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preprocessor.cc
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preprocessor.cc
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// Copyright 2010-2022 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/glop/preprocessor.h"
#include <algorithm>
#include <cmath>
#include <cstdint>
#include <deque>
#include <iomanip>
#include <ios>
#include <limits>
#include <memory>
#include <set>
#include <string>
#include <utility>
#include <vector>
#include "absl/strings/str_format.h"
#include "ortools/base/iterator_adaptors.h"
#include "ortools/base/strong_vector.h"
#include "ortools/glop/revised_simplex.h"
#include "ortools/glop/status.h"
#include "ortools/lp_data/lp_data_utils.h"
#include "ortools/lp_data/lp_types.h"
#include "ortools/lp_data/lp_utils.h"
#include "ortools/lp_data/matrix_utils.h"
namespace operations_research {
namespace glop {
using ::util::Reverse;
namespace {
// Returns an interval as an human readable string for debugging.
std::string IntervalString(Fractional lb, Fractional ub) {
return absl::StrFormat("[%g, %g]", lb, ub);
}
#if defined(_MSC_VER)
double trunc(double d) { return d > 0 ? floor(d) : ceil(d); }
#endif
} // namespace
// --------------------------------------------------------
// Preprocessor
// --------------------------------------------------------
Preprocessor::Preprocessor(const GlopParameters* parameters)
: status_(ProblemStatus::INIT),
parameters_(*parameters),
in_mip_context_(false),
infinite_time_limit_(TimeLimit::Infinite()),
time_limit_(infinite_time_limit_.get()) {}
Preprocessor::~Preprocessor() {}
// --------------------------------------------------------
// MainLpPreprocessor
// --------------------------------------------------------
#define RUN_PREPROCESSOR(name) \
RunAndPushIfRelevant(std::unique_ptr<Preprocessor>(new name(¶meters_)), \
#name, time_limit_, lp)
bool MainLpPreprocessor::Run(LinearProgram* lp) {
RETURN_VALUE_IF_NULL(lp, false);
default_logger_.EnableLogging(parameters_.log_search_progress());
default_logger_.SetLogToStdOut(parameters_.log_to_stdout());
SOLVER_LOG(logger_, "");
SOLVER_LOG(logger_, "Starting presolve...");
initial_num_rows_ = lp->num_constraints();
initial_num_cols_ = lp->num_variables();
initial_num_entries_ = lp->num_entries();
if (parameters_.use_preprocessing()) {
RUN_PREPROCESSOR(ShiftVariableBoundsPreprocessor);
// We run it a few times because running one preprocessor may allow another
// one to remove more stuff.
const int kMaxNumPasses = 20;
for (int i = 0; i < kMaxNumPasses; ++i) {
const int old_stack_size = preprocessors_.size();
RUN_PREPROCESSOR(FixedVariablePreprocessor);
RUN_PREPROCESSOR(SingletonPreprocessor);
RUN_PREPROCESSOR(ForcingAndImpliedFreeConstraintPreprocessor);
RUN_PREPROCESSOR(FreeConstraintPreprocessor);
RUN_PREPROCESSOR(ImpliedFreePreprocessor);
RUN_PREPROCESSOR(UnconstrainedVariablePreprocessor);
RUN_PREPROCESSOR(DoubletonFreeColumnPreprocessor);
RUN_PREPROCESSOR(DoubletonEqualityRowPreprocessor);
// Abort early if none of the preprocessors did something. Technically
// this is true if none of the preprocessors above needs postsolving,
// which has exactly the same meaning for these particular preprocessors.
if (preprocessors_.size() == old_stack_size) {
// We use i here because the last pass did nothing.
SOLVER_LOG(logger_, "Reached fixed point after presolve pass #", i);
break;
}
}
RUN_PREPROCESSOR(EmptyColumnPreprocessor);
RUN_PREPROCESSOR(EmptyConstraintPreprocessor);
// TODO(user): Run them in the loop above if the effect on the running time
// is good. This needs more investigation.
RUN_PREPROCESSOR(ProportionalColumnPreprocessor);
RUN_PREPROCESSOR(ProportionalRowPreprocessor);
// If DualizerPreprocessor was run, we need to do some extra preprocessing.
// This is because it currently adds a lot of zero-cost singleton columns.
const int old_stack_size = preprocessors_.size();
// TODO(user): We probably want to scale the costs before and after this
// preprocessor so that the rhs/objective of the dual are with a good
// magnitude.
