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ortools-clone/ortools/sat/var_domination.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/var_domination.h"
#include <stddef.h>
#include <algorithm>
#include <cstdint>
#include <cstdlib>
#include <limits>
#include <memory>
#include <optional>
#include <string>
#include <utility>
#include <vector>
#include "absl/container/btree_set.h"
#include "absl/container/flat_hash_map.h"
#include "absl/container/flat_hash_set.h"
#include "absl/log/check.h"
#include "absl/meta/type_traits.h"
#include "absl/strings/str_cat.h"
#include "absl/types/span.h"
#include "ortools/algorithms/dynamic_partition.h"
#include "ortools/base/hash.h"
#include "ortools/base/logging.h"
#include "ortools/base/mathutil.h"
#include "ortools/base/stl_util.h"
#include "ortools/base/strong_vector.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_utils.h"
#include "ortools/sat/integer_base.h"
#include "ortools/sat/presolve_context.h"
#include "ortools/sat/presolve_util.h"
#include "ortools/sat/solution_crush.h"
#include "ortools/sat/util.h"
#include "ortools/util/affine_relation.h"
#include "ortools/util/saturated_arithmetic.h"
#include "ortools/util/sorted_interval_list.h"
#include "ortools/util/strong_integers.h"
namespace operations_research {
namespace sat {
void VarDomination::Reset(int num_variables) {
phase_ = 0;
num_vars_with_negation_ = 2 * num_variables;
partition_ =
std::make_unique<SimpleDynamicPartition>(num_vars_with_negation_);
can_freely_decrease_.assign(num_vars_with_negation_, true);
shared_buffer_.clear();
has_initial_candidates_.assign(num_vars_with_negation_, false);
initial_candidates_.assign(num_vars_with_negation_, IntegerVariableSpan());
buffer_.clear();
dominating_vars_.assign(num_vars_with_negation_, IntegerVariableSpan());
ct_index_for_signature_ = 0;
block_down_signatures_.assign(num_vars_with_negation_, 0);
}
void VarDomination::RefinePartition(std::vector<int>* vars) {
if (vars->empty()) return;
partition_->Refine(*vars);
for (int& var : *vars) {
const IntegerVariable wrapped(var);
can_freely_decrease_[wrapped] = false;
can_freely_decrease_[NegationOf(wrapped)] = false;
var = NegationOf(wrapped).value();
}
partition_->Refine(*vars);
}
void VarDomination::CanOnlyDominateEachOther(absl::Span<const int> refs) {
if (phase_ != 0) return;
tmp_vars_.clear();
for (const int ref : refs) {
tmp_vars_.push_back(RefToIntegerVariable(ref).value());
}
RefinePartition(&tmp_vars_);
tmp_vars_.clear();
}
void VarDomination::ActivityShouldNotChange(absl::Span<const int> refs,
absl::Span<const int64_t> coeffs) {
if (phase_ != 0) return;
FillTempRanks(/*reverse_references=*/false, /*enforcements=*/{}, refs,
coeffs);
tmp_vars_.clear();
for (int i = 0; i < tmp_ranks_.size(); ++i) {
if (i > 0 && tmp_ranks_[i].rank != tmp_ranks_[i - 1].rank) {
RefinePartition(&tmp_vars_);
tmp_vars_.clear();
}
tmp_vars_.push_back(tmp_ranks_[i].var.value());
}
RefinePartition(&tmp_vars_);
tmp_vars_.clear();
}
// This correspond to a lower bounded constraint.
void VarDomination::ProcessTempRanks() {
if (phase_ == 0) {
// We actually "split" tmp_ranks_ according to the current partition and
// process each resulting list independently for a faster algo.
++ct_index_for_signature_;
for (IntegerVariableWithRank& entry : tmp_ranks_) {
can_freely_decrease_[entry.var] = false;
block_down_signatures_[entry.var] |= uint64_t{1}
<< (ct_index_for_signature_ % 64);
entry.part = partition_->PartOf(entry.var.value());
}
std::stable_sort(
tmp_ranks_.begin(), tmp_ranks_.end(),
[](const IntegerVariableWithRank& a, const IntegerVariableWithRank& b) {
return a.part < b.part;
});
int start = 0;
for (int i = 1; i < tmp_ranks_.size(); ++i) {
if (tmp_ranks_[i].part != tmp_ranks_[start].part) {
Initialize({&tmp_ranks_[start], static_cast<size_t>(i - start)});
start = i;
}
}
if (start < tmp_ranks_.size()) {
Initialize({&tmp_ranks_[start], tmp_ranks_.size() - start});
}
} else if (phase_ == 1) {
FilterUsingTempRanks();
} else {
// This is only used for debugging, and we shouldn't reach here in prod.
CheckUsingTempRanks();
}
}
void VarDomination::ActivityShouldNotDecrease(
absl::Span<const int> enforcements, absl::Span<const int> refs,
absl::Span<const int64_t> coeffs) {
FillTempRanks(/*reverse_references=*/false, enforcements, refs, coeffs);
ProcessTempRanks();
}
void VarDomination::ActivityShouldNotIncrease(
absl::Span<const int> enforcements, absl::Span<const int> refs,
absl::Span<const int64_t> coeffs) {
FillTempRanks(/*reverse_references=*/true, enforcements, refs, coeffs);
ProcessTempRanks();
}
void VarDomination::MakeRankEqualToStartOfPart(
absl::Span<IntegerVariableWithRank> span) {
const int size = span.size();
int start = 0;
int previous_value = 0;
for (int i = 0; i < size; ++i) {
const int64_t value = span[i].rank;
if (value != previous_value) {
previous_value = value;
start = i;
}
span[i].rank = start;
}
}
void VarDomination::Initialize(absl::Span<IntegerVariableWithRank> span) {
// The rank can be wrong and need to be recomputed because of how we split
// tmp_ranks_ into spans.
MakeRankEqualToStartOfPart(span);
// We made sure all the variable belongs to the same part.
if (DEBUG_MODE) {
if (span.empty()) return;
const int part = partition_->PartOf(span[0].var.value());
for (int i = 1; i < span.size(); ++i) {
CHECK_EQ(part, partition_->PartOf(span[i].var.value()));
}
}
const int future_start = shared_buffer_.size();
int first_start = -1;
const int size = span.size();
for (int i = 0; i < size; ++i) {
const IntegerVariableWithRank entry = span[i];
const int num_candidates = size - entry.rank;
// Ignore if we already have a shorter list.
if (has_initial_candidates_[entry.var]) {
if (num_candidates >= initial_candidates_[entry.var].size) continue;
}
if (first_start == -1) first_start = entry.rank;
has_initial_candidates_[entry.var] = true;
initial_candidates_[entry.var] = {
future_start - first_start + static_cast<int>(entry.rank),
num_candidates};
}
// Only store what is necessary.
// Note that since we share, we will never store more than the problem size.
if (first_start == -1) return;
for (int i = first_start; i < size; ++i) {
shared_buffer_.push_back(span[i].var);
}
}
// TODO(user): Use more heuristics to not miss as much dominance relation when
// we crop initial lists.
bool VarDomination::EndFirstPhase() {
CHECK_EQ(phase_, 0);
phase_ = 1;
// Some initial lists ar too long and will be cropped to this size.
// We will handle them slightly differently.
//
// TODO(user): Tune the initial size, 50 might be a bit large, since our
// complexity is borned by this number times the number of entries in the
// constraints. Still we should in most situation be a lot lower than that.
const int kMaxInitialSize = 50;
absl::btree_set<IntegerVariable> cropped_vars;
util_intops::StrongVector<IntegerVariable, bool> is_cropped(
num_vars_with_negation_, false);
// Fill the initial domination candidates.
int non_cropped_size = 0;
std::vector<IntegerVariable> partition_data;
const std::vector<absl::Span<const IntegerVariable>> elements_by_part =
partition_->GetParts(&partition_data);
for (IntegerVariable var(0); var < num_vars_with_negation_; ++var) {
if (can_freely_decrease_[var]) continue;
const int part = partition_->PartOf(var.value());
const int start = buffer_.size();
const uint64_t var_sig = block_down_signatures_[var];
const uint64_t not_var_sig = block_down_signatures_[NegationOf(var)];
absl::Span<const IntegerVariable> to_scan =
has_initial_candidates_[var] ? InitialDominatingCandidates(var)
: elements_by_part[part];
// Two modes, either we scan the full list, or a small subset of it.
// Not that low variable indices should appear first, so it is better not
// to randomize.
int new_size = 0;
if (to_scan.size() <= 1'000) {
for (const IntegerVariable x : to_scan) {
if (var_sig & ~block_down_signatures_[x]) continue; // !included.
if (block_down_signatures_[NegationOf(x)] & ~not_var_sig) continue;
if (PositiveVariable(x) == PositiveVariable(var)) continue;
if (can_freely_decrease_[NegationOf(x)]) continue;
++new_size;
buffer_.push_back(x);
if (new_size >= kMaxInitialSize) {
is_cropped[var] = true;
cropped_vars.insert(var);
}
}
} else {
is_cropped[var] = true;
cropped_vars.insert(var);
for (int i = 0; i < 200; ++i) {
const IntegerVariable x = to_scan[i];
if (var_sig & ~block_down_signatures_[x]) continue; // !included.
if (block_down_signatures_[NegationOf(x)] & ~not_var_sig) continue;
if (PositiveVariable(x) == PositiveVariable(var)) continue;
if (can_freely_decrease_[NegationOf(x)]) continue;
++new_size;
buffer_.push_back(x);
if (new_size >= kMaxInitialSize) break;
}
}
if (!is_cropped[var]) non_cropped_size += new_size;
dominating_vars_[var] = {start, new_size};
}
// Heuristic: To try not to remove domination relations corresponding to short
// lists during transposition (see EndSecondPhase()), we fill the cropped list
// with the transpose of the short list relations. This helps finding more
// relation in the presence of cropped lists.
