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ortools-clone/ortools/sat/precedences.cc

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// Copyright 2010-2025 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/precedences.h"
#include <stdint.h>
#include <algorithm>
#include <limits>
#include <string>
#include <tuple>
#include <utility>
#include <variant>
#include <vector>
#include "absl/algorithm/container.h"
#include "absl/container/btree_set.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/log/log.h"
#include "absl/log/vlog_is_on.h"
#include "absl/types/span.h"
#include "ortools/base/logging.h"
#include "ortools/base/mathutil.h"
#include "ortools/base/strong_vector.h"
#include "ortools/graph/topologicalsorter.h"
#include "ortools/sat/clause.h"
#include "ortools/sat/cp_constraints.h"
#include "ortools/sat/implied_bounds.h"
#include "ortools/sat/integer.h"
#include "ortools/sat/integer_base.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_base.h"
#include "ortools/sat/sat_solver.h"
#include "ortools/sat/synchronization.h"
#include "ortools/sat/util.h"
#include "ortools/util/logging.h"
#include "ortools/util/strong_integers.h"
#include "ortools/util/time_limit.h"
namespace operations_research {
namespace sat {
LinearExpression2Index Linear2Indices::AddOrGet(
LinearExpression2 original_expr) {
LinearExpression2 expr = original_expr;
DCHECK(expr.IsCanonicalized());
DCHECK_EQ(expr.DivideByGcd(), 1);
DCHECK_NE(expr.coeffs[0], 0);
DCHECK_NE(expr.coeffs[1], 0);
const bool negated = expr.NegateForCanonicalization();
auto [it, inserted] = expr_to_index_.insert({expr, exprs_.size()});
if (inserted) {
CHECK_LT(2 * exprs_.size() + 1,
std::numeric_limits<LinearExpression2Index>::max());
exprs_.push_back(expr);
}
const LinearExpression2Index result =
negated ? NegationOf(LinearExpression2Index(2 * it->second))
: LinearExpression2Index(2 * it->second);
if (!inserted) return result;
// Update our per-variable and per-pair lookup tables.
IntegerVariable var1 = PositiveVariable(expr.vars[0]);
IntegerVariable var2 = PositiveVariable(expr.vars[1]);
if (var1 > var2) std::swap(var1, var2);
var_pair_to_bounds_[{var1, var2}].push_back(result);
var_to_bounds_[var1].push_back(result);
var_to_bounds_[var2].push_back(result);
return result;
}
void Linear2Watcher::NotifyBoundChanged(LinearExpression2 expr) {
DCHECK(expr.IsCanonicalized());
DCHECK_EQ(expr.DivideByGcd(), 1);
++timestamp_;
for (const int id : propagator_ids_) {
watcher_->CallOnNextPropagate(id);
}
for (IntegerVariable var : expr.non_zero_vars()) {
var = PositiveVariable(var); // TODO(user): Be more precise?
if (var >= var_timestamp_.size()) {
var_timestamp_.resize(var + 1, 0);
}
var_timestamp_[var]++;
}
}
int64_t Linear2Watcher::VarTimestamp(IntegerVariable var) {
var = PositiveVariable(var);
return var < var_timestamp_.size() ? var_timestamp_[var] : 0;
}
bool RootLevelLinear2Bounds::AddUpperBound(LinearExpression2Index index,
IntegerValue ub) {
const LinearExpression2 expr = lin2_indices_->GetExpression(index);
const IntegerValue zero_level_ub = integer_trail_->LevelZeroUpperBound(expr);
if (ub >= zero_level_ub) {
return false;
}
if (best_upper_bounds_.size() <= index) {
best_upper_bounds_.resize(index.value() + 1, kMaxIntegerValue);
}
if (ub >= best_upper_bounds_[index]) {
return false;
}
best_upper_bounds_[index] = ub;
++num_updates_;
linear2_watcher_->NotifyBoundChanged(expr);
// Simple relations.
//
// TODO(user): Remove them each time we go back to level zero and they become
// trivially true ?
if (IntTypeAbs(expr.coeffs[0]) == 1 && IntTypeAbs(expr.coeffs[1]) == 1) {
if (index >= in_coeff_one_lookup_.size()) {
in_coeff_one_lookup_.resize(index + 1, false);
}
if (!in_coeff_one_lookup_[index]) {
const IntegerVariable a =
expr.coeffs[0] > 0 ? expr.vars[0] : NegationOf(expr.vars[0]);
const IntegerVariable b =
expr.coeffs[1] > 0 ? expr.vars[1] : NegationOf(expr.vars[1]);
coeff_one_var_lookup_.resize(integer_trail_->NumIntegerVariables());
in_coeff_one_lookup_[index] = true;
coeff_one_var_lookup_[a].push_back({b, index});
coeff_one_var_lookup_[b].push_back({a, index});
}
}
// Share.
//
// TODO(user): It seems we could change the canonicalization to only use
// positive variable? that would simplify a bit the code here and not make it
// worse elsewhere?
if (shared_linear2_bounds_ != nullptr) {
const IntegerValue lb = -LevelZeroUpperBound(NegationOf(index));
const int proto_var0 =
cp_model_mapping_->GetProtoVariableFromIntegerVariable(
PositiveVariable(expr.vars[0]));
const int proto_var1 =
cp_model_mapping_->GetProtoVariableFromIntegerVariable(
PositiveVariable(expr.vars[1]));
if (proto_var0 >= 0 && proto_var1 >= 0) {
// This is also a relation between cp_model proto variable. Share it!
// Note that since expr is canonicalized, this one should too.
SharedLinear2Bounds::Key key;
key.vars[0] = proto_var0;
key.coeffs[0] =
VariableIsPositive(expr.vars[0]) ? expr.coeffs[0] : -expr.coeffs[0];
key.vars[1] = proto_var1;
key.coeffs[1] =
VariableIsPositive(expr.vars[1]) ? expr.coeffs[1] : -expr.coeffs[1];
shared_linear2_bounds_->Add(shared_linear2_bounds_id_, key, lb, ub);
}
}
return true;
}
// TODO(user): If we add an indexing for "coeff * var" this is kind of
// easy to generalize to affine relations, not just "simple one".
int RootLevelLinear2Bounds::AugmentSimpleRelations(IntegerVariable var,
int work_limit) {
var = PositiveVariable(var);
if (var >= coeff_one_var_lookup_.size()) return 0;
if (NegationOf(var) >= coeff_one_var_lookup_.size()) return 0;
// Note that this never touches in_coeff_one_lookup_[var/NegationOf(var)],
// so it should be safe to iterate on it.