RUN_PREPROCESSOR(DualizerPreprocessor);
if (old_stack_size != preprocessors_.size()) {
RUN_PREPROCESSOR(SingletonPreprocessor);
RUN_PREPROCESSOR(FreeConstraintPreprocessor);
RUN_PREPROCESSOR(UnconstrainedVariablePreprocessor);
RUN_PREPROCESSOR(EmptyColumnPreprocessor);
RUN_PREPROCESSOR(EmptyConstraintPreprocessor);
}
RUN_PREPROCESSOR(SingletonColumnSignPreprocessor);
}
// The scaling is controlled by use_scaling, not use_preprocessing.
RUN_PREPROCESSOR(ScalingPreprocessor);
return !preprocessors_.empty();
}
#undef RUN_PREPROCESSOR
void MainLpPreprocessor::RunAndPushIfRelevant(
std::unique_ptr<Preprocessor> preprocessor, const std::string& name,
TimeLimit* time_limit, LinearProgram* lp) {
RETURN_IF_NULL(preprocessor);
RETURN_IF_NULL(time_limit);
if (status_ != ProblemStatus::INIT || time_limit->LimitReached()) return;
const double start_time = time_limit->GetElapsedTime();
preprocessor->SetTimeLimit(time_limit);
// No need to run the preprocessor if the lp is empty.
// TODO(user): without this test, the code is failing as of 2013-03-18.
if (lp->num_variables() == 0 && lp->num_constraints() == 0) {
status_ = ProblemStatus::OPTIMAL;
return;
}
if (preprocessor->Run(lp)) {
const EntryIndex new_num_entries = lp->num_entries();
const double preprocess_time = time_limit->GetElapsedTime() - start_time;
SOLVER_LOG(logger_,
absl::StrFormat(
"%-45s: %d(%d) rows, %d(%d) columns, %d(%d) entries. (%fs)",
name, lp->num_constraints().value(),
(lp->num_constraints() - initial_num_rows_).value(),
lp->num_variables().value(),
(lp->num_variables() - initial_num_cols_).value(),
// static_cast<int64_t> is needed because the Android port
// uses int32_t.
static_cast<int64_t>(new_num_entries.value()),
static_cast<int64_t>(new_num_entries.value() -
initial_num_entries_.value()),
preprocess_time));
status_ = preprocessor->status();
preprocessors_.push_back(std::move(preprocessor));
return;
} else {
// Even if a preprocessor returns false (i.e. no need for postsolve), it
// can detect an issue with the problem.
status_ = preprocessor->status();
if (status_ != ProblemStatus::INIT) {
SOLVER_LOG(logger_, name, " detected that the problem is ",
GetProblemStatusString(status_));
}
}
}
void MainLpPreprocessor::RecoverSolution(ProblemSolution* solution) const {
SCOPED_INSTRUCTION_COUNT(time_limit_);
for (const auto& p : gtl::reversed_view(preprocessors_)) {
p->RecoverSolution(solution);
}
}
void MainLpPreprocessor::DestructiveRecoverSolution(ProblemSolution* solution) {
SCOPED_INSTRUCTION_COUNT(time_limit_);
while (!preprocessors_.empty()) {
preprocessors_.back()->RecoverSolution(solution);
preprocessors_.pop_back();
}
}
// --------------------------------------------------------
// ColumnDeletionHelper
// --------------------------------------------------------
void ColumnsSaver::SaveColumn(ColIndex col, const SparseColumn& column) {
const int index = saved_columns_.size();
CHECK(saved_columns_index_.insert({col, index}).second);
saved_columns_.push_back(column);
}
void ColumnsSaver::SaveColumnIfNotAlreadyDone(ColIndex col,
const SparseColumn& column) {
const int index = saved_columns_.size();
const bool inserted = saved_columns_index_.insert({col, index}).second;
if (inserted) saved_columns_.push_back(column);
}
const SparseColumn& ColumnsSaver::SavedColumn(ColIndex col) const {
const auto it = saved_columns_index_.find(col);
CHECK(it != saved_columns_index_.end());
return saved_columns_[it->second];
}
const SparseColumn& ColumnsSaver::SavedOrEmptyColumn(ColIndex col) const {
const auto it = saved_columns_index_.find(col);
return it == saved_columns_index_.end() ? empty_column_
: saved_columns_[it->second];
}
void ColumnDeletionHelper::Clear() {
is_column_deleted_.clear();
stored_value_.clear();
}
void ColumnDeletionHelper::MarkColumnForDeletion(ColIndex col) {
MarkColumnForDeletionWithState(col, 0.0, VariableStatus::FREE);
}
void ColumnDeletionHelper::MarkColumnForDeletionWithState(
ColIndex col, Fractional fixed_value, VariableStatus status) {
DCHECK_GE(col, 0);
if (col >= is_column_deleted_.size()) {
is_column_deleted_.resize(col + 1, false);
stored_value_.resize(col + 1, 0.0);
stored_status_.resize(col + 1, VariableStatus::FREE);
}
is_column_deleted_[col] = true;
stored_value_[col] = fixed_value;
stored_status_[col] = status;
}
void ColumnDeletionHelper::RestoreDeletedColumns(
ProblemSolution* solution) const {
DenseRow new_primal_values;
VariableStatusRow new_variable_statuses;
ColIndex old_index(0);
for (ColIndex col(0); col < is_column_deleted_.size(); ++col) {
if (is_column_deleted_[col]) {
new_primal_values.push_back(stored_value_[col]);
new_variable_statuses.push_back(stored_status_[col]);
} else {
new_primal_values.push_back(solution->primal_values[old_index]);
new_variable_statuses.push_back(solution->variable_statuses[old_index]);
++old_index;
}
}
// Copy the end of the vectors and swap them with the ones in solution.
