;
if (!context.DomainContains(proto.vars(time), label)) continue;
if (time == n - 1 && !final_states.contains(head)) continue;
(*labels)[time].insert(label);
(*states)[time + 1].insert(head);
}
}
// Backward pass.
for (int time = n - 1; time >= 0; --time) {
absl::flat_hash_set<int64_t> new_states;
absl::flat_hash_set<int64_t> new_labels;
for (int t = 0; t < proto.transition_tail_size(); ++t) {
const int64_t tail = proto.transition_tail(t);
const int64_t label = proto.transition_label(t);
const int64_t head = proto.transition_head(t);
if (!(*states)[time].contains(tail)) continue;
if (!(*labels)[time].contains(label)) continue;
if (!(*states)[time + 1].contains(head)) continue;
new_labels.insert(label);
new_states.insert(tail);
}
(*labels)[time].swap(new_labels);
(*states)[time].swap(new_states);
}
}
namespace {
// Different encoding that support general demands. This is usually a pretty bad
// encoding, at least until we improve the solver on such models.
void ExpandReservoirUsingCircuit(int64_t sum_of_positive_demand,
int64_t sum_of_negative_demand,
ConstraintProto* reservoir_ct,
PresolveContext* context) {
const ReservoirConstraintProto& reservoir = reservoir_ct->reservoir();
const int num_events = reservoir.time_exprs_size();
// The encoding will create a circuit constraint and on integer variable per
// events representing the level a that event time.
CircuitConstraintProto* circuit =
context->working_model->add_constraints()->mutable_circuit();
const int64_t var_min =
std::max(reservoir.min_level(), sum_of_negative_demand);
const int64_t var_max =
std::min(reservoir.max_level(), sum_of_positive_demand);
std::vector<int> level_vars(num_events);
for (int i = 0; i < num_events; ++i) {
level_vars[i] = context->NewIntVar(Domain(var_min, var_max));
}
// For the corner case where all events are absent, we need a potential
// self-arc on the start/end circuit node.
{
circuit->add_tails(num_events);
circuit->add_heads(num_events);
circuit->add_literals(context->NewBoolVar());
}
for (int i = 0; i < num_events; ++i) {
if (!reservoir.active_literals().empty()) {
// Add self arc to represent absence.
circuit->add_tails(i);
circuit->add_heads(i);
circuit->add_literals(NegatedRef(reservoir.active_literals(i)));
}
// We need an extra circuit node for start/end of circuit.
// We use the available index 'num_events'.
{
// Circuit starts at i, level_vars[i] == demand_expr[i].
const int start_var = context->NewBoolVar();
circuit->add_tails(num_events);
circuit->add_heads(i);
circuit->add_literals(start_var);
// Add enforced linear for demand.
{
ConstraintProto* new_ct = context->working_model->add_constraints();
new_ct->add_enforcement_literal(start_var);
LinearConstraintProto* lin = new_ct->mutable_linear();
lin->add_domain(0);
lin->add_domain(0);
lin->add_vars(level_vars[i]);
lin->add_coeffs(1);
AddLinearExpressionToLinearConstraint(reservoir.level_changes(i), -1,
lin);
context->CanonicalizeLinearConstraint(new_ct);
}
// Circuit ends at i, no extra constraint there.
circuit->add_tails(i);
circuit->add_heads(num_events);
circuit->add_literals(context->NewBoolVar());
}
for (int j = 0; j < num_events; ++j) {
if (i == j) continue;
// If arc_i_j is true then:
// - active_i is true (enforced by circuit).
// - active_j is true (enforced by circuit).
// - time_i <= time_j
// - level_j == level_i + demand_j
//
// TODO(user): Unfortunately we cannot share these literal between
// reservoir except if the set of time point is exactly the same!
// otherwise if we miss one, then A "after" B in one circuit do not
// implies that there is no C in between in another!
const int arc_i_j = context->NewBoolVar();
circuit->add_tails(i);
circuit->add_heads(j);
circuit->add_literals(arc_i_j);
// Add enforced linear for time.