//
// Compute how many extra space we need for transposed values.
// Note that it cannot be more than twice.
int total_extra_space = 0;
util_intops::StrongVector<IntegerVariable, int> extra_space(
num_vars_with_negation_, 0);
for (IntegerVariable var(0); var < num_vars_with_negation_; ++var) {
for (const IntegerVariable dom : DominatingVariables(var)) {
if (!is_cropped[NegationOf(dom)]) continue;
++total_extra_space;
extra_space[NegationOf(dom)]++;
}
}
// Copy into a new buffer.
int copy_index = 0;
other_buffer_.resize(buffer_.size() + total_extra_space);
for (IntegerVariable var(0); var < num_vars_with_negation_; ++var) {
IntegerVariableSpan& s = dominating_vars_[var];
for (int i = 0; i < s.size; ++i) {
other_buffer_[copy_index + i] = buffer_[s.start + i];
}
s.start = copy_index;
copy_index += s.size + extra_space[var];
extra_space[var] = s.size; // Used below.
}
DCHECK_EQ(copy_index, other_buffer_.size());
std::swap(buffer_, other_buffer_);
gtl::STLClearObject(&other_buffer_);
// Fill the free spaces with transposed values.
// But do not use new values !
for (IntegerVariable var(0); var < num_vars_with_negation_; ++var) {
const int start = dominating_vars_[var].start;
const int size = extra_space[var];
for (int i = 0; i < size; ++i) {
const IntegerVariable dom = buffer_[start + i];
if (!is_cropped[NegationOf(dom)]) continue;
IntegerVariableSpan& s = dominating_vars_[NegationOf(dom)];
buffer_[s.start + s.size++] = NegationOf(var);
}
}
// Remove any duplicates.
//
// TODO(user): Maybe we should do that with all lists in case the
// input function are called with duplicates too.
for (const IntegerVariable var : cropped_vars) {
DCHECK(is_cropped[var]);
IntegerVariableSpan& s = dominating_vars_[var];
if (s.size == 0) continue;
IntegerVariable* pt = &buffer_[s.start];
std::sort(pt, pt + s.size);
const auto end = std::unique(pt, pt + s.size);
s.size = end - pt;
}
// We no longer need the first phase memory.
VLOG(1) << "Num initial list that where cropped: "
<< FormatCounter(cropped_vars.size());
VLOG(1) << "Shared buffer size: " << FormatCounter(shared_buffer_.size());
VLOG(1) << "Non-cropped buffer size: " << FormatCounter(non_cropped_size);
VLOG(1) << "Buffer size: " << FormatCounter(buffer_.size());
gtl::STLClearObject(&initial_candidates_);
gtl::STLClearObject(&shared_buffer_);
// A second phase is only needed if there are some potential dominance
// relations.
return !buffer_.empty();
}
void VarDomination::EndSecondPhase() {
CHECK_EQ(phase_, 1);
phase_ = 2;
// Perform intersection with transpose.
shared_buffer_.clear();
initial_candidates_.assign(num_vars_with_negation_, IntegerVariableSpan());
// Pass 1: count.
for (IntegerVariable var(0); var < num_vars_with_negation_; ++var) {
for (const IntegerVariable dom : DominatingVariables(var)) {
++initial_candidates_[NegationOf(dom)].size;
}
}
// Pass 2: compute starts.
int start = 0;
for (IntegerVariable var(0); var < num_vars_with_negation_; ++var) {
initial_candidates_[var].start = start;
start += initial_candidates_[var].size;
initial_candidates_[var].size = 0;
}
shared_buffer_.resize(start);
// Pass 3: transpose.
for (IntegerVariable var(0); var < num_vars_with_negation_; ++var) {
for (const IntegerVariable dom : DominatingVariables(var)) {
IntegerVariableSpan& span = initial_candidates_[NegationOf(dom)];
shared_buffer_[span.start + span.size++] = NegationOf(var);
}
}
// Pass 4: intersect.
int num_removed = 0;
tmp_var_to_rank_.resize(num_vars_with_negation_, -1);
for (IntegerVariable var(0); var < num_vars_with_negation_; ++var) {
for (const IntegerVariable dom : InitialDominatingCandidates(var)) {
tmp_var_to_rank_[dom] = 1;
}
int new_size = 0;
IntegerVariableSpan& span = dominating_vars_[var];
for (const IntegerVariable dom : DominatingVariables(var)) {
if (tmp_var_to_rank_[dom] != 1) {
++num_removed;
continue;
}
buffer_[span.start + new_size++] = dom;
}
span.size = new_size;
for (const IntegerVariable dom : InitialDominatingCandidates(var)) {
tmp_var_to_rank_[dom] = -1;
}
}
VLOG(1) << "Transpose removed " << FormatCounter(num_removed);
gtl::STLClearObject(&initial_candidates_);
gtl::STLClearObject(&shared_buffer_);
}
void VarDomination::FillTempRanks(bool reverse_references,
absl::Span<const int> enforcements,
absl::Span<const int> refs,
absl::Span<const int64_t> coeffs) {
tmp_ranks_.clear();
if (coeffs.empty()) {
// Simple case: all coefficients are assumed to be the same.
for (const int ref : refs) {
const IntegerVariable var =
RefToIntegerVariable(reverse_references ? NegatedRef(ref) : ref);
tmp_ranks_.push_back({var, 0, 0});
}
} else {
// Complex case: different coefficients.
for (int i = 0; i < refs.size(); ++i) {
if (coeffs[i] == 0) continue;
const IntegerVariable var = RefToIntegerVariable(
reverse_references ? NegatedRef(refs[i]) : refs[i]);
if (coeffs[i] > 0) {
tmp_ranks_.push_back({var, 0, coeffs[i]});
} else {
tmp_ranks_.push_back({NegationOf(var), 0, -coeffs[i]});
}
}
std::sort(tmp_ranks_.begin(), tmp_ranks_.end());
MakeRankEqualToStartOfPart({&tmp_ranks_[0], tmp_ranks_.size()});
}
// Add the enforcement last with a new rank. We add their negation since
// we want the activity to not decrease, and we want to allow any
// enforcement-- to dominate a variable in the constraint.
const int enforcement_rank = tmp_ranks_.size();
for (const int ref : enforcements) {
tmp_ranks_.push_back(
{RefToIntegerVariable(NegatedRef(ref)), 0, enforcement_rank});
}
}
// We take the intersection of the current dominating candidate with the
// restriction imposed by the current content of tmp_ranks_.
void VarDomination::FilterUsingTempRanks() {
// Expand ranks in temp vector.
tmp_var_to_rank_.resize(num_vars_with_negation_, -1);
for (const IntegerVariableWithRank entry : tmp_ranks_) {
tmp_var_to_rank_[entry.var] = entry.rank;
}
// The activity of the variable in tmp_rank must not decrease.
for (const IntegerVariableWithRank entry : tmp_ranks_) {
// The only variables that can be paired with a var-- in the constraints are
// the var++ in the constraints with the same rank or higher.
//
// Note that we only filter the var-- domination lists here, we do not
// remove the var-- appearing in all the lists corresponding to wrong var++.
// This is left to the transpose operation in EndSecondPhase().
{
IntegerVariableSpan& span = dominating_vars_[entry.var];
if (span.size == 0) continue;
int new_size = 0;
for (const IntegerVariable candidate : DominatingVariables(entry.var)) {
if (tmp_var_to_rank_[candidate] < entry.rank) continue;
buffer_[span.start + new_size++] = candidate;
}
span.size = new_size;
}
}
// Reset temporary vector to all -1.
for (const IntegerVariableWithRank entry : tmp_ranks_) {
tmp_var_to_rank_[entry.var] = -1;
}
}
// Slow: This is for debugging only.
void VarDomination::CheckUsingTempRanks() {
tmp_var_to_rank_.resize(num_vars_with_negation_, -1);
for (const IntegerVariableWithRank entry : tmp_ranks_) {
tmp_var_to_rank_[entry.var] = entry.rank;
}
// The activity of the variable in tmp_rank must not decrease.
for (IntegerVariable var(0); var < num_vars_with_negation_; ++var) {
const int var_rank = tmp_var_to_rank_[var];
const int negated_var_rank = tmp_var_to_rank_[NegationOf(var)];
for (const IntegerVariable dom : DominatingVariables(var)) {
CHECK(!can_freely_decrease_[NegationOf(dom)]);
// Doing X--, Y++ is compatible if the rank[X] <= rank[Y]. But we also
// need to check if doing Not(Y)-- is compatible with Not(X)++.