const ColIndex num_cols = solution->primal_values.size();
DCHECK_EQ(num_cols, solution->variable_statuses.size());
for (; old_index < num_cols; ++old_index) {
new_primal_values.push_back(solution->primal_values[old_index]);
new_variable_statuses.push_back(solution->variable_statuses[old_index]);
}
new_primal_values.swap(solution->primal_values);
new_variable_statuses.swap(solution->variable_statuses);
}
// --------------------------------------------------------
// RowDeletionHelper
// --------------------------------------------------------
void RowDeletionHelper::Clear() { is_row_deleted_.clear(); }
void RowDeletionHelper::MarkRowForDeletion(RowIndex row) {
DCHECK_GE(row, 0);
if (row >= is_row_deleted_.size()) {
is_row_deleted_.resize(row + 1, false);
}
is_row_deleted_[row] = true;
}
void RowDeletionHelper::UnmarkRow(RowIndex row) {
if (row >= is_row_deleted_.size()) return;
is_row_deleted_[row] = false;
}
const DenseBooleanColumn& RowDeletionHelper::GetMarkedRows() const {
return is_row_deleted_;
}
void RowDeletionHelper::RestoreDeletedRows(ProblemSolution* solution) const {
DenseColumn new_dual_values;
ConstraintStatusColumn new_constraint_statuses;
RowIndex old_index(0);
const RowIndex end = is_row_deleted_.size();
for (RowIndex row(0); row < end; ++row) {
if (is_row_deleted_[row]) {
new_dual_values.push_back(0.0);
new_constraint_statuses.push_back(ConstraintStatus::BASIC);
} else {
new_dual_values.push_back(solution->dual_values[old_index]);
new_constraint_statuses.push_back(
solution->constraint_statuses[old_index]);
++old_index;
}
}
// Copy the end of the vectors and swap them with the ones in solution.
const RowIndex num_rows = solution->dual_values.size();
DCHECK_EQ(num_rows, solution->constraint_statuses.size());
for (; old_index < num_rows; ++old_index) {
new_dual_values.push_back(solution->dual_values[old_index]);
new_constraint_statuses.push_back(solution->constraint_statuses[old_index]);
}
new_dual_values.swap(solution->dual_values);
new_constraint_statuses.swap(solution->constraint_statuses);
}
// --------------------------------------------------------
// EmptyColumnPreprocessor
// --------------------------------------------------------
namespace {
// Computes the status of a variable given its value and bounds. This only works
// with a value exactly at one of the bounds, or a value of 0.0 for free
// variables.
VariableStatus ComputeVariableStatus(Fractional value, Fractional lower_bound,
Fractional upper_bound) {
if (lower_bound == upper_bound) {
DCHECK_EQ(value, lower_bound);
DCHECK(IsFinite(lower_bound));
return VariableStatus::FIXED_VALUE;
}
if (value == lower_bound) {
DCHECK_NE(lower_bound, -kInfinity);
return VariableStatus::AT_LOWER_BOUND;
}
if (value == upper_bound) {
DCHECK_NE(upper_bound, kInfinity);
return VariableStatus::AT_UPPER_BOUND;
}
// TODO(user): restrict this to unbounded variables with a value of zero.