{
ConstraintProto* new_ct = context->working_model->add_constraints();
new_ct->add_enforcement_literal(arc_i_j);
LinearConstraintProto* lin = new_ct->mutable_linear();
lin->add_domain(0);
lin->add_domain(std::numeric_limits<int64_t>::max());
AddLinearExpressionToLinearConstraint(reservoir.time_exprs(j), 1, lin);
AddLinearExpressionToLinearConstraint(reservoir.time_exprs(i), -1, lin);
context->CanonicalizeLinearConstraint(new_ct);
}
// Add enforced linear for demand.
{
ConstraintProto* new_ct = context->working_model->add_constraints();
new_ct->add_enforcement_literal(arc_i_j);
LinearConstraintProto* lin = new_ct->mutable_linear();
lin->add_domain(0);
lin->add_domain(0);
lin->add_vars(level_vars[j]);
lin->add_coeffs(1);
lin->add_vars(level_vars[i]);
lin->add_coeffs(-1);
AddLinearExpressionToLinearConstraint(reservoir.level_changes(j), -1,
lin);
context->CanonicalizeLinearConstraint(new_ct);
}
}
}
reservoir_ct->Clear();
context->UpdateRuleStats("reservoir: expanded using circuit.");
}
void ExpandReservoirUsingPrecedences(int64_t sum_of_positive_demand,
int64_t sum_of_negative_demand,
ConstraintProto* reservoir_ct,
PresolveContext* context) {
const ReservoirConstraintProto& reservoir = reservoir_ct->reservoir();
const int num_events = reservoir.time_exprs_size();
const int true_literal = context->GetTrueLiteral();
const auto is_active_literal = [&reservoir, true_literal](int index) {
if (reservoir.active_literals_size() == 0) return true_literal;
return reservoir.active_literals(index);
};
// Constrains the running level to be consistent at all time_exprs.
// For this we only add a constraint at the time a given demand take place.
for (int i = 0; i < num_events; ++i) {
const int active_i = is_active_literal(i);
if (context->LiteralIsFalse(active_i)) continue;
const int64_t demand_i = context->FixedValue(reservoir.level_changes(i));
if (demand_i == 0) continue;
// No need for some constraints if the reservoir is just constrained in
// one direction.
if (demand_i > 0 && sum_of_positive_demand <= reservoir.max_level()) {
continue;
}
if (demand_i < 0 && sum_of_negative_demand >= reservoir.min_level()) {
continue;
}
ConstraintProto* new_ct = context->working_model->add_constraints();
LinearConstraintProto* new_linear = new_ct->mutable_linear();
// Add contributions from previous events.
int64_t offset = 0;
const LinearExpressionProto& time_i = reservoir.time_exprs(i);
for (int j = 0; j < num_events; ++j) {
if (i == j) continue;
const int active_j = is_active_literal(j);
if (context->LiteralIsFalse(active_j)) continue;
// Get or create the literal equivalent to
// active_i && active_j && time[j] <= time[i].
//
// TODO(user): we could get rid of active_i in the equivalence above.
// Experiments when we have enough benchmarks.
const LinearExpressionProto& time_j = reservoir.time_exprs(j);
const int j_lesseq_i = context->GetOrCreateReifiedPrecedenceLiteral(
time_j, time_i, active_j, active_i);
context->working_model->mutable_variables(j_lesseq_i)
->set_name(absl::StrCat(j, " before ", i));
const int64_t demand = context->FixedValue(reservoir.level_changes(j));
if (RefIsPositive(j_lesseq_i)) {
new_linear->add_vars(j_lesseq_i);
new_linear->add_coeffs(demand);
} else {
new_linear->add_vars(NegatedRef(j_lesseq_i));
new_linear->add_coeffs(-demand);
offset -= demand;
}
}
// Add contribution from event i.
//
// TODO(user): Alternatively we can mark the whole constraint as enforced
// only if active_i is true. Experiments with both version, right now we
// miss enough benchmarks to conclude.
if (RefIsPositive(active_i)) {
new_linear->add_vars(active_i);
new_linear->add_coeffs(demand_i);
} else {
new_linear->add_vars(NegatedRef(active_i));
new_linear->add_coeffs(-demand_i);
offset -= demand_i;
}
// Note that according to the sign of demand_i, we only need one side.