int work_done = 0;
for (const auto [a, a_index] : coeff_one_var_lookup_[var]) {
CHECK_NE(PositiveVariable(a), var);
const IntegerValue a_ub = best_upper_bounds_[a_index];
for (const auto [b, b_index] : coeff_one_var_lookup_[NegationOf(var)]) {
if (PositiveVariable(b) == PositiveVariable(a)) continue;
CHECK_NE(PositiveVariable(b), var);
if (++work_done > work_limit) return work_done;
const LinearExpression2 candidate{a, b, 1, 1};
AddUpperBound(candidate, a_ub + best_upper_bounds_[b_index]);
}
}
return work_done;
}
RootLevelLinear2Bounds::~RootLevelLinear2Bounds() {
if (!VLOG_IS_ON(1)) return;
std::vector<std::pair<std::string, int64_t>> stats;
stats.push_back({"RootLevelLinear2Bounds/num_updates", num_updates_});
shared_stats_->AddStats(stats);
}
RelationStatus RootLevelLinear2Bounds::GetLevelZeroStatus(
LinearExpression2 expr, IntegerValue lb, IntegerValue ub) const {
IntegerValue known_ub = integer_trail_->LevelZeroUpperBound(expr);
IntegerValue known_lb = integer_trail_->LevelZeroLowerBound(expr);
if (lb <= known_lb && ub >= known_ub) return RelationStatus::IS_TRUE;
if (lb > known_ub || ub < known_lb) return RelationStatus::IS_FALSE;
expr.SimpleCanonicalization();
if (expr.coeffs[0] == 0) {
return RelationStatus::IS_UNKNOWN;
}
DCHECK_NE(expr.coeffs[1], 0);
const IntegerValue gcd = expr.DivideByGcd();
ub = FloorRatio(ub, gcd);
const LinearExpression2Index index = lin2_indices_->GetIndex(expr);
if (index == kNoLinearExpression2Index) {
return RelationStatus::IS_UNKNOWN;
}
known_ub = std::min(known_ub, GetUpperBoundNoTrail(index));
known_lb = std::max(known_lb, -GetUpperBoundNoTrail(NegationOf(index)));
if (lb <= known_lb && ub >= known_ub) return RelationStatus::IS_TRUE;
if (lb > known_ub || ub < known_lb) return RelationStatus::IS_FALSE;
return RelationStatus::IS_UNKNOWN;
}
IntegerValue RootLevelLinear2Bounds::GetUpperBoundNoTrail(
LinearExpression2Index index) const {
if (best_upper_bounds_.size() <= index) {
return kMaxIntegerValue;
}
return best_upper_bounds_[index];
}
std::vector<std::pair<LinearExpression2, IntegerValue>>
RootLevelLinear2Bounds::GetSortedNonTrivialUpperBounds() const {
std::vector<std::pair<LinearExpression2, IntegerValue>> result;
for (LinearExpression2Index index = LinearExpression2Index{0};
index < best_upper_bounds_.size(); ++index) {
const IntegerValue ub = best_upper_bounds_[index];
if (ub == kMaxIntegerValue) continue;
const LinearExpression2 expr = lin2_indices_->GetExpression(index);
if (ub < integer_trail_->LevelZeroUpperBound(expr)) {
result.push_back({expr, ub});
}
}
std::sort(result.begin(), result.end());
return result;
}
std::vector<std::tuple<LinearExpression2, IntegerValue, IntegerValue>>
RootLevelLinear2Bounds::GetAllBoundsContainingVariable(
IntegerVariable var) const {
std::vector<std::tuple<LinearExpression2, IntegerValue, IntegerValue>> result;
for (const LinearExpression2Index index :
lin2_indices_->GetAllLinear2ContainingVariable(var)) {
const IntegerValue lb = -GetUpperBoundNoTrail(NegationOf(index));
const IntegerValue ub = GetUpperBoundNoTrail(index);
const LinearExpression2 expr = lin2_indices_->GetExpression(index);
const IntegerValue trail_lb = integer_trail_->LevelZeroLowerBound(expr);
const IntegerValue trail_ub = integer_trail_->LevelZeroUpperBound(expr);
if (lb <= trail_lb && ub >= trail_ub) continue;
LinearExpression2 explicit_vars_expr = expr;
if (explicit_vars_expr.vars[0] == NegationOf(var)) {
explicit_vars_expr.vars[0] = NegationOf(explicit_vars_expr.vars[0]);
explicit_vars_expr.coeffs[0] = -explicit_vars_expr.coeffs[0];
}
if (explicit_vars_expr.vars[1] == NegationOf(var)) {
explicit_vars_expr.vars[1] = NegationOf(explicit_vars_expr.vars[1]);
explicit_vars_expr.coeffs[1] = -explicit_vars_expr.coeffs[1];
}
if (explicit_vars_expr.vars[1] == var) {
std::swap(explicit_vars_expr.vars[0], explicit_vars_expr.vars[1]);
std::swap(explicit_vars_expr.coeffs[0], explicit_vars_expr.coeffs[1]);
}
DCHECK(explicit_vars_expr.vars[0] == var);
result.push_back(
{explicit_vars_expr, std::max(lb, trail_lb), std::min(ub, trail_ub)});
}
return result;
}
// Return a list of (lb <= expr <= ub), with expr.vars = {var1, var2}, where
// at least one of the bounds is non-trivial and the potential other
// non-trivial bound is tight.
std::vector<std::tuple<LinearExpression2, IntegerValue, IntegerValue>>
RootLevelLinear2Bounds::GetAllBoundsContainingVariables(
IntegerVariable var1, IntegerVariable var2) const {
std::vector<std::tuple<LinearExpression2, IntegerValue, IntegerValue>> result;
for (const LinearExpression2Index index :
lin2_indices_->GetAllLinear2ContainingVariables(var1, var2)) {
const IntegerValue lb = -GetUpperBoundNoTrail(NegationOf(index));
const IntegerValue ub = GetUpperBoundNoTrail(index);
const LinearExpression2 expr = lin2_indices_->GetExpression(index);
const IntegerValue trail_lb = integer_trail_->LevelZeroLowerBound(expr);
const IntegerValue trail_ub = integer_trail_->LevelZeroUpperBound(expr);
if (lb <= trail_lb && ub >= trail_ub) continue;
LinearExpression2 explicit_vars_expr = expr;
if (explicit_vars_expr.vars[0] == NegationOf(var1) ||
explicit_vars_expr.vars[0] == NegationOf(var2)) {
explicit_vars_expr.vars[0] = NegationOf(explicit_vars_expr.vars[0]);
explicit_vars_expr.coeffs[0] = -explicit_vars_expr.coeffs[0];
}
if (explicit_vars_expr.vars[1] == NegationOf(var1) ||
explicit_vars_expr.vars[1] == NegationOf(var2)) {
explicit_vars_expr.vars[1] = NegationOf(explicit_vars_expr.vars[1]);
explicit_vars_expr.coeffs[1] = -explicit_vars_expr.coeffs[1];
}
if (explicit_vars_expr.vars[1] == var1) {
std::swap(explicit_vars_expr.vars[0], explicit_vars_expr.vars[1]);
std::swap(explicit_vars_expr.coeffs[0], explicit_vars_expr.coeffs[1]);
}
DCHECK(explicit_vars_expr.vars[0] == var1 &&
explicit_vars_expr.vars[1] == var2);
result.push_back(
{explicit_vars_expr, std::max(lb, trail_lb), std::min(ub, trail_ub)});
}
return result;
}
absl::Span<const std::pair<IntegerVariable, LinearExpression2Index>>
RootLevelLinear2Bounds::GetVariablesInSimpleRelation(
IntegerVariable var) const {
if (var >= coeff_one_var_lookup_.size()) return {};
return coeff_one_var_lookup_[var];
}
EnforcedLinear2Bounds::~EnforcedLinear2Bounds() {
if (!VLOG_IS_ON(1)) return;
std::vector<std::pair<std::string, int64_t>> stats;
stats.push_back({"EnforcedLinear2Bounds/num_conditional_relation_updates",
num_conditional_relation_updates_});
shared_stats_->AddStats(stats);
}
void EnforcedLinear2Bounds::PushConditionalRelation(
absl::Span<const Literal> enforcements, LinearExpression2Index lin2_index,
IntegerValue rhs) {
DCHECK_EQ(trail_->CurrentDecisionLevel(), stored_level_);
// This must be currently true.
if (DEBUG_MODE) {
for (const Literal l : enforcements) {
CHECK(trail_->Assignment().LiteralIsTrue(l));
}
}
if (enforcements.empty() || trail_->CurrentDecisionLevel() == 0) {
root_level_bounds_->AddUpperBound(lin2_index, rhs);
return;
}
if (rhs >= root_level_bounds_->LevelZeroUpperBound(lin2_index)) return;
const LinearExpression2 expr = lin2_indices_->GetExpression(lin2_index);
linear2_watcher_->NotifyBoundChanged(expr);
++num_conditional_relation_updates_;
const int new_index = conditional_stack_.size();
if (conditional_relations_.size() <= lin2_index) {
conditional_relations_.resize(lin2_index.value() + 1, -1);
}
if (conditional_relations_[lin2_index] == -1) {
conditional_relations_[lin2_index] = new_index;
CreateLevelEntryIfNeeded();
conditional_stack_.emplace_back(/*prev_entry=*/-1, rhs, lin2_index,
enforcements);
if (expr.coeffs[0] == 1 && expr.coeffs[1] == 1) {
const int new_size =
std::max(expr.vars[0].value(), expr.vars[1].value()) + 1;
if (new_size > conditional_var_lookup_.size()) {
conditional_var_lookup_.resize(new_size);
}
conditional_var_lookup_[expr.vars[0]].push_back(
{expr.vars[1], lin2_index});
conditional_var_lookup_[expr.vars[1]].push_back(
{expr.vars[0], lin2_index});
}
} else {
const int prev_entry = conditional_relations_[lin2_index];
if (rhs >= conditional_stack_[prev_entry].rhs) return;
// Update.
conditional_relations_[lin2_index] = new_index;
CreateLevelEntryIfNeeded();
conditional_stack_.emplace_back(prev_entry, rhs, lin2_index, enforcements);
}
}
void EnforcedLinear2Bounds::CreateLevelEntryIfNeeded() {
const int current = trail_->CurrentDecisionLevel();
if (!level_to_stack_size_.empty() &&
level_to_stack_size_.back().first == current)
return;
level_to_stack_size_.push_back({current, conditional_stack_.size()});
}
// We only pop what is needed.