// We can't do that when postsolving infeasible problem. Don't call postsolve
// on an infeasible problem?
return VariableStatus::FREE;
}
// Returns the input with the smallest magnitude or zero if both are infinite.
Fractional MinInMagnitudeOrZeroIfInfinite(Fractional a, Fractional b) {
const Fractional value = std::abs(a) < std::abs(b) ? a : b;
return IsFinite(value) ? value : 0.0;
}
Fractional MagnitudeOrZeroIfInfinite(Fractional value) {
return IsFinite(value) ? std::abs(value) : 0.0;
}
// Returns the maximum magnitude of the finite variable bounds of the given
// linear program.
Fractional ComputeMaxVariableBoundsMagnitude(const LinearProgram& lp) {
Fractional max_bounds_magnitude = 0.0;
const ColIndex num_cols = lp.num_variables();
for (ColIndex col(0); col < num_cols; ++col) {
max_bounds_magnitude = std::max(
max_bounds_magnitude,
std::max(MagnitudeOrZeroIfInfinite(lp.variable_lower_bounds()[col]),
MagnitudeOrZeroIfInfinite(lp.variable_upper_bounds()[col])));
}
return max_bounds_magnitude;
}
} // namespace
bool EmptyColumnPreprocessor::Run(LinearProgram* lp) {
SCOPED_INSTRUCTION_COUNT(time_limit_);
RETURN_VALUE_IF_NULL(lp, false);
column_deletion_helper_.Clear();
const ColIndex num_cols = lp->num_variables();
for (ColIndex col(0); col < num_cols; ++col) {
if (lp->GetSparseColumn(col).IsEmpty()) {
const Fractional lower_bound = lp->variable_lower_bounds()[col];
const Fractional upper_bound = lp->variable_upper_bounds()[col];
const Fractional objective_coefficient =
lp->GetObjectiveCoefficientForMinimizationVersion(col);
Fractional value;
if (objective_coefficient == 0) {
// Any feasible value will do.
if (upper_bound != kInfinity) {
value = upper_bound;
} else {
if (lower_bound != -kInfinity) {
value = lower_bound;
} else {
value = Fractional(0.0);
}
}
} else {
value = objective_coefficient > 0 ? lower_bound : upper_bound;
if (!IsFinite(value)) {
VLOG(1) << "Problem INFEASIBLE_OR_UNBOUNDED, empty column " << col
<< " has a minimization cost of " << objective_coefficient
<< " and bounds"
<< " [" << lower_bound << "," << upper_bound << "]";
status_ = ProblemStatus::INFEASIBLE_OR_UNBOUNDED;
return false;
}
lp->SetObjectiveOffset(lp->objective_offset() +
value * lp->objective_coefficients()[col]);
}
column_deletion_helper_.MarkColumnForDeletionWithState(
col, value, ComputeVariableStatus(value, lower_bound, upper_bound));
}
}
lp->DeleteColumns(column_deletion_helper_.GetMarkedColumns());
return !column_deletion_helper_.IsEmpty();
}
void EmptyColumnPreprocessor::RecoverSolution(ProblemSolution* solution) const {
SCOPED_INSTRUCTION_COUNT(time_limit_);
RETURN_IF_NULL(solution);
column_deletion_helper_.RestoreDeletedColumns(solution);
}
// --------------------------------------------------------
// ProportionalColumnPreprocessor
// --------------------------------------------------------
namespace {
// Subtracts 'multiple' times the column col of the given linear program from
// the constraint bounds. That is, for a non-zero entry of coefficient c,
// c * multiple is subtracted from both the constraint upper and lower bound.
void SubtractColumnMultipleFromConstraintBound(ColIndex col,
Fractional multiple,
LinearProgram* lp) {
DenseColumn* lbs = lp->mutable_constraint_lower_bounds();
DenseColumn* ubs = lp->mutable_constraint_upper_bounds();
for (const SparseColumn::Entry e : lp->GetSparseColumn(col)) {
const RowIndex row = e.row();
const Fractional delta = multiple * e.coefficient();
(*lbs)[row] -= delta;
(*ubs)[row] -= delta;
}
// While not needed for correctness, this allows the presolved problem to
// have the same objective value as the original one.
lp->SetObjectiveOffset(lp->objective_offset() +
lp->objective_coefficients()[col] * multiple);
}
// Struct used to detect proportional columns with the same cost. For that, a
// vector of such struct will be sorted, and only the columns that end up
// together need to be compared.