if (demand_i > 0) {
new_linear->add_domain(std::numeric_limits<int64_t>::min());
new_linear->add_domain(reservoir.max_level());
} else {
new_linear->add_domain(reservoir.min_level());
new_linear->add_domain(std::numeric_limits<int64_t>::max());
}
context->CanonicalizeLinearConstraint(new_ct);
}
reservoir_ct->Clear();
context->UpdateRuleStats("reservoir: expanded using precedences");
}
void ExpandReservoir(ConstraintProto* reservoir_ct, PresolveContext* context) {
if (reservoir_ct->reservoir().min_level() >
reservoir_ct->reservoir().max_level()) {
VLOG(1) << "Empty level domain in reservoir constraint.";
return (void)context->NotifyThatModelIsUnsat();
}
const ReservoirConstraintProto& reservoir = reservoir_ct->reservoir();
const int num_events = reservoir.time_exprs_size();
int num_positives = 0;
int num_negatives = 0;
bool all_demands_are_fixed = true;
int64_t sum_of_positive_demand = 0;
int64_t sum_of_negative_demand = 0;
for (const LinearExpressionProto& demand_expr : reservoir.level_changes()) {
if (!context->IsFixed(demand_expr)) {
all_demands_are_fixed = false;
}
const int64_t max_demand = context->MaxOf(demand_expr);
if (max_demand > 0) {
num_positives++;
sum_of_positive_demand += max_demand;
}
const int64_t min_demand = context->MinOf(demand_expr);
if (min_demand < 0) {
num_negatives++;
sum_of_negative_demand += min_demand;
}
}
if (sum_of_negative_demand >= reservoir.min_level() &&
sum_of_positive_demand <= reservoir.max_level()) {
context->UpdateRuleStats("reservoir: always true");
reservoir_ct->Clear();
return;
}
// If all level_changes have the same sign, we do not care about the order,
// just the sum. We might need to create intermediate variable for quadratic
// terms though.
if (num_negatives == 0 || num_positives == 0) {
const int true_literal = context->GetTrueLiteral();
ConstraintProto* new_ct = context->working_model->add_constraints();
LinearConstraintProto* sum = new_ct->mutable_linear();
for (int i = 0; i < num_events; ++i) {
const int active = reservoir.active_literals().empty()
? true_literal
: reservoir.active_literals(i);
const LinearExpressionProto& demand = reservoir.level_changes(i);
if (context->IsFixed(demand)) {
const int64_t change = context->FixedValue(reservoir.level_changes(i));
if (RefIsPositive(active)) {
sum->add_vars(active);
sum->add_coeffs(change);
} else {
// Add (1 - not(active)) * level_change.
sum->add_vars(true_literal);
sum->add_coeffs(change);
sum->add_vars(NegatedRef(active));
sum->add_coeffs(-change);
}
} else if (context->LiteralIsTrue(active)) {
AddLinearExpressionToLinearConstraint(demand, 1, sum);
} else {
const int new_var = context->NewIntVar(
Domain(context->MinOf(demand), context->MaxOf(demand))
.UnionWith(Domain(0)));
sum->add_vars(new_var);
sum->add_coeffs(1);
// Active => new_var == demand.
{
ConstraintProto* demand_ct =
context->working_model->add_constraints();
demand_ct->add_enforcement_literal(active);
LinearConstraintProto* lin = demand_ct->mutable_linear();
lin->add_domain(0);
lin->add_domain(0);
lin->add_vars(new_var);
lin->add_coeffs(1);
AddLinearExpressionToLinearConstraint(demand, -1, lin);
context->CanonicalizeLinearConstraint(demand_ct);
}
// not(active) => new_var == 0.
context->AddImplyInDomain(NegatedRef(active), new_var, Domain(0));
}
}
sum->add_domain(reservoir.min_level());
sum->add_domain(reservoir.max_level());
context->CanonicalizeLinearConstraint(new_ct);
context->UpdateRuleStats("reservoir: simple expansion with sum");
reservoir_ct->Clear();
return;
}
// Call the correct expansion according to our parameter.
if (context->params().expand_reservoir_using_circuit()) {
ExpandReservoirUsingCircuit(sum_of_positive_demand, sum_of_negative_demand,
reservoir_ct, context);
} else {
// This one is the faster option usually.
if (all_demands_are_fixed) {
ExpandReservoirUsingPrecedences(sum_of_positive_demand,
sum_of_negative_demand, reservoir_ct,
context);
} else {
context->UpdateRuleStats(
"reservoir: skipped expansion due to variable demands");
}
}
}
// This is mainly used for testing the reservoir implementation.
void EncodeCumulativeAsReservoir(ConstraintProto* ct,
PresolveContext* context) {
if (!context->IsFixed(ct->cumulative().capacity())) {
context->UpdateRuleStats(
"cumulative -> reservoir: expansion is not supported with variable "
"capacity.");
return;
}
// Note that we know that the min_level can never go below zero, so we can
// just ignore this part of the constraint here.