CHECK_LE(var_rank, tmp_var_to_rank_[dom]);
CHECK_LE(tmp_var_to_rank_[NegationOf(dom)], negated_var_rank);
}
}
for (const IntegerVariableWithRank entry : tmp_ranks_) {
tmp_var_to_rank_[entry.var] = -1;
}
}
bool VarDomination::CanFreelyDecrease(int ref) const {
return CanFreelyDecrease(RefToIntegerVariable(ref));
}
bool VarDomination::CanFreelyDecrease(IntegerVariable var) const {
return can_freely_decrease_[var];
}
absl::Span<const IntegerVariable> VarDomination::InitialDominatingCandidates(
IntegerVariable var) const {
const IntegerVariableSpan span = initial_candidates_[var];
if (span.size == 0) return absl::Span<const IntegerVariable>();
return absl::Span<const IntegerVariable>(&shared_buffer_[span.start],
span.size);
}
absl::Span<const IntegerVariable> VarDomination::DominatingVariables(
int ref) const {
return DominatingVariables(RefToIntegerVariable(ref));
}
absl::Span<const IntegerVariable> VarDomination::DominatingVariables(
IntegerVariable var) const {
const IntegerVariableSpan span = dominating_vars_[var];
if (span.size == 0) return absl::Span<const IntegerVariable>();
return absl::Span<const IntegerVariable>(&buffer_[span.start], span.size);
}
std::string VarDomination::DominationDebugString(IntegerVariable var) const {
const int ref = IntegerVariableToRef(var);
std::string result =
absl::StrCat(PositiveRef(ref), RefIsPositive(ref) ? "--" : "++", " : ");
for (const IntegerVariable dom : DominatingVariables(var)) {
const int dom_ref = IntegerVariableToRef(dom);
absl::StrAppend(&result, PositiveRef(dom_ref),
RefIsPositive(dom_ref) ? "++" : "--", " ");
}
return result;
}
// TODO(user): No need to set locking_ct_index_[var] if num_locks_[var] > 1
void DualBoundStrengthening::CannotDecrease(absl::Span<const int> refs,
int ct_index) {
// Optim: We cache pointers to avoid refetching them in the loop.
IntegerValue* bounds = can_freely_decrease_until_.data();
int* locks = num_locks_.data();
int* locking_index = locking_ct_index_.data();
for (const int ref : refs) {
const int var = RefToIntegerVariable(ref).value();
bounds[var] = kMaxIntegerValue;
locks[var]++;
locking_index[var] = ct_index;
}
}
void DualBoundStrengthening::CannotIncrease(absl::Span<const int> refs,
int ct_index) {
// Optim: We cache pointers to avoid refetching them in the loop.
IntegerValue* bounds = can_freely_decrease_until_.data();
int* locks = num_locks_.data();
int* locking_index = locking_ct_index_.data();
for (const int ref : refs) {
const int negated_var = NegationOf(RefToIntegerVariable(ref)).value();
bounds[negated_var] = kMaxIntegerValue;
locks[negated_var]++;
locking_index[negated_var] = ct_index;
}
}
void DualBoundStrengthening::CannotMove(absl::Span<const int> refs,
int ct_index) {
// Optim: We cache pointers to avoid refetching them in the loop.
IntegerValue* bounds = can_freely_decrease_until_.data();
int* locks = num_locks_.data();
int* locking_index = locking_ct_index_.data();
for (const int ref : refs) {
const IntegerVariable var = RefToIntegerVariable(ref);
const IntegerVariable minus_var = NegationOf(var);
bounds[var.value()] = kMaxIntegerValue;
bounds[minus_var.value()] = kMaxIntegerValue;
locks[var.value()]++;
locks[minus_var.value()]++;
locking_index[var.value()] = ct_index;
locking_index[minus_var.value()] = ct_index;
}
}
template <typename LinearProto>
void DualBoundStrengthening::ProcessLinearConstraint(
bool is_objective, const PresolveContext& context,
const LinearProto& linear, int64_t min_activity, int64_t max_activity,
int ct_index) {
const int64_t lb_limit = linear.domain(linear.domain_size() - 2);
const int64_t ub_limit = linear.domain(1);
const int num_terms = linear.vars_size();
for (int i = 0; i < num_terms; ++i) {
int ref = linear.vars(i);
int64_t coeff = linear.coeffs(i);
if (coeff < 0) {
ref = NegatedRef(ref);
coeff = -coeff;
}
const int64_t min_term = coeff * context.MinOf(ref);
const int64_t max_term = coeff * context.MaxOf(ref);
const int64_t term_diff = max_term - min_term;
const IntegerVariable var = RefToIntegerVariable(ref);
// lb side.
if (min_activity < lb_limit) {
num_locks_[var]++;
locking_ct_index_[var] = ct_index;
if (min_activity + term_diff < lb_limit) {
can_freely_decrease_until_[var] = kMaxIntegerValue;
} else {
const IntegerValue slack(lb_limit - min_activity);
const IntegerValue var_diff =
CeilRatio(IntegerValue(slack), IntegerValue(coeff));
can_freely_decrease_until_[var] =
std::max(can_freely_decrease_until_[var],
IntegerValue(context.MinOf(ref)) + var_diff);
}
}
if (is_objective) {
// We never want to increase the objective value. Note that if the
// objective is lower bounded, we checked that on the lb side above.
num_locks_[NegationOf(var)]++;
can_freely_decrease_until_[NegationOf(var)] = kMaxIntegerValue;
continue;
}
// ub side.
if (max_activity > ub_limit) {
num_locks_[NegationOf(var)]++;
locking_ct_index_[NegationOf(var)] = ct_index;
if (max_activity - term_diff > ub_limit) {
can_freely_decrease_until_[NegationOf(var)] = kMaxIntegerValue;
} else {
const IntegerValue slack(max_activity - ub_limit);
const IntegerValue var_diff =
CeilRatio(IntegerValue(slack), IntegerValue(coeff));
can_freely_decrease_until_[NegationOf(var)] =
std::max(can_freely_decrease_until_[NegationOf(var)],
-IntegerValue(context.MaxOf(ref)) + var_diff);
}
}
}
}
namespace {
// This is used to detect if two linear constraint are equivalent if the literal
// ref is mapped to another value. We fill a vector that will only be equal
// to another such vector if the two constraint differ only there.
void TransformLinearWithSpecialBoolean(const ConstraintProto& ct, int ref,
std::vector<int64_t>* output) {
DCHECK_EQ(ct.constraint_case(), ConstraintProto::kLinear);
output->clear();
// Deal with enforcement.
// We only detect NegatedRef() here.
if (!ct.enforcement_literal().empty()) {
output->push_back(ct.enforcement_literal().size());
for (const int literal : ct.enforcement_literal()) {
if (literal == NegatedRef(ref)) {
output->push_back(std::numeric_limits<int32_t>::max()); // Sentinel
} else {
output->push_back(literal);
}
}
}
// Deal with linear part.
// We look for both literal and not(literal) here.
int64_t offset = 0;
output->push_back(ct.linear().vars().size());
for (int i = 0; i < ct.linear().vars().size(); ++i) {
const int v = ct.linear().vars(i);
const int64_t c = ct.linear().coeffs(i);
if (v == ref) {
output->push_back(std::numeric_limits<int32_t>::max()); // Sentinel
output->push_back(c);
} else if (v == NegatedRef(ref)) {
// c * v = -c * (1 - v) + c
output->push_back(std::numeric_limits<int32_t>::max()); // Sentinel
output->push_back(-c);
offset += c;
} else {
output->push_back(v);
output->push_back(c);
}
}
// Domain.
for (const int64_t value : ct.linear().domain()) {
output->push_back(CapSub(value, offset));
}
}
} // namespace
bool DualBoundStrengthening::Strengthen(PresolveContext* context) {
SolutionCrush& crush = context->solution_crush();
num_deleted_constraints_ = 0;
const CpModelProto& cp_model = *context->working_model;
const int num_vars = cp_model.variables_size();
int64_t num_fixed_vars = 0;
for (int var = 0; var < num_vars; ++var) {
if (context->IsFixed(var)) continue;
// Fix to lb?
const int64_t lb = context->MinOf(var);
const int64_t ub_limit = std::max(lb, CanFreelyDecreaseUntil(var));
if (ub_limit == lb) {
++num_fixed_vars;
CHECK(context->IntersectDomainWith(var, Domain(lb)));
continue;
}
// Fix to ub?
const int64_t ub = context->MaxOf(var);
const int64_t lb_limit =
std::min(ub, -CanFreelyDecreaseUntil(NegatedRef(var)));
if (lb_limit == ub) {
++num_fixed_vars;
CHECK(context->IntersectDomainWith(var, Domain(ub)));
continue;
}
// Here we can fix to any value in [ub_limit, lb_limit] that is compatible
// with the current domain. We prefer zero or the lowest possible magnitude.
if (lb_limit > ub_limit) {
const Domain domain =
context->DomainOf(var).IntersectionWith(Domain(ub_limit, lb_limit));
if (!domain.IsEmpty()) {
int64_t value = domain.Contains(0) ? 0 : domain.Min();
if (value != 0) {
for (const int64_t bound : domain.FlattenedIntervals()) {
if (std::abs(bound) < std::abs(value)) value = bound;
}
}
++num_fixed_vars;
context->UpdateRuleStats("dual: fix variable with multiple choices");
CHECK(context->IntersectDomainWith(var, Domain(value)));
continue;
}
}
// Here we can reduce the domain, but we must be careful when the domain
// has holes.
if (lb_limit > lb || ub_limit < ub) {
const int64_t new_ub =
ub_limit < ub
? context->DomainOf(var)
.IntersectionWith(
Domain(ub_limit, std::numeric_limits<int64_t>::max()))
.Min()
: ub;
const int64_t new_lb =
lb_limit > lb
? context->DomainOf(var)
.IntersectionWith(
Domain(std::numeric_limits<int64_t>::min(), lb_limit))
.Max()
: lb;
context->UpdateRuleStats("dual: reduced domain");
CHECK(context->IntersectDomainWith(var, Domain(new_lb, new_ub)));
}
}
if (num_fixed_vars > 0) {
context->UpdateRuleStats("dual: fix variable", num_fixed_vars);
}
// For detecting near-duplicate constraint that can be made equivalent.