struct ColumnWithRepresentativeAndScaledCost {
ColumnWithRepresentativeAndScaledCost(ColIndex _col, ColIndex _representative,
Fractional _scaled_cost)
: col(_col), representative(_representative), scaled_cost(_scaled_cost) {}
ColIndex col;
ColIndex representative;
Fractional scaled_cost;
bool operator<(const ColumnWithRepresentativeAndScaledCost& other) const {
if (representative == other.representative) {
if (scaled_cost == other.scaled_cost) {
return col < other.col;
}
return scaled_cost < other.scaled_cost;
}
return representative < other.representative;
}
};
} // namespace
bool ProportionalColumnPreprocessor::Run(LinearProgram* lp) {
SCOPED_INSTRUCTION_COUNT(time_limit_);
RETURN_VALUE_IF_NULL(lp, false);
ColMapping mapping = FindProportionalColumns(
lp->GetSparseMatrix(), parameters_.preprocessor_zero_tolerance());
// Compute some statistics and make each class representative point to itself
// in the mapping. Also store the columns that are proportional to at least
// another column in proportional_columns to iterate on them more efficiently.
//
// TODO(user): Change FindProportionalColumns for this?
int num_proportionality_classes = 0;
std::vector<ColIndex> proportional_columns;
for (ColIndex col(0); col < mapping.size(); ++col) {
const ColIndex representative = mapping[col];
if (representative != kInvalidCol) {
if (mapping[representative] == kInvalidCol) {
proportional_columns.push_back(representative);
++num_proportionality_classes;
mapping[representative] = representative;
}
proportional_columns.push_back(col);
}
}
if (proportional_columns.empty()) return false;
VLOG(1) << "The problem contains " << proportional_columns.size()
<< " columns which belong to " << num_proportionality_classes
<< " proportionality classes.";
// Note(user): using the first coefficient may not give the best precision.
const ColIndex num_cols = lp->num_variables();
column_factors_.assign(num_cols, 0.0);
for (const ColIndex col : proportional_columns) {
const SparseColumn& column = lp->GetSparseColumn(col);
column_factors_[col] = column.GetFirstCoefficient();
}
// This is only meaningful for column representative.
//
// The reduced cost of a column is 'cost - dual_values.column' and we know
// that for all proportional columns, 'dual_values.column /
// column_factors_[col]' is the same. Here, we bound this quantity which is
// related to the cost 'slope' of a proportional column:
// cost / column_factors_[col].
DenseRow slope_lower_bound(num_cols, -kInfinity);
DenseRow slope_upper_bound(num_cols, +kInfinity);
for (const ColIndex col : proportional_columns) {
const ColIndex representative = mapping[col];
// We reason in terms of a minimization problem here.
const bool is_rc_positive_or_zero =
(lp->variable_upper_bounds()[col] == kInfinity);
const bool is_rc_negative_or_zero =
(lp->variable_lower_bounds()[col] == -kInfinity);
bool is_slope_upper_bounded = is_rc_positive_or_zero;
bool is_slope_lower_bounded = is_rc_negative_or_zero;
if (column_factors_[col] < 0.0) {
std::swap(is_slope_lower_bounded, is_slope_upper_bounded);
}
const Fractional slope =
lp->GetObjectiveCoefficientForMinimizationVersion(col) /
column_factors_[col];
if (is_slope_lower_bounded) {
slope_lower_bound[representative] =
std::max(slope_lower_bound[representative], slope);
}
if (is_slope_upper_bounded) {
slope_upper_bound[representative] =
std::min(slope_upper_bound[representative], slope);
}
}
// Deal with empty slope intervals.
for (const ColIndex col : proportional_columns) {
const ColIndex representative = mapping[col];
// This is only needed for class representative columns.
if (representative == col) {
if (!IsSmallerWithinFeasibilityTolerance(
slope_lower_bound[representative],
slope_upper_bound[representative])) {
VLOG(1) << "Problem INFEASIBLE_OR_UNBOUNDED, no feasible dual values"
<< " can satisfy the constraints of the proportional columns"
<< " with representative " << representative << "."