ConstraintProto reservoir_ct;
auto* reservoir = reservoir_ct.mutable_reservoir();
reservoir->set_min_level(std::numeric_limits<int64_t>::min());
reservoir->set_max_level(context->FixedValue(ct->cumulative().capacity()));
const int true_literal = context->GetTrueLiteral();
const int num_intervals = ct->cumulative().intervals().size();
for (int i = 0; i < num_intervals; ++i) {
const auto& interval_ct =
context->working_model->constraints(ct->cumulative().intervals(i));
const auto& interval = interval_ct.interval();
*reservoir->add_time_exprs() = interval.start();
*reservoir->add_time_exprs() = interval.end();
const LinearExpressionProto& demand = ct->cumulative().demands(i);
*reservoir->add_level_changes() = demand;
LinearExpressionProto& negated = *reservoir->add_level_changes();
negated.set_offset(-demand.offset());
for (int j = 0; j < demand.vars().size(); ++j) {
negated.add_vars(demand.vars(j));
negated.add_coeffs(-demand.coeffs(j));
}
if (interval_ct.enforcement_literal().empty()) {
reservoir->add_active_literals(true_literal);
reservoir->add_active_literals(true_literal);
} else {
CHECK_EQ(interval_ct.enforcement_literal().size(), 1);
reservoir->add_active_literals(interval_ct.enforcement_literal(0));
reservoir->add_active_literals(interval_ct.enforcement_literal(0));
}
}
// Now expand it and clear the cumulative.
ct->Clear();
context->UpdateRuleStats("cumulative: expanded into reservoir");
ExpandReservoir(&reservoir_ct, context);
}
void ExpandIntMod(ConstraintProto* ct, PresolveContext* context) {
const LinearArgumentProto& int_mod = ct->int_mod();
const LinearExpressionProto& mod_expr = int_mod.exprs(1);
if (context->IsFixed(mod_expr)) return;
const LinearExpressionProto& expr = int_mod.exprs(0);
const LinearExpressionProto& target_expr = int_mod.target();
// We reduce the domain of target_expr to avoid later overflow.
if (!context->IntersectDomainWith(
target_expr, context->DomainSuperSetOf(expr).PositiveModuloBySuperset(
context->DomainSuperSetOf(mod_expr)))) {
return;
}
// Create a new constraint with the same enforcement as ct.
auto new_enforced_constraint = [&]() {
ConstraintProto* new_ct = context->working_model->add_constraints();
*new_ct->mutable_enforcement_literal() = ct->enforcement_literal();
return new_ct;
};
// div_expr = expr / mod_expr.
const int div_var = context->NewIntVar(
context->DomainSuperSetOf(expr).PositiveDivisionBySuperset(
context->DomainSuperSetOf(mod_expr)));
LinearExpressionProto div_expr;
div_expr.add_vars(div_var);
div_expr.add_coeffs(1);
LinearArgumentProto* const div_proto =
new_enforced_constraint()->mutable_int_div();
*div_proto->mutable_target() = div_expr;
*div_proto->add_exprs() = expr;
*div_proto->add_exprs() = mod_expr;
// Create prod_expr = div_expr * mod_expr.
const Domain prod_domain =
context->DomainOf(div_var)
.ContinuousMultiplicationBy(context->DomainSuperSetOf(mod_expr))
.IntersectionWith(context->DomainSuperSetOf(expr).AdditionWith(
context->DomainSuperSetOf(target_expr).Negation()));
const int prod_var = context->NewIntVar(prod_domain);
LinearExpressionProto prod_expr;
prod_expr.add_vars(prod_var);
prod_expr.add_coeffs(1);
LinearArgumentProto* const int_prod =
new_enforced_constraint()->mutable_int_prod();
*int_prod->mutable_target() = prod_expr;
*int_prod->add_exprs() = div_expr;
*int_prod->add_exprs() = mod_expr;
// expr - prod_expr = target_expr.