// hash -> (ct_index, modified ref).
absl::flat_hash_set<int> equiv_ct_index_set;
absl::flat_hash_map<uint64_t, std::pair<int, int>> equiv_modified_constraints;
std::vector<int64_t> temp_data;
std::vector<int64_t> other_temp_data;
std::string s;
// If there is only one blocking constraint, we can simplify the problem in
// a few situation.
//
// TODO(user): Cover all the cases.
std::vector<bool> processed(num_vars, false);
int64_t num_bool_in_near_duplicate_ct = 0;
for (IntegerVariable var(0); var < num_locks_.size(); ++var) {
const int ref = VarDomination::IntegerVariableToRef(var);
const int positive_ref = PositiveRef(ref);
if (processed[positive_ref]) continue;
if (context->IsFixed(positive_ref)) continue;
if (context->VariableIsNotUsedAnymore(positive_ref)) continue;
if (context->VariableWasRemoved(positive_ref)) continue;
if (num_locks_[var] != 1) continue;
if (locking_ct_index_[var] == -1) {
context->UpdateRuleStats(
"TODO dual: only one unspecified blocking constraint?");
continue;
}
const int ct_index = locking_ct_index_[var];
const ConstraintProto& ct = context->working_model->constraints(ct_index);
if (ct.constraint_case() == ConstraintProto::CONSTRAINT_NOT_SET) {
// TODO(user): Fix variable right away rather than waiting for next call.
continue;
}
if (ct.constraint_case() == ConstraintProto::kAtMostOne) {
context->UpdateRuleStats("TODO dual: tighten at most one");
continue;
}
if (ct.constraint_case() != ConstraintProto::kBoolAnd) {
// If we have an enforcement literal then we can always add the
// implication "not enforced" => var at its lower bound.
// If we also have enforced => fixed var, then var is in affine relation
// with the enforced literal and we can remove one variable.
//
// TODO(user): We can also deal with more than one enforcement.
if (ct.enforcement_literal().size() == 1 &&
PositiveRef(ct.enforcement_literal(0)) != positive_ref) {
const int enf = ct.enforcement_literal(0);
const int64_t bound = RefIsPositive(ref) ? context->MinOf(positive_ref)
: context->MaxOf(positive_ref);
const Domain implied =
context->DomainOf(positive_ref)
.IntersectionWith(
context->deductions.ImpliedDomain(enf, positive_ref));
if (implied.IsEmpty()) {
context->UpdateRuleStats("dual: fix variable");
if (!context->SetLiteralToFalse(enf)) return false;
if (!context->IntersectDomainWith(positive_ref, Domain(bound))) {
return false;
}
continue;
}
if (implied.IsFixed()) {
// Corner case.
if (implied.FixedValue() == bound) {
context->UpdateRuleStats("dual: fix variable");
if (!context->IntersectDomainWith(positive_ref, implied)) {
return false;
}
continue;
}
// Note(user): If we have enforced => var fixed, we could actually
// just have removed var from the constraint it was implied by
// another constraint. If not, because of the new affine relation we
// could remove it right away.
processed[PositiveRef(enf)] = true;
processed[positive_ref] = true;
context->UpdateRuleStats("dual: affine relation");
// The new affine relation added below can break the hint if hint(enf)
// is 0. In this case the only constraint blocking `ref` from
// decreasing [`ct` = enf => (var = implied)] does not apply. We can
// thus set the hint of `positive_ref` to `bound` to preserve the hint
// feasibility.
crush.SetVarToValueIf(positive_ref, bound, NegatedRef(enf));
if (RefIsPositive(enf)) {
// positive_ref = enf * implied + (1 - enf) * bound.
if (!context->StoreAffineRelation(
positive_ref, enf, implied.FixedValue() - bound, bound)) {
return false;
}
} else {
// enf_var = PositiveRef(enf).
// positive_ref = (1 - enf_var) * implied + enf_var * bound.
if (!context->StoreAffineRelation(positive_ref, PositiveRef(enf),
bound - implied.FixedValue(),
implied.FixedValue())) {
return false;
}
}
continue;
}
if (context->CanBeUsedAsLiteral(positive_ref)) {
// If we have a literal, we always add the implication.
// This seems like a good thing to do.
processed[PositiveRef(enf)] = true;
processed[positive_ref] = true;
context->UpdateRuleStats("dual: add implication");
// The new implication can break the hint if hint(enf) is 0 and
// hint(ref) is 1. In this case the only locking constraint `ct` does
// not apply and thus does not prevent decreasing the hint of ref in
// order to preserve the hint feasibility.
crush.SetLiteralToValueIf(ref, false, NegatedRef(enf));
context->AddImplication(NegatedRef(enf), NegatedRef(ref));
context->UpdateNewConstraintsVariableUsage();
continue;
}
// We can add an implication not_enforced => var to its bound ?
context->UpdateRuleStats("TODO dual: add implied bound");
}
// We can make enf equivalent to the constraint instead of just =>. This
// seems useful since internally we always use fully reified encoding.
if (ct.constraint_case() == ConstraintProto::kLinear &&
ct.linear().vars().size() == 1 &&
ct.enforcement_literal().size() == 1 &&
ct.enforcement_literal(0) == NegatedRef(ref)) {
const int var = ct.linear().vars(0);
const Domain var_domain = context->DomainOf(var);
const Domain rhs = ReadDomainFromProto(ct.linear())
.InverseMultiplicationBy(ct.linear().coeffs(0))
.IntersectionWith(var_domain);
if (rhs.IsEmpty()) {
context->UpdateRuleStats("linear1: infeasible");
if (!context->SetLiteralToFalse(ct.enforcement_literal(0))) {
return false;
}
processed[PositiveRef(ref)] = true;
processed[PositiveRef(var)] = true;
context->working_model->mutable_constraints(ct_index)->Clear();
context->UpdateConstraintVariableUsage(ct_index);
continue;
}
if (rhs == var_domain) {
context->UpdateRuleStats("linear1: always true");
processed[PositiveRef(ref)] = true;
processed[PositiveRef(var)] = true;
context->working_model->mutable_constraints(ct_index)->Clear();
context->UpdateConstraintVariableUsage(ct_index);
continue;
}
const Domain complement = rhs.Complement().IntersectionWith(var_domain);
if (rhs.IsFixed() || complement.IsFixed()) {
context->UpdateRuleStats("dual: make encoding equiv");
const int64_t value =
rhs.IsFixed() ? rhs.FixedValue() : complement.FixedValue();
int encoding_lit;
if (context->HasVarValueEncoding(var, value, &encoding_lit)) {
// If it is different, we have an equivalence now, and we can
// remove the constraint.
if (rhs.IsFixed()) {
if (encoding_lit == NegatedRef(ref)) continue;
// Extending `ct` = "not(ref) => encoding_lit" to an equality can
// break the hint only if hint(ref) = hint(encoding_lit) = 1. But
// in this case `ct` is actually not blocking ref from decreasing.
// We can thus set its hint to 0 to preserve the hint feasibility.
crush.SetLiteralToValueIf(ref, false, encoding_lit);
if (!context->StoreBooleanEqualityRelation(encoding_lit,
NegatedRef(ref))) {
return false;
}
} else {
if (encoding_lit == ref) continue;
// Extending `ct` = "not(ref) => not(encoding_lit)" to an equality
// can break the hint only if hint(encoding_lit) = 0 and hint(ref)
// = 1. But in this case `ct` is actually not blocking ref from
// decreasing. We can thus set its hint to 0 to preserve the hint
// feasibility.
crush.SetLiteralToValueIf(ref, false, NegatedRef(encoding_lit));
if (!context->StoreBooleanEqualityRelation(encoding_lit, ref)) {
return false;
}
}
context->working_model->mutable_constraints(ct_index)->Clear();
context->UpdateConstraintVariableUsage(ct_index);
processed[PositiveRef(ref)] = true;
processed[PositiveRef(var)] = true;
// `encoding_lit` was maybe a new variable added during this loop,
// so make sure we cannot go out-of-bound.
if (PositiveRef(encoding_lit) < processed.size()) {
processed[PositiveRef(encoding_lit)] = true;
}
continue;
}
processed[PositiveRef(ref)] = true;
processed[PositiveRef(var)] = true;
// The `new_ct` constraint `ref` => (`var` in `complement`) below can
// break the hint if hint(var) is not in `complement`. In this case,
// set the hint of `ref` to false. This should be safe since the only
// constraint blocking `ref` from decreasing is `ct` = not(ref) =>
// (`var` in `rhs`) -- which does not apply when `ref` is true.