<< " the associated quantity must be in ["
<< slope_lower_bound[representative] << ","
<< slope_upper_bound[representative] << "].";
status_ = ProblemStatus::INFEASIBLE_OR_UNBOUNDED;
return false;
}
}
}
// Now, fix the columns that can be fixed to one of their bounds.
for (const ColIndex col : proportional_columns) {
const ColIndex representative = mapping[col];
const Fractional slope =
lp->GetObjectiveCoefficientForMinimizationVersion(col) /
column_factors_[col];
// The scaled reduced cost is slope - quantity.
bool variable_can_be_fixed = false;
Fractional target_bound = 0.0;
const Fractional lower_bound = lp->variable_lower_bounds()[col];
const Fractional upper_bound = lp->variable_upper_bounds()[col];
if (!IsSmallerWithinFeasibilityTolerance(slope_lower_bound[representative],
slope)) {
// The scaled reduced cost is < 0.
variable_can_be_fixed = true;
target_bound = (column_factors_[col] >= 0.0) ? upper_bound : lower_bound;
} else if (!IsSmallerWithinFeasibilityTolerance(
slope, slope_upper_bound[representative])) {
// The scaled reduced cost is > 0.
variable_can_be_fixed = true;
target_bound = (column_factors_[col] >= 0.0) ? lower_bound : upper_bound;
}
if (variable_can_be_fixed) {
// Clear mapping[col] so this column will not be considered for the next
// stage.
mapping[col] = kInvalidCol;
if (!IsFinite(target_bound)) {
VLOG(1) << "Problem INFEASIBLE_OR_UNBOUNDED.";
status_ = ProblemStatus::INFEASIBLE_OR_UNBOUNDED;
return false;
} else {
SubtractColumnMultipleFromConstraintBound(col, target_bound, lp);
column_deletion_helper_.MarkColumnForDeletionWithState(
col, target_bound,
ComputeVariableStatus(target_bound, lower_bound, upper_bound));
}
}
}
// Merge the variables with the same scaled cost.
std::vector<ColumnWithRepresentativeAndScaledCost> sorted_columns;
for (const ColIndex col : proportional_columns) {
const ColIndex representative = mapping[col];
// This test is needed because we already removed some columns.
if (mapping[col] != kInvalidCol) {
sorted_columns.push_back(ColumnWithRepresentativeAndScaledCost(
col, representative,
lp->objective_coefficients()[col] / column_factors_[col]));
}
}
std::sort(sorted_columns.begin(), sorted_columns.end());
// All this will be needed during postsolve.
merged_columns_.assign(num_cols, kInvalidCol);
lower_bounds_.assign(num_cols, -kInfinity);
upper_bounds_.assign(num_cols, kInfinity);
new_lower_bounds_.assign(num_cols, -kInfinity);
new_upper_bounds_.assign(num_cols, kInfinity);
for (int i = 0; i < sorted_columns.size();) {
const ColIndex target_col = sorted_columns[i].col;
const ColIndex target_representative = sorted_columns[i].representative;
const Fractional target_scaled_cost = sorted_columns[i].scaled_cost;
// Save the initial bounds before modifying them.
lower_bounds_[target_col] = lp->variable_lower_bounds()[target_col];
upper_bounds_[target_col] = lp->variable_upper_bounds()[target_col];
int num_merged = 0;
for (++i; i < sorted_columns.size(); ++i) {
if (sorted_columns[i].representative != target_representative) break;
if (std::abs(sorted_columns[i].scaled_cost - target_scaled_cost) >=
parameters_.preprocessor_zero_tolerance()) {
break;
}
++num_merged;
const ColIndex col = sorted_columns[i].col;
const Fractional lower_bound = lp->variable_lower_bounds()[col];
const Fractional upper_bound = lp->variable_upper_bounds()[col];
lower_bounds_[col] = lower_bound;
upper_bounds_[col] = upper_bound;
merged_columns_[col] = target_col;
// This is a bit counter intuitive, but when a column is divided by x,
// the corresponding bounds have to be multiplied by x.
const Fractional bound_factor =
column_factors_[col] / column_factors_[target_col];
// We need to shift the variable so that a basic solution of the new
// problem can easily be converted to a basic solution of the original
// problem.
// A feasible value for the variable must be chosen, and the variable must
// be shifted by this value. This is done to make sure that it will be
// possible to recreate a basic solution of the original problem from a
// basic solution of the pre-solved problem during post-solve.
const Fractional target_value =
MinInMagnitudeOrZeroIfInfinite(lower_bound, upper_bound);
Fractional lower_diff = (lower_bound - target_value) * bound_factor;
Fractional upper_diff = (upper_bound - target_value) * bound_factor;
if (bound_factor < 0.0) {
std::swap(lower_diff, upper_diff);
}
lp->SetVariableBounds(
target_col, lp->variable_lower_bounds()[target_col] + lower_diff,
lp->variable_upper_bounds()[target_col] + upper_diff);
SubtractColumnMultipleFromConstraintBound(col, target_value, lp);
column_deletion_helper_.MarkColumnForDeletionWithState(
col, target_value,
ComputeVariableStatus(target_value, lower_bound, upper_bound));
}
// If at least one column was merged, the target column must be shifted like
// the other columns in the same equivalence class for the same reason (see
// above).