void EnforcedLinear2Bounds::SetLevel(int level) {
stored_level_ = level;
while (!level_to_stack_size_.empty() &&
level_to_stack_size_.back().first > level) {
const int target = level_to_stack_size_.back().second;
DCHECK_GE(conditional_stack_.size(), target);
while (conditional_stack_.size() > target) {
const ConditionalEntry& back = conditional_stack_.back();
if (back.prev_entry != -1) {
conditional_relations_[back.key] = back.prev_entry;
} else {
conditional_relations_[back.key] = -1;
const LinearExpression2 expr = lin2_indices_->GetExpression(back.key);
if (expr.coeffs[0] == 1 && expr.coeffs[1] == 1) {
DCHECK_EQ(conditional_var_lookup_[expr.vars[0]].back().first,
expr.vars[1]);
DCHECK_EQ(conditional_var_lookup_[expr.vars[1]].back().first,
expr.vars[0]);
conditional_var_lookup_[expr.vars[0]].pop_back();
conditional_var_lookup_[expr.vars[1]].pop_back();
}
}
conditional_stack_.pop_back();
}
level_to_stack_size_.pop_back();
}
}
void EnforcedLinear2Bounds::AddReasonForUpperBoundLowerThan(
LinearExpression2Index index, IntegerValue ub,
std::vector<Literal>* literal_reason,
std::vector<IntegerLiteral>* /*unused*/) const {
DCHECK_EQ(trail_->CurrentDecisionLevel(), stored_level_);
if (ub >= root_level_bounds_->LevelZeroUpperBound(index)) return;
DCHECK_LT(index, conditional_relations_.size());
const int entry_index = conditional_relations_[index];
DCHECK_NE(entry_index, -1);
const ConditionalEntry& entry = conditional_stack_[entry_index];
if (DEBUG_MODE) {
for (const Literal l : entry.enforcements) {
CHECK(trail_->Assignment().LiteralIsTrue(l));
}
}
DCHECK_LE(entry.rhs, ub);
for (const Literal l : entry.enforcements) {
literal_reason->push_back(l.Negated());
}
}
IntegerValue EnforcedLinear2Bounds::GetUpperBoundFromEnforced(
LinearExpression2Index index) const {
DCHECK_EQ(trail_->CurrentDecisionLevel(), stored_level_);
if (index >= conditional_relations_.size()) {
return kMaxIntegerValue;
}
const int entry_index = conditional_relations_[index];
if (entry_index == -1) {
return kMaxIntegerValue;
} else {
const ConditionalEntry& entry = conditional_stack_[entry_index];
if (DEBUG_MODE) {
for (const Literal l : entry.enforcements) {
CHECK(trail_->Assignment().LiteralIsTrue(l));
}
}
// Note(user): We used to check
// entry.rhs <= root_level_bounds_->LevelZeroUpperBound(index));
// But that assumed level zero bounds where only added at level zero, if we
// add them at an higher level, some of the enforced relations here might be
// worse than the fixed one we have. This is not a big deal, as we will not
// add then again on bactrack, and we should use the level-zero reason in
// that case.
return entry.rhs;
}
}
bool TransitivePrecedencesEvaluator::Build() {
const int64_t in_timestamp = root_level_bounds_->num_updates();
if (in_timestamp <= build_timestamp_) return true;
build_timestamp_ = in_timestamp;
const std::vector<std::pair<LinearExpression2, IntegerValue>>
root_relations_sorted =
root_level_bounds_->GetSortedNonTrivialUpperBounds();
int max_node = 0;
for (const auto [expr, _] : root_relations_sorted) {
max_node = std::max(max_node, PositiveVariable(expr.vars[0]).value());
max_node = std::max(max_node, PositiveVariable(expr.vars[1]).value());
}
max_node++; // For negation.
// Is it a DAG?
// Get a topological order of the DAG formed by all the arcs that are present.
//
// TODO(user): This can fail if we don't have a DAG. But in the end we
// don't really need a topological order, just something that is close to
// one so that we can compute an approximated transitive closure in O(n^2) and
// not O(n^3). We could use an heuristic instead, like as long as there is
// node with an in-degree of zero, add them to the order and update the
// in-degree of the other (by removing outgoing arcs). If there is a cycle
// (i.e. no node with no incoming arc), pick one with a small in-degree
// randomly.
DenseIntStableTopologicalSorter sorter(max_node);
for (const auto [expr, negated_offset] : root_relations_sorted) {
// Coefficients should be positive.
DCHECK_GT(expr.coeffs[0], 0);
DCHECK_GT(expr.coeffs[1], 0);
// TODO(user): Support negative offset?
//
// Note that if we only have >= 0 ones, if we do have a cycle, we could
// make sure all variables are the same, and otherwise, we have a DAG or a
// conflict.
const IntegerValue offset = -negated_offset;
if (offset < 0) continue;
if (expr.coeffs[0] != 1 || expr.coeffs[1] != 1) {
// TODO(user): Support non-1 coefficients.
continue;
}
// We have two arcs.
sorter.AddEdge(expr.vars[0].value(), NegationOf(expr.vars[1]).value());
sorter.AddEdge(expr.vars[1].value(), NegationOf(expr.vars[0]).value());
}
int next;
bool graph_has_cycle = false;
topological_order_.clear();
while (sorter.GetNext(&next, &graph_has_cycle, nullptr)) {
topological_order_.push_back(IntegerVariable(next));
if (graph_has_cycle) {
is_dag_ = false;
return true;
}
}
is_dag_ = !graph_has_cycle;
// Lets get the transitive closure if it is cheap. This is also a way not to
// add too many relations per call.
int total_work = 0;
const int kWorkLimit = params_->transitive_precedences_work_limit();
if (kWorkLimit > 0) {
for (const IntegerVariable var : topological_order_) {
const int work = root_level_bounds_->AugmentSimpleRelations(
var, kWorkLimit - total_work);
total_work += work;
if (total_work >= kWorkLimit) break;
}
}
build_timestamp_ = root_level_bounds_->num_updates();
VLOG(2) << "Full precedences. Work=" << total_work
<< " Relations=" << root_relations_sorted.size()
<< " num_added=" << build_timestamp_ - in_timestamp;
return true;
}
// TODO(user): There is probably little need for that function. For small
// problem, we already augment root_level_bounds_ will all the relation obtained
// by transitive closure, so this algo only need to look at direct dependency in
// root_level_bounds_->GetVariablesInSimpleRelation(). And for large graph, we
// probably do not want this.
void TransitivePrecedencesEvaluator::ComputeFullPrecedences(
absl::Span<const IntegerVariable> vars,
std::vector<FullIntegerPrecedence>* output) {
output->clear();
Build(); // Will do nothing if we are up to date.
if (!is_dag_) return;
// Compute all precedences.
// We loop over the node in topological order, and we maintain for all
// variable we encounter, the list of "to_consider" variables that are before.
//
// TODO(user): use vector of fixed size.
absl::flat_hash_set<IntegerVariable> is_interesting;
absl::flat_hash_set<IntegerVariable> to_consider(vars.begin(), vars.end());
absl::flat_hash_map<IntegerVariable,
absl::flat_hash_map<IntegerVariable, IntegerValue>>
vars_before_with_offset;
absl::flat_hash_map<IntegerVariable, IntegerValue> tail_map;
for (const IntegerVariable tail_var : topological_order_) {
if (!to_consider.contains(tail_var) &&
!vars_before_with_offset.contains(tail_var)) {
continue;
}
// We copy the data for tail_var here, because the pointer is not stable.
// TODO(user): optimize when needed.
tail_map.clear();
{
const auto it = vars_before_with_offset.find(tail_var);
if (it != vars_before_with_offset.end()) {
tail_map = it->second;
}
}
// We look for tail_var + offset <= head_var.
for (const auto [neg_head_var, index] :
root_level_bounds_->GetVariablesInSimpleRelation(tail_var)) {
const IntegerVariable head_var = NegationOf(neg_head_var);
const IntegerValue arc_offset =
-root_level_bounds_->GetUpperBoundNoTrail(index);
// No need to create an empty entry in this case.
if (tail_map.empty() && !to_consider.contains(tail_var)) continue;
auto& to_update = vars_before_with_offset[head_var];
for (const auto& [var_before, offset] : tail_map) {
if (!to_update.contains(var_before)) {
to_update[var_before] = arc_offset + offset;
} else {
to_update[var_before] =
std::max(arc_offset + offset, to_update[var_before]);
}
}
if (to_consider.contains(tail_var)) {
if (!to_update.contains(tail_var)) {
to_update[tail_var] = arc_offset;
} else {
to_update[tail_var] = std::max(arc_offset, to_update[tail_var]);
}
}
// Small filtering heuristic: if we have (before) < tail, and tail < head,
// we really do not need to list (before, tail) < head. We only need that
// if the list of variable before head contains some variable that are not
// already before tail.
if (to_update.size() > tail_map.size() + 1) {
is_interesting.insert(head_var);
} else {
is_interesting.erase(head_var);
}
}
// Extract the output for tail_var. Because of the topological ordering, the
// data for tail_var is already final now.
//
// TODO(user): Release the memory right away.
if (!is_interesting.contains(tail_var)) continue;
if (tail_map.size() == 1) continue;
FullIntegerPrecedence data;
data.var = tail_var;
IntegerValue min_offset = kMaxIntegerValue;
for (int i = 0; i < vars.size(); ++i) {
const auto offset_it = tail_map.find(vars[i]);
if (offset_it == tail_map.end()) continue;
data.indices.push_back(i);
data.offsets.push_back(offset_it->second);
min_offset = std::min(data.offsets.back(), min_offset);
}
output->push_back(std::move(data));
}
}
void EnforcedLinear2Bounds::CollectPrecedences(
absl::Span<const IntegerVariable> vars,
std::vector<PrecedenceData>* output) {
const int needed_size = integer_trail_->NumIntegerVariables().value();
var_to_degree_.resize(needed_size);
var_to_last_index_.resize(needed_size);
var_with_positive_degree_.resize(needed_size);
tmp_precedences_.clear();
// We first compute the degree/size in order to perform the transposition.