crush.SetLiteralToValueIfLinearConstraintViolated(
ref, false, {{var, 1}}, complement);
ConstraintProto* new_ct = context->working_model->add_constraints();
new_ct->add_enforcement_literal(ref);
new_ct->mutable_linear()->add_vars(var);
new_ct->mutable_linear()->add_coeffs(1);
FillDomainInProto(complement, new_ct->mutable_linear());
context->UpdateNewConstraintsVariableUsage();
if (rhs.IsFixed()) {
context->StoreLiteralImpliesVarEqValue(NegatedRef(ref), var, value);
context->StoreLiteralImpliesVarNEqValue(ref, var, value);
} else if (complement.IsFixed()) {
context->StoreLiteralImpliesVarNEqValue(NegatedRef(ref), var,
value);
context->StoreLiteralImpliesVarEqValue(ref, var, value);
}
continue;
}
}
// If we have two Booleans, each with a single blocking constraint that is
// the same if we "swap" the Booleans reference, then we can make the
// Booleans equivalent. This is because they will be forced to their bad
// value only if it is needed by the other part of their respective
// blocking constraints. This is related to the
// FindAlmostIdenticalLinearConstraints() except that here we can deal
// with non-equality or enforced constraints.
//
// TODO(user): Generalize to non-Boolean. Also for Boolean, we might
// miss some possible reduction if replacing X by 1 - X make a constraint
// near-duplicate of another.
//
// TODO(user): We can generalize to non-linear constraint.
//
// Optimization: Skip if this constraint was already used as a single
// blocking constraint of another variable. If this is the case, it cannot
// be equivalent to another constraint with "var" substituted, since
// otherwise var would have two blocking constraint. We can safely skip
// it. this make sure this is in O(num_entries) and not more.
if (equiv_ct_index_set.insert(ct_index).second &&
ct.constraint_case() == ConstraintProto::kLinear &&
context->CanBeUsedAsLiteral(ref)) {
TransformLinearWithSpecialBoolean(ct, ref, &temp_data);
const uint64_t hash =
fasthash64(temp_data.data(), temp_data.size() * sizeof(int64_t),
uint64_t{0xa5b85c5e198ed849});
const auto [it, inserted] =
equiv_modified_constraints.insert({hash, {ct_index, ref}});
if (!inserted) {
// Already present!
const auto [other_c_with_same_hash, other_ref] = it->second;
CHECK_NE(other_c_with_same_hash, ct_index);
const auto& other_ct =
context->working_model->constraints(other_c_with_same_hash);
TransformLinearWithSpecialBoolean(other_ct, other_ref,
&other_temp_data);
if (temp_data == other_temp_data) {
// Corner case: We just discovered l => ct and not(l) => ct.
// So ct must just always be true. And since that was the only
// blocking constraint for l, we can just set l to an arbitrary
// value.
if (ref == NegatedRef(other_ref)) {
context->UpdateRuleStats(
"dual: detected l => ct and not(l) => ct with unused l!");
if (!context->IntersectDomainWith(ref, Domain(0))) {
return false;
}
continue;
}
// We have a true equality. The two ref can be made equivalent.
if (!processed[PositiveRef(other_ref)]) {
++num_bool_in_near_duplicate_ct;
processed[PositiveRef(ref)] = true;
processed[PositiveRef(other_ref)] = true;
// If the two hints are different, and since both refs have an
// equivalent blocking constraint, then the constraint is actually
// not blocking the ref at 1 from decreasing. Hence we can set its
// hint to false to preserve the hint feasibility despite the new
// Boolean equality constraint.
crush.UpdateLiteralsToFalseIfDifferent(ref, other_ref);
if (!context->StoreBooleanEqualityRelation(ref, other_ref)) {
return false;
}
// We can delete one of the constraint since they are duplicate
// now.
++num_deleted_constraints_;
context->working_model->mutable_constraints(ct_index)->Clear();
context->UpdateConstraintVariableUsage(ct_index);
continue;
}
}
}
}
// Other potential cases?
if (!ct.enforcement_literal().empty()) {
if (ct.constraint_case() == ConstraintProto::kLinear &&
ct.linear().vars().size() == 1 &&
ct.enforcement_literal().size() == 1 &&
ct.enforcement_literal(0) == NegatedRef(ref)) {
context->UpdateRuleStats("TODO dual: make linear1 equiv");
} else {
context->UpdateRuleStats(
"TODO dual: only one blocking enforced constraint?");
}
} else {
context->UpdateRuleStats("TODO dual: only one blocking constraint?");
}
continue;
}
if (ct.enforcement_literal().size() != 1) continue;
// If (a => b) is the only constraint blocking a literal a in the up
// direction, then we can set a == b !
//
// Recover a => b where a is having an unique up_lock (i.e this constraint).
// Note that if many implications are encoded in the same bool_and, we have
// to be careful that a is appearing in just one of them.
//
// TODO(user): Make sure implication graph is transitively reduced to not
// miss such reduction. More generally, this might only use the graph rather
// than the encoding into bool_and / at_most_one ? Basically if a =>
// all_direct_deduction, we can transform it into a <=> all_direct_deduction
// if that is interesting. This could always be done on a max-2sat problem
// in one of the two direction. Also think about max-2sat specific presolve.
int a = ct.enforcement_literal(0);
int b = 1;
if (PositiveRef(a) == positive_ref &&
num_locks_[RefToIntegerVariable(NegatedRef(a))] == 1) {
// Here, we can only add the equivalence if the literal is the only
// on the lhs, otherwise there is actually more lock.
if (ct.bool_and().literals().size() != 1) continue;
b = ct.bool_and().literals(0);
} else {
bool found = false;
b = NegatedRef(ct.enforcement_literal(0));
for (const int lhs : ct.bool_and().literals()) {
if (PositiveRef(lhs) == positive_ref &&
num_locks_[RefToIntegerVariable(lhs)] == 1) {
found = true;
a = NegatedRef(lhs);
break;
}
}
CHECK(found);
}
CHECK_EQ(num_locks_[RefToIntegerVariable(NegatedRef(a))], 1);
processed[PositiveRef(a)] = true;
processed[PositiveRef(b)] = true;
// If hint(a) is false we can always set it to hint(b) since this can only
// increase its value. If hint(a) is true then hint(b) must be true as well
// if the hint is feasible, due to the a => b constraint. Setting hint(a) to
// hint(b) is thus always safe. The opposite is true as well.
crush.MakeLiteralsEqual(a, b);
if (!context->StoreBooleanEqualityRelation(a, b)) return false;
context->UpdateRuleStats("dual: enforced equivalence");
}
if (num_bool_in_near_duplicate_ct) {
context->UpdateRuleStats(
"dual: equivalent Boolean in near-duplicate constraints",
num_bool_in_near_duplicate_ct);
}
VLOG(2) << "Num deleted constraints: " << num_deleted_constraints_;
return true;
}
void ScanModelForDominanceDetection(PresolveContext& context,
VarDomination* var_domination) {
if (context.ModelIsUnsat()) return;
const CpModelProto& cp_model = *context.working_model;
const int num_vars = cp_model.variables().size();
var_domination->Reset(num_vars);
for (int var = 0; var < num_vars; ++var) {
// Ignore variables that have been substituted already or are unused.
if (context.IsFixed(var) || context.VariableWasRemoved(var) ||
context.VariableIsNotUsedAnymore(var)) {
var_domination->CanOnlyDominateEachOther({var});
continue;
}
// Deal with the affine relations that are not part of the proto.
// Those only need to be processed in the first pass.
const AffineRelation::Relation r = context.GetAffineRelation(var);
if (r.representative != var) {
if (r.coeff == 1) {
var_domination->CanOnlyDominateEachOther(
{NegatedRef(var), r.representative});
} else if (r.coeff == -1) {
var_domination->CanOnlyDominateEachOther({var, r.representative});
} else {
var_domination->CanOnlyDominateEachOther({var});
var_domination->CanOnlyDominateEachOther({r.representative});
}
}
}
// First scan: update the partition.
const int num_constraints = cp_model.constraints_size();
std::vector<bool> c_is_free_to_increase(num_constraints);
std::vector<bool> c_is_free_to_decrease(num_constraints);
for (int c = 0; c < num_constraints; ++c) {
const ConstraintProto& ct = cp_model.constraints(c);
switch (ct.constraint_case()) {
case ConstraintProto::kBoolOr:
break;
case ConstraintProto::kBoolAnd:
break;
case ConstraintProto::kAtMostOne:
break;
case ConstraintProto::kExactlyOne:
var_domination->ActivityShouldNotChange(ct.exactly_one().literals(),
/*coeffs=*/{});
break;
case ConstraintProto::kLinear: {
// TODO(user): Maybe we should avoid recomputing that here.
const auto [min_activity, max_activity] =
context.ComputeMinMaxActivity(ct.linear());
const bool domain_is_simple = ct.linear().domain().size() == 2;
const bool free_to_increase =
domain_is_simple && ct.linear().domain(1) >= max_activity;
const bool free_to_decrease =
domain_is_simple && ct.linear().domain(0) <= min_activity;
c_is_free_to_increase[c] = free_to_increase;
c_is_free_to_decrease[c] = free_to_decrease;
if (free_to_decrease && free_to_increase) break;
if (!free_to_increase && !free_to_decrease) {
var_domination->ActivityShouldNotChange(ct.linear().vars(),
ct.linear().coeffs());
}
break;
}
default:
// We cannot infer anything if we don't know the constraint.