LinearConstraintProto* const lin =
new_enforced_constraint()->mutable_linear();
lin->add_domain(0);
lin->add_domain(0);
AddLinearExpressionToLinearConstraint(expr, 1, lin);
AddLinearExpressionToLinearConstraint(prod_expr, -1, lin);
AddLinearExpressionToLinearConstraint(target_expr, -1, lin);
ct->Clear();
context->UpdateRuleStats("int_mod: expanded");
}
void ExpandNonBinaryIntProd(ConstraintProto* ct, PresolveContext* context) {
CHECK_GT(ct->int_prod().exprs_size(), 2);
std::deque<LinearExpressionProto> terms(
{ct->int_prod().exprs().begin(), ct->int_prod().exprs().end()});
while (terms.size() > 2) {
const LinearExpressionProto& left = terms[0];
const LinearExpressionProto& right = terms[1];
const Domain new_domain =
context->DomainSuperSetOf(left).ContinuousMultiplicationBy(
context->DomainSuperSetOf(right));
const int new_var = context->NewIntVar(new_domain);
LinearArgumentProto* const int_prod =
context->working_model->add_constraints()->mutable_int_prod();
*int_prod->add_exprs() = left;
*int_prod->add_exprs() = right;
int_prod->mutable_target()->add_vars(new_var);
int_prod->mutable_target()->add_coeffs(1);
terms.pop_front();
terms.pop_front();
terms.push_back(int_prod->target());
}
LinearArgumentProto* const final_int_prod =
context->working_model->add_constraints()->mutable_int_prod();
*final_int_prod->add_exprs() = terms[0];
*final_int_prod->add_exprs() = terms[1];
*final_int_prod->mutable_target() = ct->int_prod().target();
context->UpdateRuleStats(absl::StrCat(
"int_prod: expanded int_prod with arity ", ct->int_prod().exprs_size()));
ct->Clear();
}
// TODO(user): Move this into the presolve instead?
void ExpandIntProdWithBoolean(int bool_ref,
const LinearExpressionProto& int_expr,
const LinearExpressionProto& product_expr,
PresolveContext* context) {
ConstraintProto* const one = context->working_model->add_constraints();
one->add_enforcement_literal(bool_ref);
one->mutable_linear()->add_domain(0);
one->mutable_linear()->add_domain(0);
AddLinearExpressionToLinearConstraint(int_expr, 1, one->mutable_linear());
AddLinearExpressionToLinearConstraint(product_expr, -1,
one->mutable_linear());
ConstraintProto* const zero = context->working_model->add_constraints();
zero->add_enforcement_literal(NegatedRef(bool_ref));
zero->mutable_linear()->add_domain(0);
zero->mutable_linear()->add_domain(0);
AddLinearExpressionToLinearConstraint(product_expr, 1,
zero->mutable_linear());
}
void ExpandIntProd(ConstraintProto* ct, PresolveContext* context) {
const LinearArgumentProto& int_prod = ct->int_prod();
if (int_prod.exprs_size() > 2) {
ExpandNonBinaryIntProd(ct, context);
return;
}
if (int_prod.exprs_size() != 2) return;
const LinearExpressionProto& a = int_prod.exprs(0);
const LinearExpressionProto& b = int_prod.exprs(1);
const LinearExpressionProto& p = int_prod.target();
int literal;
const bool a_is_literal = context->ExpressionIsALiteral(a, &literal);
const bool b_is_literal = context->ExpressionIsALiteral(b, &literal);
// We expand if exactly one of {a, b} is a literal. If both are literals, it
// will be presolved into a better version.
if (a_is_literal && !b_is_literal) {
ExpandIntProdWithBoolean(literal, b, p, context);
ct->Clear();
context->UpdateRuleStats("int_prod: expanded product with Boolean var");
} else if (b_is_literal) {
ExpandIntProdWithBoolean(literal, a, p, context);
ct->Clear();
context->UpdateRuleStats("int_prod: expanded product with Boolean var");
}
}
void ExpandInverse(ConstraintProto* ct, PresolveContext* context) {
const auto& f_direct = ct->inverse().f_direct();
const auto& f_inverse = ct->inverse().f_inverse();
const int n = f_direct.size();
CHECK_EQ(n, f_inverse.size());
// Make sure the domains are included in [0, n - 1).
// Note that if a variable and its negation appear, the domains will be set to
// zero here.