// Note that we also remove duplicates.
int num_relevants = 0;
IntegerVariable* var_with_positive_degree = var_with_positive_degree_.data();
int* var_to_degree = var_to_degree_.data();
int* var_to_last_index = var_to_last_index_.data();
const auto process =
[&](int var_index,
absl::Span<const std::pair<IntegerVariable, LinearExpression2Index>>
v) {
for (const auto [other, lin2_index] : v) {
const IntegerVariable after = NegationOf(other);
DCHECK_LT(after, needed_size);
if (var_to_degree[after.value()] == 0) {
var_with_positive_degree[num_relevants++] = after;
} else {
// We do not want duplicates.
if (var_to_last_index[after.value()] == var_index) continue;
}
tmp_precedences_.push_back({after, var_index, lin2_index});
var_to_degree[after.value()]++;
var_to_last_index[after.value()] = var_index;
}
};
for (int var_index = 0; var_index < vars.size(); ++var_index) {
const IntegerVariable var = vars[var_index];
process(var_index, root_level_bounds_->GetVariablesInSimpleRelation(var));
if (var < conditional_var_lookup_.size()) {
process(var_index, conditional_var_lookup_[var]);
}
}
// Permute tmp_precedences_ into the output to put it in the correct order.
// For that we transform var_to_degree to point to the first position of
// each lbvar in the output vector.
int start = 0;
const absl::Span<const IntegerVariable> relevant_variables =
absl::MakeSpan(var_with_positive_degree, num_relevants);
for (const IntegerVariable var : relevant_variables) {
const int degree = var_to_degree[var.value()];
if (degree > 1) {
var_to_degree[var.value()] = start;
start += degree;
} else {
// Optimization: we remove degree one relations.
var_to_degree[var.value()] = -1;
}
}
output->resize(start);
for (const auto& precedence : tmp_precedences_) {
// Note that it is okay to increase the -1 pos since they appear only once.
const int pos = var_to_degree[precedence.var.value()]++;
if (pos < 0) continue;
(*output)[pos] = precedence;
}
// Cleanup var_to_degree, note that we don't need to clean
// var_to_last_index_.
for (const IntegerVariable var : relevant_variables) {
var_to_degree[var.value()] = 0;
}
}
ConditionalLinear2Bounds::~ConditionalLinear2Bounds() {
if (!VLOG_IS_ON(1)) return;
std::vector<std::pair<std::string, int64_t>> stats;
stats.push_back({"ConditionalLinear2Bounds/num_enforced_relations",
num_enforced_relations_});
stats.push_back({"ConditionalLinear2Bounds/num_encoded_equivalences",
num_encoded_equivalences_});
shared_stats_->AddStats(stats);
}
void ConditionalLinear2Bounds::Add(Literal lit, LinearExpression2 expr,
IntegerValue lhs, IntegerValue rhs) {
expr.SimpleCanonicalization();
if (expr.coeffs[0] == 0 || expr.coeffs[1] == 0) return;
expr.CanonicalizeAndUpdateBounds(lhs, rhs);
CHECK_NE(lit.Index(), kNoLiteralIndex);
num_enforced_relations_++;
relations_.push_back(
{.enforcement = lit, .expr = expr, .lhs = lhs, .rhs = rhs});
}
void ConditionalLinear2Bounds::AddPartialRelation(Literal lit,
IntegerVariable a,
IntegerVariable b) {
DCHECK_NE(a, kNoIntegerVariable);
DCHECK_NE(b, kNoIntegerVariable);
DCHECK_NE(a, b);
Add(lit, LinearExpression2(a, b, 1, 1), 0, 0);
}
void ConditionalLinear2Bounds::Build() {
DCHECK(!is_built_);
is_built_ = true;
std::vector<std::pair<LiteralIndex, int>> literal_key_values;
const int num_relations = relations_.size();
literal_key_values.reserve(num_enforced_relations_);
for (int i = 0; i < num_relations; ++i) {
const Relation& r = relations_[i];
literal_key_values.emplace_back(r.enforcement.Index(), i);
}
lit_to_relations_.ResetFromPairs(literal_key_values);
lit_to_relations_.Add({}); // One extra unit size to make sure the negation
// cannot be out of bounds in lit_to_relations_.
// If we have "l => (x <= 6)" and "~l => (x >= 9)" we can push
// "l <=> (x <= 6)" to the repository of fully encoded linear2 bounds.
// More generally, if we have:
//
// l => (expr <= a)
// ~l => (expr >= b)
//
// And if moreover a < b, we have the following truth table:
//
// l | expr <= a | a < expr < b | expr >= b
// --+-----------+---------------+----------
// 0 | false | false | true (from "~l => (expr >= b)")
// 1 | true | false | false (from "l => (expr <= a)")
//
// So we can generalize the expressions to equivalences:
// l <=> (expr <= a)
// ~l <=> (expr >= b)
// (a < expr < b) is impossible
absl::flat_hash_map<LinearExpression2, IntegerValue> lin2_to_upper_bound;
for (LiteralIndex lit_index{0}; lit_index < lit_to_relations_.size() - 1;
++lit_index) {
const Literal lit(lit_index);
lin2_to_upper_bound.clear();
const absl::Span<const int> relations = lit_to_relations_[lit_index];
const absl::Span<const int> relations_negation =
lit_to_relations_[lit.NegatedIndex()];
if (relations.empty() || relations_negation.empty()) continue;
for (const int relation_index : relations) {
const Relation& r = relations_[relation_index];
DCHECK(r.expr.IsCanonicalized());
LinearExpression2 expr = r.expr;
{
const auto [it, inserted] = lin2_to_upper_bound.insert({expr, r.rhs});
if (!inserted) {
it->second = std::min(it->second, r.rhs);
}
}
{
expr.Negate();
const auto [it, inserted] = lin2_to_upper_bound.insert({expr, -r.lhs});
if (!inserted) {
it->second = std::min(it->second, -r.lhs);
}
}
}
for (const int relation_index : relations_negation) {
const Relation& r = relations_[relation_index];
DCHECK(r.expr.IsCanonicalized());
// Let's work with lower bounds only.
const IntegerValue lower_bounds[2] = {r.lhs, -r.rhs};
LinearExpression2 exprs[2] = {r.expr, r.expr};
exprs[1].Negate();
for (int i = 0; i < 2; ++i) {
// We have here "~l => (exprs[i] >= lower_bounds[i])".
const auto it = lin2_to_upper_bound.find(exprs[i]);
if (it != lin2_to_upper_bound.end()) {
const IntegerValue ub = it->second;
// Here we have "l => expr <= ub".
if (ub >= lower_bounds[i]) {
// Don't obey the "a < b" condition
continue;
}
num_encoded_equivalences_++;
// Make both relationships two-way.
reified_linear2_bounds_->AddBoundEncodingIfNonTrivial(lit, exprs[i],
ub);
LinearExpression2 expr = exprs[i];
expr.Negate();
reified_linear2_bounds_->AddBoundEncodingIfNonTrivial(
lit.Negated(), expr, -lower_bounds[i]);
}
}
}
}
}
bool PropagateLocalBounds(
const IntegerTrail& integer_trail,
const RootLevelLinear2Bounds& root_level_bounds,
const ConditionalLinear2Bounds& repository,
const ImpliedBounds& implied_bounds, Literal lit,
const absl::flat_hash_map<IntegerVariable, IntegerValue>& input,
absl::flat_hash_map<IntegerVariable, IntegerValue>* output) {
DCHECK_NE(lit.Index(), kNoLiteralIndex);
auto get_lower_bound = [&](IntegerVariable var) {
const auto it = input.find(var);
if (it != input.end()) return it->second;
return integer_trail.LevelZeroLowerBound(var);
};
auto get_upper_bound = [&](IntegerVariable var) {
return -get_lower_bound(NegationOf(var));
};
auto update_lower_bound_by_var = [&](IntegerVariable var, IntegerValue lb) {
if (lb <= integer_trail.LevelZeroLowerBound(var)) return;
const auto [it, inserted] = output->insert({var, lb});
if (!inserted) {
it->second = std::max(it->second, lb);
}
};
auto update_upper_bound_by_var = [&](IntegerVariable var, IntegerValue ub) {
update_lower_bound_by_var(NegationOf(var), -ub);
};
auto update_var_bounds = [&](const LinearExpression2& expr, IntegerValue lhs,
IntegerValue rhs) {
if (expr.coeffs[0] == 0) return;
// lb(b.y) <= b.y <= ub(b.y) and lhs <= a.x + b.y <= rhs imply
// ceil((lhs - ub(b.y)) / a) <= x <= floor((rhs - lb(b.y)) / a)
if (expr.coeffs[1] != 0) {
lhs = lhs - expr.coeffs[1] * get_upper_bound(expr.vars[1]);
rhs = rhs - expr.coeffs[1] * get_lower_bound(expr.vars[1]);
}
update_lower_bound_by_var(expr.vars[0],
MathUtil::CeilOfRatio(lhs, expr.coeffs[0]));
update_upper_bound_by_var(expr.vars[0],
MathUtil::FloorOfRatio(rhs, expr.coeffs[0]));
};
auto update_var_bounds_from_relation = [&](Relation r) {
DCHECK(r.expr.IsCanonicalized());
update_var_bounds(r.expr, r.lhs, r.rhs);
std::swap(r.expr.vars[0], r.expr.vars[1]);
std::swap(r.expr.coeffs[0], r.expr.coeffs[1]);
update_var_bounds(r.expr, r.lhs, r.rhs);
};
for (const int relation_index :
repository.IndicesOfRelationsEnforcedBy(lit)) {
const Relation& r = repository.relation(relation_index);
if (r.expr.coeffs[0] == 0) continue;
update_var_bounds_from_relation(r);
}
for (const auto& [var, unused] : input) {
for (const auto& [expr, lb, ub] :
root_level_bounds.GetAllBoundsContainingVariable(var)) {
// Note: GetAllBoundsContainingVariable() does not return canonicalized
// expr on purpose.