// TODO(user): Handle enforcement better here.
for (const int var : context.ConstraintToVars(c)) {
var_domination->CanOnlyDominateEachOther({var});
}
break;
}
}
// The objective is handled like a <= constraints, or an == constraint if
// there is a non-trivial domain.
if (cp_model.has_objective()) {
// Important: We need to write the objective first to make sure it is up to
// date.
context.WriteObjectiveToProto();
const auto [min_activity, max_activity] =
context.ComputeMinMaxActivity(cp_model.objective());
const auto& domain = cp_model.objective().domain();
if (domain.empty() || (domain.size() == 2 && domain[0] <= min_activity)) {
// do nothing for now.
} else {
var_domination->ActivityShouldNotChange(cp_model.objective().vars(),
cp_model.objective().coeffs());
}
}
// Now do two more scan.
// - the phase_ = 0 initialize candidate list, then EndFirstPhase()
// - the phase_ = 1 filter them, then EndSecondPhase();
std::vector<int> tmp;
for (int phase = 0; phase < 2; phase++) {
for (int c = 0; c < num_constraints; ++c) {
const ConstraintProto& ct = cp_model.constraints(c);
switch (ct.constraint_case()) {
case ConstraintProto::kBoolOr:
var_domination->ActivityShouldNotDecrease(ct.enforcement_literal(),
ct.bool_or().literals(),
/*coeffs=*/{});
break;
case ConstraintProto::kBoolAnd:
// We process it like n clauses.
//
// TODO(user): the way we process that is a bit restrictive. By
// working on the implication graph we could detect more dominance
// relations. Since if a => b we say that a++ can only be paired with
// b--, but it could actually be paired with any variables that when
// dereased implies b = 0. This is a bit mitigated by the fact that
// we regroup when we can such implications into big at most ones.
tmp.clear();
for (const int ref : ct.enforcement_literal()) {
tmp.push_back(NegatedRef(ref));
}
for (const int ref : ct.bool_and().literals()) {
tmp.push_back(ref);
var_domination->ActivityShouldNotDecrease(/*enforcements=*/{}, tmp,
/*coeffs=*/{});
tmp.pop_back();
}
break;
case ConstraintProto::kAtMostOne:
var_domination->ActivityShouldNotIncrease(ct.enforcement_literal(),
ct.at_most_one().literals(),
/*coeffs=*/{});
break;
case ConstraintProto::kLinear: {
const bool free_to_increase = c_is_free_to_increase[c];
const bool free_to_decrease = c_is_free_to_decrease[c];
if (free_to_decrease && free_to_increase) break;
if (free_to_increase) {
var_domination->ActivityShouldNotDecrease(ct.enforcement_literal(),
ct.linear().vars(),
ct.linear().coeffs());
} else if (free_to_decrease) {
var_domination->ActivityShouldNotIncrease(ct.enforcement_literal(),
ct.linear().vars(),
ct.linear().coeffs());
} else {
if (!ct.enforcement_literal().empty()) {
var_domination->ActivityShouldNotIncrease(
/*enforcements=*/{}, ct.enforcement_literal(), /*coeffs=*/{});
}
}
break;
}
default:
break;
}
}
// The objective is handled like a <= constraints, or an == constraint if
// there is a non-trivial domain.
if (cp_model.has_objective()) {
const auto [min_activity, max_activity] =
context.ComputeMinMaxActivity(cp_model.objective());
const auto& domain = cp_model.objective().domain();
if (domain.empty() || (domain.size() == 2 && domain[0] <= min_activity)) {
var_domination->ActivityShouldNotIncrease(
/*enforcements=*/{}, cp_model.objective().vars(),
cp_model.objective().coeffs());
}
}
if (phase == 0) {
// Early abort if no possible relations can be found.
//
// TODO(user): We might be able to detect that nothing can be done earlier
// during the constraint scanning.
if (!var_domination->EndFirstPhase()) return;
} else {
CHECK_EQ(phase, 1);
var_domination->EndSecondPhase();
}
}
// Some statistics.
int64_t num_unconstrained_refs = 0;
int64_t num_dominated_refs = 0;
int64_t num_dominance_relations = 0;
for (int var = 0; var < num_vars; ++var) {
if (context.IsFixed(var)) continue;
for (const int ref : {var, NegatedRef(var)}) {
if (var_domination->CanFreelyDecrease(ref)) {
num_unconstrained_refs++;
} else if (!var_domination->DominatingVariables(ref).empty()) {
num_dominated_refs++;
num_dominance_relations +=
var_domination->DominatingVariables(ref).size();
}
}
}
if (num_unconstrained_refs == 0 && num_dominated_refs == 0) return;
VLOG(1) << "Dominance:"
<< " num_unconstrained_refs=" << num_unconstrained_refs
<< " num_dominated_refs=" << num_dominated_refs
<< " num_dominance_relations=" << num_dominance_relations;
}
void ScanModelForDualBoundStrengthening(
const PresolveContext& context,
DualBoundStrengthening* dual_bound_strengthening) {
if (context.ModelIsUnsat()) return;
const CpModelProto& cp_model = *context.working_model;
const int num_vars = cp_model.variables().size();
dual_bound_strengthening->Reset(num_vars);
for (int var = 0; var < num_vars; ++var) {
// Ignore variables that have been substituted already or are unused.
if (context.IsFixed(var) || context.VariableWasRemoved(var) ||
context.VariableIsNotUsedAnymore(var)) {
dual_bound_strengthening->CannotMove({var});
continue;
}
// Deal with the affine relations that are not part of the proto.
// Those only need to be processed in the first pass.
const AffineRelation::Relation r = context.GetAffineRelation(var);
if (r.representative != var) {
dual_bound_strengthening->CannotMove({var, r.representative});
}
}
const int num_constraints = cp_model.constraints_size();
for (int c = 0; c < num_constraints; ++c) {
const ConstraintProto& ct = cp_model.constraints(c);
dual_bound_strengthening->CannotIncrease(ct.enforcement_literal(), c);
switch (ct.constraint_case()) {
case ConstraintProto::kBoolOr:
dual_bound_strengthening->CannotDecrease(ct.bool_or().literals(), c);
break;
case ConstraintProto::kBoolAnd:
dual_bound_strengthening->CannotDecrease(ct.bool_and().literals(), c);
break;
case ConstraintProto::kAtMostOne:
dual_bound_strengthening->CannotIncrease(ct.at_most_one().literals(),
c);
break;
case ConstraintProto::kExactlyOne:
dual_bound_strengthening->CannotMove(ct.exactly_one().literals(), c);
break;
case ConstraintProto::kLinear: {
// TODO(user): Maybe we should avoid recomputing that here.
const auto [min_activity, max_activity] =
context.ComputeMinMaxActivity(ct.linear());
dual_bound_strengthening->ProcessLinearConstraint(
false, context, ct.linear(), min_activity, max_activity, c);
break;
}
default:
// We cannot infer anything if we don't know the constraint.
// TODO(user): Handle enforcement better here.
dual_bound_strengthening->CannotMove(context.ConstraintToVars(c), c);
break;
}
}
// The objective is handled like a <= constraints, or an == constraint if
// there is a non-trivial domain.
if (cp_model.has_objective()) {
// WARNING: The proto objective might not be up to date, so we need to
// write it first.
context.WriteObjectiveToProto();
const auto [min_activity, max_activity] =
context.ComputeMinMaxActivity(cp_model.objective());
dual_bound_strengthening->ProcessLinearConstraint(
true, context, cp_model.objective(), min_activity, max_activity);
}
}
namespace {
// Decrements the solution hint of `ref` by the minimum amount necessary to be
// in `domain`, and increments the solution hint of one or more
// `dominating_variables` by the same total amount (or less if it is not
// possible to exactly match this amount).