if (num_merged > 0) {
merged_columns_[target_col] = target_col;
const Fractional target_value = MinInMagnitudeOrZeroIfInfinite(
lower_bounds_[target_col], upper_bounds_[target_col]);
lp->SetVariableBounds(
target_col, lp->variable_lower_bounds()[target_col] - target_value,
lp->variable_upper_bounds()[target_col] - target_value);
SubtractColumnMultipleFromConstraintBound(target_col, target_value, lp);
new_lower_bounds_[target_col] = lp->variable_lower_bounds()[target_col];
new_upper_bounds_[target_col] = lp->variable_upper_bounds()[target_col];
}
}
lp->DeleteColumns(column_deletion_helper_.GetMarkedColumns());
return !column_deletion_helper_.IsEmpty();
}
void ProportionalColumnPreprocessor::RecoverSolution(
ProblemSolution* solution) const {
SCOPED_INSTRUCTION_COUNT(time_limit_);
RETURN_IF_NULL(solution);
column_deletion_helper_.RestoreDeletedColumns(solution);
// The rest of this function is to unmerge the columns so that the solution be
// primal-feasible.
const ColIndex num_cols = merged_columns_.size();
DenseBooleanRow is_representative_basic(num_cols, false);
DenseBooleanRow is_distance_to_upper_bound(num_cols, false);
DenseRow distance_to_bound(num_cols, 0.0);
DenseRow wanted_value(num_cols, 0.0);
// The first pass is a loop over the representatives to compute the current
// distance to the new bounds.
for (ColIndex col(0); col < num_cols; ++col) {
if (merged_columns_[col] == col) {
const Fractional value = solution->primal_values[col];
const Fractional distance_to_upper_bound = new_upper_bounds_[col] - value;
const Fractional distance_to_lower_bound = value - new_lower_bounds_[col];
if (distance_to_upper_bound < distance_to_lower_bound) {
distance_to_bound[col] = distance_to_upper_bound;
is_distance_to_upper_bound[col] = true;
} else {
distance_to_bound[col] = distance_to_lower_bound;
is_distance_to_upper_bound[col] = false;
}
is_representative_basic[col] =
solution->variable_statuses[col] == VariableStatus::BASIC;
// Restore the representative value to a feasible value of the initial
// variable. Now all the merged variable are at a feasible value.
wanted_value[col] = value;
solution->primal_values[col] = MinInMagnitudeOrZeroIfInfinite(
lower_bounds_[col], upper_bounds_[col]);
solution->variable_statuses[col] = ComputeVariableStatus(
solution->primal_values[col], lower_bounds_[col], upper_bounds_[col]);
}
}
// Second pass to correct the values.
for (ColIndex col(0); col < num_cols; ++col) {
const ColIndex representative = merged_columns_[col];
if (representative != kInvalidCol) {
if (IsFinite(distance_to_bound[representative])) {
// If the distance is finite, then each variable is set to its
// corresponding bound (the one from which the distance is computed) and
// is then changed by as much as possible until the distance is zero.
const Fractional bound_factor =
column_factors_[col] / column_factors_[representative];
const Fractional scaled_distance =
distance_to_bound[representative] / std::abs(bound_factor);
const Fractional width = upper_bounds_[col] - lower_bounds_[col];
const bool to_upper_bound =
(bound_factor > 0.0) == is_distance_to_upper_bound[representative];
if (width <= scaled_distance) {
solution->primal_values[col] =
to_upper_bound ? lower_bounds_[col] : upper_bounds_[col];
solution->variable_statuses[col] =
ComputeVariableStatus(solution->primal_values[col],
lower_bounds_[col], upper_bounds_[col]);
distance_to_bound[representative] -= width * std::abs(bound_factor);
} else {
solution->primal_values[col] =
to_upper_bound ? upper_bounds_[col] - scaled_distance
: lower_bounds_[col] + scaled_distance;
solution->variable_statuses[col] =
is_representative_basic[representative]
? VariableStatus::BASIC
: ComputeVariableStatus(solution->primal_values[col],
lower_bounds_[col],
upper_bounds_[col]);
distance_to_bound[representative] = 0.0;
is_representative_basic[representative] = false;
}
} else {
// If the distance is not finite, then only one variable needs to be
// changed from its current feasible value in order to have a
// primal-feasible solution.