Relation r{Literal(kNoLiteralIndex), expr, lb, ub};
r.expr.SimpleCanonicalization();
update_var_bounds_from_relation(r);
}
const auto [lb, ub] = implied_bounds.GetImpliedBounds(lit, var);
update_var_bounds_from_relation(Relation{
lit, LinearExpression2(kNoIntegerVariable, var, 0, 1), lb, ub});
}
// Check feasibility.
// TODO(user): we might do that earlier?
for (const auto [var, lb] : *output) {
if (lb > integer_trail.LevelZeroUpperBound(var)) return false;
}
return true;
}
void GreaterThanAtLeastOneOfDetector::AddRelationIfNonTrivial(
const Relation& r,
std::vector<VariableConditionalAffineBound>* clause_bounds) const {
const Literal l = r.enforcement;
auto add_if_non_trivial = [&](Literal cond, IntegerVariable var,
AffineExpression expr) {
if (integer_trail_.LevelZeroLowerBound(var) <
integer_trail_.LevelZeroUpperBound(expr)) {
clause_bounds->push_back({cond, var, expr});
}
};
DCHECK_NE(r.expr.vars[0], kNoIntegerVariable);
DCHECK_NE(r.expr.vars[1], kNoIntegerVariable);
if (r.lhs != kMinIntegerValue) {
for (int i = 0; i < 2; ++i) {
const AffineExpression affine_lb = r.expr.GetAffineLowerBound(
i, r.lhs, integer_trail_.LevelZeroLowerBound(r.expr.vars[1 - i]));
add_if_non_trivial(l, r.expr.vars[i], affine_lb);
}
}
if (r.rhs != kMaxIntegerValue) {
LinearExpression2 negated_expr(r.expr);
negated_expr.Negate();
for (int i = 0; i < 2; ++i) {
const AffineExpression affine_lb = negated_expr.GetAffineLowerBound(
i, -r.rhs,
integer_trail_.LevelZeroLowerBound(negated_expr.vars[1 - i]));
add_if_non_trivial(l, negated_expr.vars[i], affine_lb);
}
}
}
bool GreaterThanAtLeastOneOfDetector::AddRelationFromBounds(
IntegerVariable var, absl::Span<const Literal> clause,
absl::Span<const VariableConditionalAffineBound> bounds, Model* model) {
std::vector<AffineExpression> exprs;
std::vector<Literal> selectors;
absl::flat_hash_set<LiteralIndex> used;
for (const VariableConditionalAffineBound& bound : bounds) {
DCHECK_EQ(bound.var, var);
// Note that duplicate selector are supported.
selectors.push_back(bound.enforcement_literal);
used.insert(bound.enforcement_literal);
exprs.push_back(bound.bound);
}
// The enforcement of the new constraint are simply the literal not used
// above.
std::vector<Literal> enforcements;
for (const Literal l : clause) {
if (!used.contains(l.Index())) {
enforcements.push_back(l.Negated());
}
}
// No point adding a constraint if there is not at least two different
// literals in selectors.
if (used.size() <= 1) return false;
total_num_expressions_ += exprs.size();
++num_detected_constraints_;
maximum_num_expressions_ =
std::max(maximum_num_expressions_, static_cast<int64_t>(exprs.size()));
// Add the constraint.
GreaterThanAtLeastOneOfPropagator* constraint =
new GreaterThanAtLeastOneOfPropagator(var, exprs, selectors, enforcements,
model);
constraint->RegisterWith(model->GetOrCreate<GenericLiteralWatcher>());
model->TakeOwnership(constraint);
return true;
}
int GreaterThanAtLeastOneOfDetector::
AddGreaterThanAtLeastOneOfConstraintsFromClause(
const absl::Span<const Literal> clause, Model* model,
const CompactVectorVector<LiteralIndex, IntegerLiteral>&
implied_bounds_by_literal) {
CHECK_EQ(model->GetOrCreate<Trail>()->CurrentDecisionLevel(), 0);
if (clause.size() < 2) return 0;
std::vector<VariableConditionalAffineBound> clause_bounds;
// Collect all relations impacted by this clause from conditional linear2.
for (const Literal l : clause) {
for (const int index :
repository_.IndicesOfRelationsEnforcedBy(l.Index())) {
const Relation& r = repository_.relation(index);
AddRelationIfNonTrivial(r, &clause_bounds);
}
for (const IntegerLiteral& i_lit : implied_bounds_by_literal[l.Index()]) {
if (integer_trail_.LevelZeroLowerBound(i_lit.var) < i_lit.bound) {
clause_bounds.push_back({l, i_lit.var, AffineExpression(i_lit.bound)});
}
}
}
if (clause_bounds.size() <= 1) return 0;
// Stable sort to regroup by var.
absl::c_stable_sort(
clause_bounds,
[](const VariableConditionalAffineBound& a,
const VariableConditionalAffineBound& b) { return a.var < b.var; });
// We process the info with same variable together.
int num_added_constraints = 0;
for (int i = 0; i < clause_bounds.size();) {
const int start = i;
const IntegerVariable var = clause_bounds[start].var;
for (; i < clause_bounds.size() && clause_bounds[i].var == var; ++i) {
}
const int end = i;
absl::Span<const VariableConditionalAffineBound> bounds =
absl::MakeSpan(clause_bounds).subspan(start, end - start);
// Skip single relations, we are not interested in these.
if (bounds.size() < 2) continue;
// Heuristic. Look for full or almost full clauses.
//
// TODO(user): We could add GreaterThanAtLeastOneOf() with more enforcement
// literals. Experiment.
if (bounds.size() + 1 < clause.size()) continue;
if (AddRelationFromBounds(var, clause, bounds, model)) {
++num_added_constraints;
}
}
return num_added_constraints;
}
int GreaterThanAtLeastOneOfDetector::
AddGreaterThanAtLeastOneOfConstraintsWithClauseAutoDetection(Model* model) {
auto* time_limit = model->GetOrCreate<TimeLimit>();
auto* solver = model->GetOrCreate<SatSolver>();
// Fill the set of interesting relations for each variables.
std::vector<VariableConditionalAffineBound> clause_bounds;
for (int index = 0; index < repository_.size(); ++index) {
const Relation& r = repository_.relation(index);
if (r.enforcement.Index() == kNoLiteralIndex) continue;
AddRelationIfNonTrivial(r, &clause_bounds);
}
for (const auto& [literal_var_pair, bound] :
implied_bounds_.GetModelImpliedBounds()) {
if (integer_trail_.LevelZeroLowerBound(literal_var_pair.second) < bound) {
clause_bounds.push_back(VariableConditionalAffineBound{
.enforcement_literal = Literal(literal_var_pair.first),
.var = literal_var_pair.second,
.bound = AffineExpression(bound)});
}
}
// Stable sort to regroup by var.
// TODO(user): We should probably also sort by enforcement literal,
// and regroup entry with same variable/enforcement if that happen often to
// have more than one such entry.
absl::c_stable_sort(
clause_bounds,
[](const VariableConditionalAffineBound& a,
const VariableConditionalAffineBound& b) { return a.var < b.var; });
int num_added_constraints = 0;
for (int i = 0; i < clause_bounds.size();) {
const int start = i;
const IntegerVariable var = clause_bounds[start].var;
for (; i < clause_bounds.size() && clause_bounds[i].var == var; ++i) {
}
const int end = i;
absl::Span<const VariableConditionalAffineBound> bounds =
absl::MakeSpan(clause_bounds).subspan(start, end - start);
if (bounds.size() <= 1) continue;
if (time_limit->LimitReached()) return num_added_constraints;
// Detect set of incoming arcs for which at least one must be present.
// TODO(user): Find more than one disjoint set of incoming arcs.