//
// `domain` must be an interval with the same lower bound as `ref`'s current
// domain D in `context`, and whose upper bound must be in D.
void MaybeUpdateRefHintFromDominance(
PresolveContext& context, int ref, const Domain& domain,
absl::Span<const IntegerVariable> dominating_variables) {
DCHECK_EQ(domain.NumIntervals(), 1);
DCHECK_EQ(domain.Min(), context.DomainOf(ref).Min());
DCHECK(context.DomainOf(ref).Contains(domain.Max()));
std::vector<std::pair<int, Domain>> dominating_refs;
dominating_refs.reserve(dominating_variables.size());
for (const IntegerVariable var : dominating_variables) {
const int dominating_ref = VarDomination::IntegerVariableToRef(var);
dominating_refs.push_back(
{dominating_ref, context.DomainOf(dominating_ref)});
}
context.solution_crush().UpdateRefsWithDominance(
ref, domain.Min(), domain.Max(), dominating_refs);
}
bool ProcessAtMostOne(
absl::Span<const int> literals, const std::string& message,
const VarDomination& var_domination,
util_intops::StrongVector<IntegerVariable, bool>* in_constraints,
PresolveContext* context) {
for (const int ref : literals) {
(*in_constraints)[VarDomination::RefToIntegerVariable(ref)] = true;
}
for (const int ref : literals) {
if (context->IsFixed(ref)) continue;
const auto dominating_ivars = var_domination.DominatingVariables(ref);
for (const IntegerVariable ivar : dominating_ivars) {
const int iref = VarDomination::IntegerVariableToRef(ivar);
if (!(*in_constraints)[ivar]) continue;
if (context->IsFixed(iref)) {
continue;
}
// We can set the dominated variable to false. If the hint value of `ref`
// is 1 then the hint value of `iref` should be 0 due to the "at most one"
// constraint. Hence the hint feasibility can always be preserved (if the
// hint value of `ref` is 0 the hint does not need to be updated).
context->UpdateRuleStats(message);
context->solution_crush().UpdateLiteralsWithDominance(ref, iref);
if (!context->SetLiteralToFalse(ref)) return false;
break;
}
}
for (const int ref : literals) {
(*in_constraints)[VarDomination::RefToIntegerVariable(ref)] = false;
}
return true;
}
} // namespace
bool ExploitDominanceRelations(const VarDomination& var_domination,
PresolveContext* context) {
const CpModelProto& cp_model = *context->working_model;
const int num_vars = cp_model.variables_size();
// Abort early if there is nothing to do.
bool work_to_do = false;
for (int var = 0; var < num_vars; ++var) {
if (context->IsFixed(var)) continue;
if (!var_domination.DominatingVariables(var).empty() ||
!var_domination.DominatingVariables(NegatedRef(var)).empty()) {
work_to_do = true;
break;
}
}
if (!work_to_do) return true;
const int64_t saved_num_operations = context->num_presolve_operations;
// Strenghtening via domination. When a variable is dominated by a bunch of
// other, either we can do (var--, dom++) or if we can't (i.e all dominated
// variable at their upper bound) then maybe all constraint are satisfied if
// var is high enough and we can also decrease it.
util_intops::StrongVector<IntegerVariable, int> can_freely_decrease_count(
num_vars * 2, 0);
util_intops::StrongVector<IntegerVariable, int64_t> can_freely_decrease_until(
num_vars * 2, std::numeric_limits<int64_t>::min());
// Temporary data that we fill/clear for each linear constraint.
util_intops::StrongVector<IntegerVariable, int64_t> var_lb_to_ub_diff(
num_vars * 2, 0);
// Temporary data used for boolean constraints.
util_intops::StrongVector<IntegerVariable, bool> in_constraints(num_vars * 2,
false);
SolutionCrush& crush = context->solution_crush();
absl::flat_hash_set<std::pair<int, int>> implications;
const int num_constraints = cp_model.constraints_size();
for (int c = 0; c < num_constraints; ++c) {
const ConstraintProto& ct = cp_model.constraints(c);
if (ct.constraint_case() == ConstraintProto::kBoolAnd) {
if (ct.enforcement_literal().size() != 1) continue;
const int a = ct.enforcement_literal(0);
if (context->IsFixed(a)) continue;
for (const int b : ct.bool_and().literals()) {
if (context->IsFixed(b)) continue;
implications.insert({a, b});
implications.insert({NegatedRef(b), NegatedRef(a)});
// If (a--, b--) is valid, we can always set a to false. If the hint
// value of `a` is 1 then the hint value of `b` should be 1 due to the
// a => b constraint. Hence the hint feasibility can always be preserved
// (if the hint value of `a` is 0 the hint does not need to be updated).
for (const IntegerVariable ivar :
var_domination.DominatingVariables(a)) {
const int ref = VarDomination::IntegerVariableToRef(ivar);
if (ref == NegatedRef(b)) {
context->UpdateRuleStats("domination: in implication");
crush.UpdateLiteralsWithDominance(a, ref);
if (!context->SetLiteralToFalse(a)) return false;
break;
}
}
if (context->IsFixed(a)) break;
// If (b++, a++) is valid, then we can always set b to true. If the hint
// value of `b` is 0 then the hint value of `a` should be 0 due to the
// a => b constraint. Hence the hint feasibility can always be preserved
// (if the hint value of `b` is 1 the hint does not need to be updated).
for (const IntegerVariable ivar :
var_domination.DominatingVariables(NegatedRef(b))) {
const int ref = VarDomination::IntegerVariableToRef(ivar);
if (ref == a) {
context->UpdateRuleStats("domination: in implication");
crush.UpdateLiteralsWithDominance(NegatedRef(b), ref);
if (!context->SetLiteralToTrue(b)) return false;
break;
}
}
}
continue;
}
if (!ct.enforcement_literal().empty()) continue;
// TODO(user): More generally, combine with probing? if a dominated
// variable implies one of its dominant to zero, then it can be set to
// zero. It seems adding the implication below should have the same
// effect? but currently it requires a lot of presolve rounds.
const auto add_implications = [&implications](absl::Span<const int> lits) {
if (lits.size() > 3) return;
for (int i = 0; i < lits.size(); ++i) {
for (int j = 0; j < lits.size(); ++j) {
if (i == j) continue;
implications.insert({lits[i], NegatedRef(lits[j])});
}
}
};
if (ct.constraint_case() == ConstraintProto::kAtMostOne) {
add_implications(ct.at_most_one().literals());
if (!ProcessAtMostOne(ct.at_most_one().literals(),
"domination: in at most one", var_domination,
&in_constraints, context)) {
return false;
}
} else if (ct.constraint_case() == ConstraintProto::kExactlyOne) {
add_implications(ct.exactly_one().literals());
if (!ProcessAtMostOne(ct.exactly_one().literals(),
"domination: in exactly one", var_domination,
&in_constraints, context)) {
return false;
}
}
if (ct.constraint_case() != ConstraintProto::kLinear) continue;
int num_dominated = 0;
for (const int var : context->ConstraintToVars(c)) {
if (!var_domination.DominatingVariables(var).empty()) ++num_dominated;
if (!var_domination.DominatingVariables(NegatedRef(var)).empty()) {
++num_dominated;
}
}
if (num_dominated == 0) continue;
// Precompute.
int64_t min_activity = 0;
int64_t max_activity = 0;
const int num_terms = ct.linear().vars_size();
for (int i = 0; i < num_terms; ++i) {
int ref = ct.linear().vars(i);
int64_t coeff = ct.linear().coeffs(i);
if (coeff < 0) {
ref = NegatedRef(ref);
coeff = -coeff;
}
const int64_t min_term = coeff * context->MinOf(ref);
const int64_t max_term = coeff * context->MaxOf(ref);
min_activity += min_term;
max_activity += max_term;
const IntegerVariable ivar = VarDomination::RefToIntegerVariable(ref);
var_lb_to_ub_diff[ivar] = max_term - min_term;
var_lb_to_ub_diff[NegationOf(ivar)] = min_term - max_term;
}
const int64_t rhs_lb = ct.linear().domain(0);
const int64_t rhs_ub = ct.linear().domain(ct.linear().domain_size() - 1);
if (max_activity < rhs_lb || min_activity > rhs_ub) {
return context->NotifyThatModelIsUnsat("linear equation unsat.");
}
// Returns the change magnitude in min-activity (resp. max-activity) if all
// the given variables are fixed to their upper bound.
const auto get_delta = [context, &var_lb_to_ub_diff](
bool use_min_side,
absl::Span<const IntegerVariable> vars) {
int64_t delta = 0;
for (const IntegerVariable var : vars) {
// Tricky: For now we skip complex domain as we are not sure they
// can be moved correctly.
if (context->DomainOf(VarDomination::IntegerVariableToRef(var))
.NumIntervals() != 1) {
continue;
}
if (use_min_side) {
delta += std::max(int64_t{0}, var_lb_to_ub_diff[var]);
} else {
delta += std::max(int64_t{0}, -var_lb_to_ub_diff[var]);
}
}
return delta;
};
// Look for dominated var.
for (int i = 0; i < num_terms; ++i) {
const int ref = ct.linear().vars(i);
const int64_t coeff = ct.linear().coeffs(i);
const int64_t coeff_magnitude = std::abs(coeff);
if (context->IsFixed(ref)) continue;
// For strenghtening using domination, just consider >= constraint.
const bool only_lb = max_activity <= rhs_ub;
const bool only_ub = min_activity >= rhs_lb;
if (only_lb || only_ub) {
// Always transform to coeff_magnitude * current_ref + ... >=
const int current_ref = (coeff > 0) == only_lb ? ref : NegatedRef(ref);
const int64_t shifted_rhs =
only_lb ? rhs_lb - min_activity : max_activity - rhs_ub;
const IntegerVariable current_ivar =
VarDomination::RefToIntegerVariable(current_ref);
can_freely_decrease_count[NegationOf(current_ivar)]++;
const int64_t delta = get_delta(
only_lb, var_domination.DominatingVariables(current_ivar));
if (delta > 0) {
// When all dominated var are at their upper bound, we miss 'slack'
// to make the constraint trivially satisfiable.
const int64_t slack = shifted_rhs - delta;
const int64_t current_lb = context->MinOf(current_ref);
// Any increase such that coeff * delta >= slack make the constraint
// trivial.