//
// TODO(user): Add support for UNSAT at expansion. This should create empty
// domain if UNSAT, so it should still work correctly.
absl::flat_hash_set<int> used_variables;
for (const int ref : f_direct) {
used_variables.insert(PositiveRef(ref));
if (!context->IntersectDomainWith(ref, Domain(0, n - 1))) {
VLOG(1) << "Empty domain for a variable in ExpandInverse()";
return;
}
}
for (const int ref : f_inverse) {
used_variables.insert(PositiveRef(ref));
if (!context->IntersectDomainWith(ref, Domain(0, n - 1))) {
VLOG(1) << "Empty domain for a variable in ExpandInverse()";
return;
}
}
// If we have duplicate variables, we make sure the domain are reduced
// as the loop below might not detect incompatibilities.
if (used_variables.size() != 2 * n) {
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
// Note that if we don't have the same sign, both domain are at zero.
if (PositiveRef(f_direct[i]) != PositiveRef(f_inverse[j])) continue;
// We can't have i or j as value if i != j.
if (i == j) continue;
if (!context->IntersectDomainWith(
f_direct[i], Domain::FromValues({i, j}).Complement())) {
return;
}
}
}
}
// Reduce the domains of each variable by checking that the inverse value
// exists.
std::vector<int64_t> possible_values;
// Propagate from one vector to its counterpart.
const auto filter_inverse_domain =
[context, n, &possible_values](const auto& direct, const auto& inverse) {
// Propagate from the inverse vector to the direct vector.
for (int i = 0; i < n; ++i) {
possible_values.clear();
const Domain domain = context->DomainOf(direct[i]);
bool removed_value = false;
for (const int64_t j : domain.Values()) {
if (context->DomainOf(inverse[j]).Contains(i)) {
possible_values.push_back(j);
} else {
removed_value = true;
}
}
if (removed_value) {
if (!context->IntersectDomainWith(
direct[i], Domain::FromValues(possible_values))) {
VLOG(1) << "Empty domain for a variable in ExpandInverse()";
return false;
}
}
}
return true;
};
// Note that this should reach the fixed point in one pass.
// However, if we have duplicate variable, I am not sure.
if (!filter_inverse_domain(f_direct, f_inverse)) return;
if (!filter_inverse_domain(f_inverse, f_direct)) return;
// Expand the inverse constraint by associating literal to var == value
// and sharing them between the direct and inverse variables.
//
// Note that this is only correct because the domain are tight now.
for (int i = 0; i < n; ++i) {
const int f_i = f_direct[i];
for (const int64_t j : context->DomainOf(f_i).Values()) {
// We have f[i] == j <=> r[j] == i;
const int r_j = f_inverse[j];
int r_j_i;
if (context->HasVarValueEncoding(r_j, i, &r_j_i)) {
context->InsertVarValueEncoding(r_j_i, f_i, j);
} else {
const int f_i_j = context->GetOrCreateVarValueEncoding(f_i, j);
context->InsertVarValueEncoding(f_i_j, r_j, i);
}
}
}
ct->Clear();
context->UpdateRuleStats("inverse: expanded");
}
void ExpandLinMax(ConstraintProto* ct, PresolveContext* context) {
const int num_exprs = ct->lin_max().exprs().size();
if (num_exprs < 2) return;
// We have a special treatment for Abs, Earliness, Tardiness, and all
// affine_max where there is only one variable present in all the expressions.
if (ExpressionsContainsOnlyOneVar(ct->lin_max().exprs())) return;
// We will create 2 * num_exprs constraints for target = max(a1, .., an).
// First.