// TODO(user): call MinimizeCoreWithPropagation() on the clause.
solver->Backtrack(0);
if (solver->ModelIsUnsat()) return num_added_constraints;
std::vector<Literal> clause;
for (const VariableConditionalAffineBound& bound : bounds) {
const Literal literal = bound.enforcement_literal;
if (solver->Assignment().LiteralIsFalse(literal)) continue;
const SatSolver::Status status =
solver->EnqueueDecisionAndBacktrackOnConflict(literal.Negated());
if (status == SatSolver::INFEASIBLE) return num_added_constraints;
if (status == SatSolver::ASSUMPTIONS_UNSAT) {
// We need to invert it, since a clause is not all false.
clause = solver->GetLastIncompatibleDecisions();
for (Literal& ref : clause) ref = ref.Negated();
break;
}
}
solver->Backtrack(0);
if (clause.size() <= 1) continue;
// Recover the indices corresponding to this clause.
const absl::btree_set<Literal> clause_set(clause.begin(), clause.end());
std::vector<VariableConditionalAffineBound> for_cur_clause;
for (const VariableConditionalAffineBound& bound : bounds) {
const Literal literal = bound.enforcement_literal;
if (clause_set.contains(literal)) {
for_cur_clause.push_back(bound);
}
}
if (AddRelationFromBounds(bounds[0].var, clause, for_cur_clause, model)) {
++num_added_constraints;
}
}
solver->Backtrack(0);
return num_added_constraints;
}
int GreaterThanAtLeastOneOfDetector::AddGreaterThanAtLeastOneOfConstraints(
Model* model, bool auto_detect_clauses) {
auto* time_limit = model->GetOrCreate<TimeLimit>();
auto* solver = model->GetOrCreate<SatSolver>();
auto* clauses = model->GetOrCreate<ClauseManager>();
auto* logger = model->GetOrCreate<SolverLogger>();
int num_added_constraints = 0;
SOLVER_LOG(logger, "[Precedences] num_relations=", repository_.size(),
" num_clauses=", clauses->AllClausesInCreationOrder().size());
CompactVectorVector<LiteralIndex, IntegerLiteral> implied_bounds_by_literal;
{
const auto& all_implied_bounds = implied_bounds_.GetModelImpliedBounds();
std::vector<LiteralIndex> implied_bounds_conditions;
std::vector<IntegerLiteral> implied_bounds_integer_lit;
implied_bounds_conditions.reserve(all_implied_bounds.size());
implied_bounds_integer_lit.reserve(all_implied_bounds.size());
for (const auto& [literal_var_pair, bound] : all_implied_bounds) {
implied_bounds_conditions.push_back(literal_var_pair.first);
implied_bounds_integer_lit.push_back(
IntegerLiteral::GreaterOrEqual(literal_var_pair.second, bound));
}
implied_bounds_by_literal.ResetFromFlatMapping(
std::move(implied_bounds_conditions),
std::move(implied_bounds_integer_lit), 2 * solver->NumVariables());
}
// We have two possible approaches. For now, we prefer the first one except if
// there is too many clauses in the problem.
//
// TODO(user): Do more extensive experiment. Remove the second approach as
// it is more time consuming? or identify when it make sense. Note that the
// first approach also allows to use "incomplete" at least one between arcs.
if (!auto_detect_clauses &&
clauses->AllClausesInCreationOrder().size() < 1e6) {
// TODO(user): This does not take into account clause of size 2 since they
// are stored in the BinaryImplicationGraph instead. Some ideas specific
// to size 2:
// - There can be a lot of such clauses, but it might be nice to consider
// them. we need to experiments.
// - The automatic clause detection might be a better approach and it
// could be combined with probing.
for (const SatClause* clause : clauses->AllClausesInCreationOrder()) {
if (time_limit->LimitReached()) return num_added_constraints;
if (solver->ModelIsUnsat()) return num_added_constraints;
num_added_constraints += AddGreaterThanAtLeastOneOfConstraintsFromClause(
clause->AsSpan(), model, implied_bounds_by_literal);
}
// It is common that there is only two alternatives to push a variable.
// In this case, our presolve most likely made sure that the two are
// controlled by a single Boolean. This allows to detect this and add the
// appropriate greater than at least one of.
const int num_booleans = solver->NumVariables();
if (num_booleans < 1e6) {
for (int i = 0; i < num_booleans; ++i) {
if (time_limit->LimitReached()) return num_added_constraints;
if (solver->ModelIsUnsat()) return num_added_constraints;
num_added_constraints +=
AddGreaterThanAtLeastOneOfConstraintsFromClause(
{Literal(BooleanVariable(i), true),
Literal(BooleanVariable(i), false)},
model, implied_bounds_by_literal);
}
}
} else {
num_added_constraints +=
AddGreaterThanAtLeastOneOfConstraintsWithClauseAutoDetection(model);
}
if (num_added_constraints > 0) {
SOLVER_LOG(logger, "[Precedences] Added ", num_added_constraints,
" GreaterThanAtLeastOneOf() constraints.");
}
return num_added_constraints;
}
GreaterThanAtLeastOneOfDetector::~GreaterThanAtLeastOneOfDetector() {
if (!VLOG_IS_ON(1)) return;
std::vector<std::pair<std::string, int64_t>> stats;
stats.push_back({"GreaterThanAtLeastOneOfDetector/total_num_expressions",
total_num_expressions_});
stats.push_back({"GreaterThanAtLeastOneOfDetector/maximum_num_expressions",
maximum_num_expressions_});
stats.push_back({"GreaterThanAtLeastOneOfDetector/num_detected_constraints",
num_detected_constraints_});
shared_stats_->AddStats(stats);
}
ReifiedLinear2Bounds::ReifiedLinear2Bounds(Model* model)
: best_root_level_bounds_(model->GetOrCreate<RootLevelLinear2Bounds>()),
lin2_indices_(model->GetOrCreate<Linear2Indices>()),
shared_stats_(model->GetOrCreate<SharedStatistics>()) {
int index = 0;
model->GetOrCreate<LevelZeroCallbackHelper>()->callbacks.push_back(
[index = index, trail = model->GetOrCreate<Trail>(), this]() mutable {
DCHECK_EQ(trail->CurrentDecisionLevel(), 0);
absl::flat_hash_set<Literal> relevant_true_literals;
for (; index < trail->Index(); ++index) {
const Literal l = (*trail)[index];
if (variable_appearing_in_reified_relations_.contains(l.Variable())) {
relevant_true_literals.insert(l);
}
}
if (relevant_true_literals.empty()) return true;
// Linear scan.
for (const auto [l, expr_index, ub] : all_reified_relations_) {
if (relevant_true_literals.contains(l)) {
++num_relations_fixed_at_root_level_;
best_root_level_bounds_->AddUpperBound(expr_index, ub);
VLOG(2) << "New fixed precedence: "
<< lin2_indices_->GetExpression(expr_index) << " <= " << ub
<< " (was reified by " << l << ")";
} else if (relevant_true_literals.contains(l.Negated())) {
++num_relations_fixed_at_root_level_;
best_root_level_bounds_->AddLowerBound(expr_index, ub + 1);
VLOG(2) << "New fixed precedence: "
<< lin2_indices_->GetExpression(expr_index) << " > " << ub
<< " (was reified by not(" << l << "))";
}
}
return true;
});
}
ReifiedLinear2Bounds::~ReifiedLinear2Bounds() {
if (!VLOG_IS_ON(1)) return;
std::vector<std::pair<std::string, int64_t>> stats;
stats.push_back(
{"ReifiedLinear2Bounds/num_linear3_relations", num_linear3_relations_});
stats.push_back(
{"ReifiedLinear2Bounds/num_literal_relations", relation_to_lit_.size()});
stats.push_back({"ReifiedLinear2Bounds/num_relations_fixed_at_root_level",
num_relations_fixed_at_root_level_});
shared_stats_->AddStats(stats);
}
void ReifiedLinear2Bounds::AddBoundEncodingIfNonTrivial(Literal l,
LinearExpression2 expr,
IntegerValue ub) {
DCHECK(expr.IsCanonicalized());
DCHECK_EQ(expr.DivideByGcd(), 1);
const RelationStatus status =
best_root_level_bounds_->GetLevelZeroStatus(expr, kMinIntegerValue, ub);
if (status != RelationStatus::IS_UNKNOWN) return;
if (expr.vars[0] == kNoIntegerVariable) {
// For a single Affine GetEncodedBound() will return the IntegerLiteral
// without needing any indexing.