//
// Note(user): It look like even if any of the upper bound of the
// dominating var decrease, this should still be valid. Here we only
// decrease such a bound due to a dominance relation, so the slack
// when all dominating variable are at their bound should not really
// decrease.
const int64_t min_delta =
slack <= 0 ? 0 : MathUtil::CeilOfRatio(slack, coeff_magnitude);
can_freely_decrease_until[current_ivar] = std::max(
can_freely_decrease_until[current_ivar], current_lb + min_delta);
can_freely_decrease_count[current_ivar]++;
}
}
for (const int current_ref : {ref, NegatedRef(ref)}) {
const absl::Span<const IntegerVariable> dominated_by =
var_domination.DominatingVariables(current_ref);
if (dominated_by.empty()) continue;
const bool ub_side = (coeff > 0) == (current_ref == ref);
if (ub_side) {
if (max_activity <= rhs_ub) continue;
} else {
if (min_activity >= rhs_lb) continue;
}
const int64_t slack =
ub_side ? rhs_ub - min_activity : max_activity - rhs_lb;
// Compute the delta in min-activity if all dominating var moves to
// their other bound.
const int64_t delta = get_delta(ub_side, dominated_by);
const int64_t lb = context->MinOf(current_ref);
if (delta + coeff_magnitude > slack) {
context->UpdateRuleStats("domination: fixed to lb.");
const Domain reduced_domain = Domain(lb);
MaybeUpdateRefHintFromDominance(*context, current_ref, reduced_domain,
dominated_by);
if (!context->IntersectDomainWith(current_ref, reduced_domain)) {
return false;
}
// We need to update the precomputed quantities.
const IntegerVariable current_var =
VarDomination::RefToIntegerVariable(current_ref);
if (ub_side) {
CHECK_GE(var_lb_to_ub_diff[current_var], 0);
max_activity -= var_lb_to_ub_diff[current_var];
} else {
CHECK_LE(var_lb_to_ub_diff[current_var], 0);
min_activity -= var_lb_to_ub_diff[current_var];
}
var_lb_to_ub_diff[current_var] = 0;
var_lb_to_ub_diff[NegationOf(current_var)] = 0;
continue;
}
const IntegerValue diff = FloorRatio(IntegerValue(slack - delta),
IntegerValue(coeff_magnitude));
int64_t new_ub = lb + diff.value();
if (new_ub < context->MaxOf(current_ref)) {
// Tricky: If there are holes, we can't just reduce the domain to
// new_ub if it is not a valid value, so we need to compute the
// Min() of the intersection.
new_ub = context->DomainOf(current_ref).ValueAtOrAfter(new_ub);
}
if (new_ub < context->MaxOf(current_ref)) {
context->UpdateRuleStats("domination: reduced ub.");
const Domain reduced_domain = Domain(lb, new_ub);
MaybeUpdateRefHintFromDominance(*context, current_ref, reduced_domain,
dominated_by);
if (!context->IntersectDomainWith(current_ref, reduced_domain)) {
return false;
}
// We need to update the precomputed quantities.
const IntegerVariable current_var =
VarDomination::RefToIntegerVariable(current_ref);
if (ub_side) {
CHECK_GE(var_lb_to_ub_diff[current_var], 0);
max_activity -= var_lb_to_ub_diff[current_var];
} else {
CHECK_LE(var_lb_to_ub_diff[current_var], 0);
min_activity -= var_lb_to_ub_diff[current_var];
}
const int64_t new_diff = std::abs(coeff_magnitude * (new_ub - lb));
if (ub_side) {
var_lb_to_ub_diff[current_var] = new_diff;
var_lb_to_ub_diff[NegationOf(current_var)] = -new_diff;
max_activity += new_diff;
} else {
var_lb_to_ub_diff[current_var] = -new_diff;
var_lb_to_ub_diff[NegationOf(current_var)] = +new_diff;
min_activity -= new_diff;
}
}
}
}
// Restore.
for (const int ref : ct.linear().vars()) {
const IntegerVariable ivar = VarDomination::RefToIntegerVariable(ref);
var_lb_to_ub_diff[ivar] = 0;
var_lb_to_ub_diff[NegationOf(ivar)] = 0;
}
}
// For any dominance relation still left (i.e. between non-fixed vars), if
// the variable are Boolean and X is dominated by Y, we can add
// (X = 1) => (Y = 1). But, as soon as we do that, we break some symmetry
// and cannot add any incompatible relations.
//
// EX: It is possible that X dominate Y and Y dominate X if they are both
// appearing in exactly the same constraint with the same coefficient.
//
// TODO(user): if both variable are in a bool_or, this will allow us to
// remove the dominated variable. Maybe we should exploit that to decide
// which implication we add. Or just remove such variable and not add the
// implications?
//
// TODO(user): generalize to non Booleans?
int num_added = 0;
util_intops::StrongVector<IntegerVariable, bool> increase_is_forbidden(
2 * num_vars, false);
for (int positive_ref = 0; positive_ref < num_vars; ++positive_ref) {
if (context->IsFixed(positive_ref)) continue;
if (context->VariableIsNotUsedAnymore(positive_ref)) continue;
if (context->VariableWasRemoved(positive_ref)) continue;
// Increase the count for variable in the objective to account for the
// kObjectiveConstraint in their VarToConstraints() list.
if (!context->ObjectiveDomainIsConstraining()) {
const int64_t obj_coeff = context->ObjectiveCoeff(positive_ref);
if (obj_coeff > 0) {
can_freely_decrease_count[VarDomination::RefToIntegerVariable(
positive_ref)]++;
} else if (obj_coeff < 0) {
can_freely_decrease_count[NegationOf(
VarDomination::RefToIntegerVariable(positive_ref))]++;
}
}
for (const int ref : {positive_ref, NegatedRef(positive_ref)}) {
const IntegerVariable var = VarDomination::RefToIntegerVariable(ref);
if (increase_is_forbidden[NegationOf(var)]) continue;
if (can_freely_decrease_count[var] ==
context->VarToConstraints(positive_ref).size()) {
// We need to account for domain with hole, hence the ValueAtOrAfter().
int64_t lb = can_freely_decrease_until[var];
lb = context->DomainOf(ref).ValueAtOrAfter(lb);
if (lb < context->MaxOf(ref)) {
// We have a candidate, however, we need to make sure the dominating
// variable upper bound didn't change.
//
// TODO(user): It look like testing this is not really necessary.
// The reduction done by this class seem to be order independent.
bool ok = true;
const absl::Span<const IntegerVariable> dominating_vars =
var_domination.DominatingVariables(var);
for (const IntegerVariable dom : dominating_vars) {
// Note that we assumed that a fixed point was reached before this
// is called, so modified_domains should have been empty as we
// entered this function. If not, the code is still correct, but we
// might miss some reduction, they will still likely be done later
// though.
if (increase_is_forbidden[dom] ||
context->modified_domains[PositiveRef(
VarDomination::IntegerVariableToRef(dom))]) {
ok = false;
break;
}
}
if (increase_is_forbidden[NegationOf(var)]) {
ok = false;
}
if (ok) {
// TODO(user): Is this needed?
increase_is_forbidden[var] = true;
context->UpdateRuleStats(
"domination: dual strenghtening using dominance");
const Domain reduced_domain = Domain(context->MinOf(ref), lb);
MaybeUpdateRefHintFromDominance(*context, ref, reduced_domain,
dominating_vars);
if (!context->IntersectDomainWith(ref, reduced_domain)) {
return false;
}
// The rest of the loop only care about Booleans.
// And if this was boolean, we would have fixed it.
// If it became Boolean, we wait for the next call.
// TODO(user): maybe the last point can be improved.
continue;
}
}
}
if (!context->CanBeUsedAsLiteral(positive_ref)) continue;
for (const IntegerVariable dom :
var_domination.DominatingVariables(ref)) {
if (increase_is_forbidden[dom]) continue;
const int dom_ref = VarDomination::IntegerVariableToRef(dom);
if (context->IsFixed(dom_ref)) continue;
if (context->VariableIsNotUsedAnymore(dom_ref)) continue;
if (context->VariableWasRemoved(dom_ref)) continue;
if (!context->CanBeUsedAsLiteral(dom_ref)) continue;
if (implications.contains({ref, dom_ref})) continue;
++num_added;
context->AddImplication(ref, dom_ref);
// The newly added implication can break the hint only if the hint value
// of `ref` is 1 and the hint value of `dom_ref` is 0. In this case the
// call below fixes it by negating both values. Otherwise it does
// nothing and thus preserves its feasibility.
crush.UpdateLiteralsWithDominance(ref, dom_ref);
context->UpdateNewConstraintsVariableUsage();
implications.insert({ref, dom_ref});
implications.insert({NegatedRef(dom_ref), NegatedRef(ref)});
// dom-- or var++ are now forbidden.
increase_is_forbidden[var] = true;
increase_is_forbidden[NegationOf(dom)] = true;
}
}
}
if (num_added > 0) {
VLOG(1) << "Added " << num_added << " domination implications.";
context->UpdateRuleStats("domination: added implications", num_added);
}
// TODO(user): We should probably be able to do something with this.
if (saved_num_operations == context->num_presolve_operations) {
context->UpdateRuleStats("TODO domination: unexploited dominations");
}
return true;
}
} // namespace sat
} // namespace operations_research
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