// - target >= ai
for (const LinearExpressionProto& expr : ct->lin_max().exprs()) {
ConstraintProto* new_ct = context->working_model->add_constraints();
LinearConstraintProto* lin = new_ct->mutable_linear();
lin->add_domain(0);
lin->add_domain(std::numeric_limits<int64_t>::max());
AddLinearExpressionToLinearConstraint(ct->lin_max().target(), 1, lin);
AddLinearExpressionToLinearConstraint(expr, -1, lin);
context->CanonicalizeLinearConstraint(new_ct);
}
// Second, for each expr, create a new boolean bi, and add bi => target >= ai
// With exactly_one(bi)
std::vector<int> enforcement_literals;
enforcement_literals.reserve(num_exprs);
if (num_exprs == 2) {
const int new_bool = context->NewBoolVar();
enforcement_literals.push_back(new_bool);
enforcement_literals.push_back(NegatedRef(new_bool));
} else {
ConstraintProto* exactly_one = context->working_model->add_constraints();
for (int i = 0; i < num_exprs; ++i) {
const int new_bool = context->NewBoolVar();
exactly_one->mutable_exactly_one()->add_literals(new_bool);
enforcement_literals.push_back(new_bool);
}
}
for (int i = 0; i < num_exprs; ++i) {
ConstraintProto* new_ct = context->working_model->add_constraints();
new_ct->add_enforcement_literal(enforcement_literals[i]);
LinearConstraintProto* lin = new_ct->mutable_linear();
lin->add_domain(std::numeric_limits<int64_t>::min());
lin->add_domain(0);
AddLinearExpressionToLinearConstraint(ct->lin_max().target(), 1, lin);
AddLinearExpressionToLinearConstraint(ct->lin_max().exprs(i), -1, lin);
context->CanonicalizeLinearConstraint(new_ct);
}
context->UpdateRuleStats("lin_max: expanded lin_max");
ct->Clear();
}
// A[V] == V means for all i, V == i => A_i == i
void ExpandElementWithTargetEqualIndex(ConstraintProto* ct,
PresolveContext* context) {
const ElementConstraintProto& element = ct->element();
DCHECK_EQ(element.index(), element.target());
const int index_ref = element.index();
std::vector<int64_t> valid_indices;
for (const int64_t v : context->DomainOf(index_ref).Values()) {
if (!context->DomainContains(element.vars(v), v)) continue;
valid_indices.push_back(v);
}
if (valid_indices.size() < context->DomainOf(index_ref).Size()) {
if (!context->IntersectDomainWith(index_ref,
Domain::FromValues(valid_indices))) {
VLOG(1) << "No compatible variable domains in "
"ExpandElementWithTargetEqualIndex()";
return;
}
context->UpdateRuleStats("element: reduced index domain");
}
for (const int64_t v : context->DomainOf(index_ref).Values()) {
const int var = element.vars(v);
if (context->MinOf(var) == v && context->MaxOf(var) == v) continue;
context->AddImplyInDomain(
context->GetOrCreateVarValueEncoding(index_ref, v), var, Domain(v));
}
context->UpdateRuleStats(
"element: expanded with special case target = index");
ct->Clear();
}
// Special case if the array of the element is filled with constant values.
void ExpandConstantArrayElement(ConstraintProto* ct, PresolveContext* context) {
const ElementConstraintProto& element = ct->element();
const int index_ref = element.index();
const int target_ref = element.target();
// Index and target domain have been reduced before calling this function.
const Domain index_domain = context->DomainOf(index_ref);
const Domain target_domain = context->DomainOf(target_ref);
// This BoolOrs implements the deduction that if all index literals pointing
// to the same value in the constant array are false, then this value is no
// no longer valid for the target variable. They are created only for values
// that have multiples literals supporting them.
// Order is not important.
absl::flat_hash_map<int64_t, BoolArgumentProto*> supports;
{
absl::flat_hash_map<int64_t, int> constant_var_values_usage;
for (const int64_t v : index_domain.Values()) {
DCHECK(context->IsFixed(element.vars(v)));
const int64_t value = context->MinOf(element.vars(v));
if (++constant_var_values_usage[value] == 2) {
// First time we cross > 1.
BoolArgumentProto* const support =
context->working_model->add_constraints()->mutable_bool_or();
const int target_literal =
context->GetOrCreateVarValueEncoding(target_ref, value);
support->add_literals(NegatedRef(target_literal));
supports[value] = support;
}
}
}
{
// While this is not strictly needed since all value in the index will be
// covered, it allows to easily detect this fact in the presolve.
auto* exactly_one =
context->working_model->add_constraints()->mutable_exactly_one();
for (const int64_t v : index_domain.Values()) {
const int index_literal =
context->GetOrCreateVarValueEncoding(index_ref, v);
exactly_one->add_literals(index_literal);
const int64_t value = context->MinOf(element.vars(v));
const auto& it = supports.find(value);
if (it != supports.end()) {
// The encoding literal for 'value' of the target_ref has been
// created before.