return;
}
const LinearExpression2Index expr_index = lin2_indices_->AddOrGet(expr);
relation_to_lit_.insert({{expr_index, ub}, l});
variable_appearing_in_reified_relations_.insert(l.Variable());
all_reified_relations_.push_back({l, expr_index, ub});
}
std::variant<ReifiedLinear2Bounds::ReifiedBoundType, Literal, IntegerLiteral>
ReifiedLinear2Bounds::GetEncodedBound(LinearExpression2 expr, IntegerValue ub) {
DCHECK(expr.IsCanonicalized());
DCHECK_EQ(expr.DivideByGcd(), 1);
const RelationStatus status =
best_root_level_bounds_->GetLevelZeroStatus(expr, kMinIntegerValue, ub);
if (status == RelationStatus::IS_TRUE) {
return ReifiedBoundType::kAlwaysTrue;
}
if (status == RelationStatus::IS_FALSE) {
return ReifiedBoundType::kAlwaysFalse;
}
if (expr.vars[0] == kNoIntegerVariable) {
DCHECK_NE(expr.vars[1], kNoIntegerVariable);
DCHECK_EQ(expr.coeffs[1], 1);
return IntegerLiteral::LowerOrEqual(expr.vars[1], ub);
}
const LinearExpression2Index expr_index = lin2_indices_->GetIndex(expr);
if (expr_index == kNoLinearExpression2Index) {
return ReifiedBoundType::kNoLiteralStored;
}
const auto it = relation_to_lit_.find({expr_index, ub});
if (it != relation_to_lit_.end()) return it->second;
if (linear3_bounds_.size() <= expr_index) {
return ReifiedBoundType::kNoLiteralStored;
}
const auto [affine_expr, divisor] = linear3_bounds_[expr_index];
if (divisor == 0) {
return ReifiedBoundType::kNoLiteralStored;
}
const IntegerValue affine_bound = CapProdI(ub, divisor);
if (affine_bound == kMaxIntegerValue) {
return ReifiedBoundType::kNoLiteralStored;
}
return affine_expr.LowerOrEqual(affine_bound);
}
void ReifiedLinear2Bounds::AddLinear3(absl::Span<const IntegerVariable> vars,
absl::Span<const int64_t> coeffs,
int64_t activity) {
DCHECK_EQ(vars.size(), 3);
DCHECK_EQ(coeffs.size(), 3);
for (int i = 0; i < vars.size(); ++i) {
LinearExpression2 expr(vars[i], vars[(i + 1) % 3], coeffs[i],
coeffs[(i + 1) % 3]);
AffineExpression affine_expr(vars[(i + 2) % 3], -coeffs[(i + 2) % 3],
activity);
expr.SimpleCanonicalization();
const IntegerValue gcd = expr.DivideByGcd();
const LinearExpression2Index expr_index = lin2_indices_->AddOrGet(expr);
if (linear3_bounds_.size() <= expr_index) {
linear3_bounds_.resize(expr_index + 1, {AffineExpression(), 0});
}
auto& [old_affine_expr, old_divisor] = linear3_bounds_[expr_index];
if (old_divisor == 0 || old_divisor > gcd) {
linear3_bounds_[expr_index] = {affine_expr, gcd};
if (old_divisor == 0) ++num_linear3_relations_;
}
}
}
std::pair<AffineExpression, IntegerValue> ReifiedLinear2Bounds::GetLinear3Bound(
LinearExpression2Index lin2_index) const {
DCHECK_LT(lin2_index, linear3_bounds_.size());
DCHECK_GT(linear3_bounds_[lin2_index].second, 0);
return linear3_bounds_[lin2_index];
}
Linear2BoundsFromLinear3::Linear2BoundsFromLinear3(Model* model)
: integer_trail_(model->GetOrCreate<IntegerTrail>()),
trail_(model->GetOrCreate<Trail>()),
linear2_watcher_(model->GetOrCreate<Linear2Watcher>()),
watcher_(model->GetOrCreate<GenericLiteralWatcher>()),
shared_stats_(model->GetOrCreate<SharedStatistics>()),
root_level_bounds_(model->GetOrCreate<RootLevelLinear2Bounds>()),
lin2_indices_(model->GetOrCreate<Linear2Indices>()) {}
Linear2BoundsFromLinear3::~Linear2BoundsFromLinear3() {
if (!VLOG_IS_ON(1)) return;
std::vector<std::pair<std::string, int64_t>> stats;
stats.push_back(
{"Linear2BoundsFromLinear3/num_affine_updates", num_affine_updates_});
shared_stats_->AddStats(stats);
}
// Note that for speed we do not compare to the trivial or root level bounds.
//
// It is okay to still store it in the hash-map, since at worst we will have no
// more entries than 3 * number_of_linear3_in_the_problem.
bool Linear2BoundsFromLinear3::AddAffineUpperBound(
LinearExpression2Index lin2_index, IntegerValue lin_expr_gcd,
AffineExpression affine_ub) {
// At level zero, just add it to root_level_bounds_.
if (trail_->CurrentDecisionLevel() == 0 || affine_ub.IsConstant()) {
root_level_bounds_->AddUpperBound(
lin2_index, FloorRatio(integer_trail_->LevelZeroUpperBound(affine_ub),
lin_expr_gcd));
return false; // Not important.
}
// We have gcd * canonical_expr <= affine_ub,
// so we do need to store a "divisor".
if (lin2_index >= best_affine_ub_.size()) {
best_affine_ub_.resize(lin2_index.value() + 1, {AffineExpression(), 0});
}
auto& [old_affine_ub, old_divisor] = best_affine_ub_[lin2_index];
if (old_divisor != 0) {
// We have an affine bound for this expr in the map. Can be exactly the
// same, a better one or a worse one.
//
// Note that we expect exactly the same most of the time as it should be
// rare to have many linear3 "competing" for the same linear2 bound.
if (old_affine_ub == affine_ub && old_divisor == lin_expr_gcd) {
linear2_watcher_->NotifyBoundChanged(
lin2_indices_->GetExpression(lin2_index));
return false;
}
const IntegerValue new_ub =
FloorRatioWithTest(integer_trail_->UpperBound(affine_ub), lin_expr_gcd);
const IntegerValue old_ub = FloorRatioWithTest(
integer_trail_->UpperBound(old_affine_ub), old_divisor);
if (old_ub <= new_ub) return false; // old bound is better.
best_affine_ub_[lin2_index] = {affine_ub, lin_expr_gcd}; // Overwrite.
} else {
// Note that this should almost never happen (only once per lin2).
best_affine_ub_[lin2_index] = {affine_ub, lin_expr_gcd};
}
++num_affine_updates_;
linear2_watcher_->NotifyBoundChanged(
lin2_indices_->GetExpression(lin2_index));
return true;
}
IntegerValue Linear2BoundsFromLinear3::GetUpperBoundFromLinear3(
LinearExpression2Index lin2_index) const {
if (lin2_index >= best_affine_ub_.size()) return kMaxIntegerValue;
auto [affine, divisor] = best_affine_ub_[lin2_index];
if (divisor == 0) return kMaxIntegerValue;
return FloorRatio(integer_trail_->UpperBound(affine), divisor);
}
void Linear2BoundsFromLinear3::AddReasonForUpperBoundLowerThan(
LinearExpression2Index lin2_index, IntegerValue ub,
std::vector<Literal>* /*literal_reason*/,
std::vector<IntegerLiteral>* integer_reason) const {
DCHECK_LE(GetUpperBoundFromLinear3(lin2_index), ub);
DCHECK_LT(lin2_index, best_affine_ub_.size());
// We want the reason for "expr <= ub"
// knowing that expr <= affine / divisor.
const auto [affine, divisor] = best_affine_ub_[lin2_index];
DCHECK_NE(divisor, 0);
integer_reason->push_back(affine.LowerOrEqual(CapProdI(ub + 1, divisor) - 1));
}
Linear2Bounds::~Linear2Bounds() {
if (!VLOG_IS_ON(1)) return;
std::vector<std::pair<std::string, int64_t>> stats;
stats.push_back({"Linear2Bounds/enqueue_trivial", enqueue_trivial_});
stats.push_back({"Linear2Bounds/enqueue_degenerate", enqueue_degenerate_});
stats.push_back({"Linear2Bounds/enqueue_true_at_root_level",
enqueue_true_at_root_level_});
stats.push_back({"Linear2Bounds/enqueue_conflict_false_at_root_level",
enqueue_conflict_false_at_root_level_});
stats.push_back({"Linear2Bounds/enqueue_individual_var_bounds",
enqueue_individual_var_bounds_});
stats.push_back(
{"Linear2Bounds/enqueue_literal_encoding", enqueue_literal_encoding_});
stats.push_back({"Linear2Bounds/enqueue_integer_linear3_encoding",
enqueue_integer_linear3_encoding_});
shared_stats_->AddStats(stats);
}
IntegerValue Linear2Bounds::UpperBound(
LinearExpression2Index lin2_index) const {
return std::min(
NonTrivialUpperBound(lin2_index),
integer_trail_->UpperBound(lin2_indices_->GetExpression(lin2_index)));
}
IntegerValue Linear2Bounds::UpperBound(LinearExpression2 expr) const {
expr.SimpleCanonicalization();
if (expr.coeffs[0] == 0) {
return integer_trail_->UpperBound(expr);
}
DCHECK_NE(expr.coeffs[1], 0);
const IntegerValue gcd = expr.DivideByGcd();
IntegerValue ub = integer_trail_->UpperBound(expr);
// TODO(user): remove this when the UB in the trail in the current level is
// never worse than in the root level.