const int target_literal =
context->GetOrCreateVarValueEncoding(target_ref, value);
context->AddImplication(index_literal, target_literal);
it->second->add_literals(index_literal);
} else {
// Try to reuse the literal of the index.
context->InsertVarValueEncoding(index_literal, target_ref, value);
}
}
}
context->UpdateRuleStats("element: expanded value element");
ct->Clear();
}
// General element when the array contains non fixed variables.
void ExpandVariableElement(ConstraintProto* ct, PresolveContext* context) {
const ElementConstraintProto& element = ct->element();
const int index_ref = element.index();
const int target_ref = element.target();
const Domain index_domain = context->DomainOf(index_ref);
BoolArgumentProto* exactly_one =
context->working_model->add_constraints()->mutable_exactly_one();
for (const int64_t v : index_domain.Values()) {
const int var = element.vars(v);
const Domain var_domain = context->DomainOf(var);
const int index_lit = context->GetOrCreateVarValueEncoding(index_ref, v);
exactly_one->add_literals(index_lit);
if (var_domain.IsFixed()) {
context->AddImplyInDomain(index_lit, target_ref, var_domain);
} else {
// We make sure we only use positive ref.
//
// TODO(user): Get rid of this code once we accept affine in element
// constraint.
ConstraintProto* const ct = context->working_model->add_constraints();
ct->add_enforcement_literal(index_lit);
if (RefIsPositive(var)) {
ct->mutable_linear()->add_vars(var);
ct->mutable_linear()->add_coeffs(1);
} else {
ct->mutable_linear()->add_vars(NegatedRef(var));
ct->mutable_linear()->add_coeffs(-1);
}
if (RefIsPositive(target_ref)) {
ct->mutable_linear()->add_vars(target_ref);
ct->mutable_linear()->add_coeffs(-1);
} else {
ct->mutable_linear()->add_vars(NegatedRef(target_ref));
ct->mutable_linear()->add_coeffs(1);
}
ct->mutable_linear()->add_domain(0);
ct->mutable_linear()->add_domain(0);
// Note that this should have been checked at model validation.
DCHECK(!PossibleIntegerOverflow(*context->working_model,
ct->mutable_linear()->vars(),
ct->mutable_linear()->coeffs()))
<< google::protobuf::ShortFormat(*ct);
}
}
context->UpdateRuleStats("element: expanded");
ct->Clear();
}
void ExpandElement(ConstraintProto* ct, PresolveContext* context) {
const ElementConstraintProto& element = ct->element();
const int index_ref = element.index();
const int target_ref = element.target();
const int size = element.vars_size();
// Reduce the domain of the index to be compatible with the array of
// variables. Note that the element constraint is 0 based.
if (!context->IntersectDomainWith(index_ref, Domain(0, size - 1))) {
VLOG(1) << "Empty domain for the index variable in ExpandElement()";
return;
}
// Special case when index = target.
if (index_ref == target_ref) {
ExpandElementWithTargetEqualIndex(ct, context);
return;
}
// Reduces the domain of the index and the target.
bool all_constants = true;
std::vector<int64_t> valid_indices;
const Domain index_domain = context->DomainOf(index_ref);
const Domain target_domain = context->DomainOf(target_ref);
Domain reached_domain;
for (const int64_t v : index_domain.Values()) {
const Domain var_domain = context->DomainOf(element.vars(v));
if (var_domain.IntersectionWith(target_domain).IsEmpty()) continue;
valid_indices.push_back(v);
reached_domain = reached_domain.UnionWith(var_domain);
if (var_domain.Min() != var_domain.Max()) {
all_constants = false;
}
}
if (valid_indices.size() < index_domain.Size()) {
if (!context->IntersectDomainWith(index_ref,
Domain::FromValues(valid_indices))) {
VLOG(1) << "No compatible variable domains in ExpandElement()";
return;
}
context->UpdateRuleStats("element: reduced index domain");
}
// We know the target_domain is not empty as this would have triggered the
// above check.
bool target_domain_changed = false;
if (!context->IntersectDomainWith(target_ref, reached_domain,
&target_domain_changed)) {
return;
}
if (target_domain_changed) {
context->UpdateRuleStats("element: reduced target domain");
}
if (all_constants) {
ExpandConstantArrayElement(ct, context);
return;
}
ExpandVariableElement(ct, context);
}