ub = std::min(ub, integer_trail_->LevelZeroUpperBound(expr));
const LinearExpression2Index index = lin2_indices_->GetIndex(expr);
if (index != kNoLinearExpression2Index) {
ub = std::min(ub, root_level_bounds_->GetUpperBoundNoTrail(index));
ub = std::min(ub, enforced_bounds_->GetUpperBoundFromEnforced(index));
ub = std::min(ub, linear3_bounds_->GetUpperBoundFromLinear3(index));
}
return CapProdI(gcd, ub);
}
void Linear2Bounds::AddReasonForUpperBoundLowerThan(
LinearExpression2 expr, IntegerValue ub,
std::vector<Literal>* literal_reason,
std::vector<IntegerLiteral>* integer_reason) const {
DCHECK_LE(UpperBound(expr), ub);
// Explanation are by order of preference, with no reason needed first.
if (integer_trail_->LevelZeroUpperBound(expr) <= ub) {
return;
}
expr.SimpleCanonicalization();
const IntegerValue gcd = expr.DivideByGcd();
ub = FloorRatio(ub, gcd);
const LinearExpression2Index index = lin2_indices_->GetIndex(expr);
if (index != kNoLinearExpression2Index) {
// No reason.
if (root_level_bounds_->GetUpperBoundNoTrail(index) <= ub) {
return;
}
// This one is a single literal.
if (enforced_bounds_->GetUpperBoundFromEnforced(index) <= ub) {
return enforced_bounds_->AddReasonForUpperBoundLowerThan(
index, ub, literal_reason, integer_reason);
}
// This one is a single var upper bound.
if (linear3_bounds_->GetUpperBoundFromLinear3(index) <= ub) {
return linear3_bounds_->AddReasonForUpperBoundLowerThan(
index, ub, literal_reason, integer_reason);
}
}
// Trivial linear2 bounds from its variables.
const IntegerValue implied_ub = integer_trail_->UpperBound(expr);
const IntegerValue slack = ub - implied_ub;
DCHECK_GE(slack, 0);
expr.Negate(); // AppendRelaxedLinearReason() explains a lower bound.
absl::Span<const IntegerVariable> vars = expr.non_zero_vars();
absl::Span<const IntegerValue> coeffs = expr.non_zero_coeffs();
integer_trail_->AppendRelaxedLinearReason(slack, coeffs, vars,
integer_reason);
}
RelationStatus Linear2Bounds::GetStatus(LinearExpression2 expr, IntegerValue lb,
IntegerValue ub) const {
expr.SimpleCanonicalization();
const IntegerValue gcd = expr.DivideByGcd();
const LinearExpression2Index index = lin2_indices_->GetIndex(expr);
IntegerValue known_ub;
IntegerValue known_lb;
if (index == kNoLinearExpression2Index) {
known_ub = CapProdI(gcd, integer_trail_->UpperBound(expr));
expr.Negate();
known_lb = -CapProdI(gcd, integer_trail_->UpperBound(expr));
} else {
known_ub = CapProdI(gcd, UpperBound(index));
known_lb = -CapProdI(gcd, UpperBound(NegationOf(index)));
}
if (lb <= known_lb && ub >= known_ub) return RelationStatus::IS_TRUE;
if (lb > known_ub || ub < known_lb) return RelationStatus::IS_FALSE;
return RelationStatus::IS_UNKNOWN;
}
bool Linear2Bounds::EnqueueLowerOrEqual(
LinearExpression2 expr, IntegerValue ub,
absl::Span<const Literal> literal_reason,
absl::Span<const IntegerLiteral> integer_reason) {
using ReifiedBoundType = ReifiedLinear2Bounds::ReifiedBoundType;
expr.SimpleCanonicalization();
const IntegerValue gcd = expr.DivideByGcd();
ub = FloorRatio(ub, gcd);
// We have many different scenarios here, each one pushing something different
// in the trail.
// Trivial.
if (expr.coeffs[0] == 0 && expr.coeffs[1] == 0) {
++enqueue_trivial_;
if (ub >= 0) {
return true;
} else {
return integer_trail_->ReportConflict(literal_reason, integer_reason);
}
}
// Degenerate single variable case, just push the IntegerLiteral.
if (expr.coeffs[0] == 0) {
++enqueue_degenerate_;
return integer_trail_->Enqueue(
IntegerLiteral::LowerOrEqual(expr.vars[1], ub), literal_reason,
integer_reason);
}
// TODO(user): also check partially-encoded bounds, e.g. (expr <= ub) => l,
// which might be in ConditionalLinear2Bounds as ~l => (-expr <= - ub - 1).
const auto reified_bound = reified_lin2_bounds_->GetEncodedBound(expr, ub);
// Already true.
if (std::holds_alternative<ReifiedBoundType>(reified_bound) &&
std::get<ReifiedBoundType>(reified_bound) ==
ReifiedBoundType::kAlwaysTrue) {
++enqueue_true_at_root_level_;
return true;
}
// Conflict (ub < lb).
if (std::holds_alternative<ReifiedBoundType>(reified_bound) &&
std::get<ReifiedBoundType>(reified_bound) ==
ReifiedBoundType::kAlwaysFalse) {
++enqueue_conflict_false_at_root_level_;
// It's false at level zero, so we can just report a conflict.
return integer_trail_->ReportConflict(literal_reason, integer_reason);
}
// Now all the cases below are pushing a proper linear2 bound. If we are at
// level zero, store this in the root_level_bounds_.
if (trail_->CurrentDecisionLevel() == 0) {
root_level_bounds_->AddUpperBound(expr, ub);
}
// We don't have anything encoding this linear2 bound. Push the bounds of
// its two variables.
if (std::holds_alternative<ReifiedBoundType>(reified_bound) &&
std::get<ReifiedBoundType>(reified_bound) ==
ReifiedBoundType::kNoLiteralStored) {
// TODO(user): create a Linear2 trail and enqueue this bound there.
++enqueue_individual_var_bounds_;
const ReasonIndex reason_index =
integer_trail_->AppendReasonToInternalBuffers(literal_reason,
integer_reason);
if (reason_index >= saved_reasons_.size()) {
saved_reasons_.resize(reason_index + 1);
}
// We require positive coefficients here.
CHECK_GT(expr.coeffs[0], 0);
CHECK_GT(expr.coeffs[1], 0);
saved_reasons_[reason_index] = expr;
// This is a simple linear2 propagation with lazy reason.
// It will be explained by Explain() below.
const IntegerValue min_activity =
integer_trail_->LowerBound(expr.vars[0]) * expr.coeffs[0] +
integer_trail_->LowerBound(expr.vars[1]) * expr.coeffs[1];
const IntegerValue linear_slack = ub - min_activity;
CHECK_GE(linear_slack, 0); // Conflict should already be dealt with.
for (int i = 0; i < 2; ++i) {
const IntegerValue div = linear_slack / expr.coeffs[i];
const IntegerValue new_ub =
integer_trail_->LowerBound(expr.vars[i]) + div;
const IntegerValue propagation_slack =
(div + 1) * expr.coeffs[i] - linear_slack - 1;
if (!integer_trail_->EnqueueWithLazyReason(
IntegerLiteral::LowerOrEqual(expr.vars[i], new_ub),
reason_index.value(), propagation_slack, this)) {
return false;
}
}
return true;
}
// We have a literal encoding for this linear2 bound, push it.
if (std::holds_alternative<Literal>(reified_bound)) {
++enqueue_literal_encoding_;
const Literal literal = std::get<Literal>(reified_bound);
if (!integer_trail_->SafeEnqueueLiteral(literal, literal_reason,
integer_reason)) {
return false;
}
enforced_bounds_->PushConditionalRelation({literal}, expr, ub);
return true;
}
// We can encode this linear2 bound with an IntegerLiteral (probably coming
// from a linear3). Push the IntegerLiteral.
if (std::holds_alternative<IntegerLiteral>(reified_bound)) {
++enqueue_integer_linear3_encoding_;
// Immediately push the affine bound to Linear2BoundsFromLinear3 so that the
// new linear2 bound is visible without needing to wait for the propagation
// fix point.
const auto [affine, divisor] =
reified_lin2_bounds_->GetLinear3Bound(lin2_indices_->GetIndex(expr));
linear3_bounds_->AddAffineUpperBound(lin2_indices_->GetIndex(expr), divisor,
affine);
const IntegerLiteral literal = std::get<IntegerLiteral>(reified_bound);
return integer_trail_->Enqueue(literal, literal_reason, integer_reason);
}
LOG(FATAL) << "Unknown reified bound type";
return false;
}
void Linear2Bounds::Explain(int id, IntegerLiteral /*to_explain*/,
IntegerReason* reason) {
const ReasonIndex reason_index(id);
reason->boolean_literals_at_false =
integer_trail_->LiteralReasonAsSpan(reason_index);
reason->integer_literals = integer_trail_->IntegerReasonAsSpan(reason_index);
// Recover the linear reason from our LinearExpression2 expr.
// Slack should already be set.
reason->vars = saved_reasons_[reason_index].non_zero_vars();
reason->coeffs = saved_reasons_[reason_index].non_zero_coeffs();
}
} // namespace sat
} // namespace operations_research
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