const Fractional error = wanted_value[representative];
if (error == 0.0) {
if (is_representative_basic[representative]) {
solution->variable_statuses[col] = VariableStatus::BASIC;
is_representative_basic[representative] = false;
}
} else {
const Fractional bound_factor =
column_factors_[col] / column_factors_[representative];
const bool use_this_variable =
(error * bound_factor > 0.0) ? (upper_bounds_[col] == kInfinity)
: (lower_bounds_[col] == -kInfinity);
if (use_this_variable) {
wanted_value[representative] = 0.0;
solution->primal_values[col] += error / bound_factor;
if (is_representative_basic[representative]) {
solution->variable_statuses[col] = VariableStatus::BASIC;
is_representative_basic[representative] = false;
} else {
// This should not happen on an OPTIMAL or FEASIBLE solution.
DCHECK(solution->status != ProblemStatus::OPTIMAL &&
solution->status != ProblemStatus::PRIMAL_FEASIBLE);
solution->variable_statuses[col] = VariableStatus::FREE;
}
}
}
}
}
}
}
// --------------------------------------------------------
// ProportionalRowPreprocessor
// --------------------------------------------------------
bool ProportionalRowPreprocessor::Run(LinearProgram* lp) {
SCOPED_INSTRUCTION_COUNT(time_limit_);
RETURN_VALUE_IF_NULL(lp, false);
const RowIndex num_rows = lp->num_constraints();
const SparseMatrix& transpose = lp->GetTransposeSparseMatrix();
// Use the first coefficient of each row to compute the proportionality
// factor. Note that the sign is important.
//
// Note(user): using the first coefficient may not give the best precision.
row_factors_.assign(num_rows, 0.0);
for (RowIndex row(0); row < num_rows; ++row) {
const SparseColumn& row_transpose = transpose.column(RowToColIndex(row));
if (!row_transpose.IsEmpty()) {
row_factors_[row] = row_transpose.GetFirstCoefficient();
}
}
// The new row bounds (only meaningful for the proportional rows).
DenseColumn lower_bounds(num_rows, -kInfinity);
DenseColumn upper_bounds(num_rows, +kInfinity);
// Where the new bounds are coming from. Only for the constraints that stay
// in the lp and are modified, kInvalidRow otherwise.
upper_bound_sources_.assign(num_rows, kInvalidRow);
lower_bound_sources_.assign(num_rows, kInvalidRow);
// Initialization.
// We need the first representative of each proportional row class to point to
// itself for the loop below. TODO(user): Already return such a mapping from
// FindProportionalColumns()?
ColMapping mapping = FindProportionalColumns(
transpose, parameters_.preprocessor_zero_tolerance());
DenseBooleanColumn is_a_representative(num_rows, false);
int num_proportional_rows = 0;
for (RowIndex row(0); row < num_rows; ++row) {
const ColIndex representative_row_as_col = mapping[RowToColIndex(row)];
if (representative_row_as_col != kInvalidCol) {
mapping[representative_row_as_col] = representative_row_as_col;
is_a_representative[ColToRowIndex(representative_row_as_col)] = true;
++num_proportional_rows;
}
}
// Compute the bound of each representative as implied by the rows
// which are proportional to it. Also keep the source row of each bound.
for (RowIndex row(0); row < num_rows; ++row) {
const ColIndex row_as_col = RowToColIndex(row);
if (mapping[row_as_col] != kInvalidCol) {
// For now, delete all the rows that are proportional to another one.
// Note that we will unmark the final representative of this class later.
row_deletion_helper_.MarkRowForDeletion(row);
const RowIndex representative_row = ColToRowIndex(mapping[row_as_col]);
const Fractional factor =
row_factors_[representative_row] / row_factors_[row];
Fractional implied_lb = factor * lp->constraint_lower_bounds()[row];
Fractional implied_ub = factor * lp->constraint_upper_bounds()[row];
if (factor < 0.0) {
std::swap(implied_lb, implied_ub);
}
// TODO(user): if the bounds are equal, use the largest row in magnitude?
if (implied_lb >= lower_bounds[representative_row]) {
lower_bounds[representative_row] = implied_lb;
lower_bound_sources_[representative_row] = row;
}
if (implied_ub <= upper_bounds[representative_row]) {
upper_bounds[representative_row] = implied_ub;
upper_bound_sources_[representative_row] = row;
}
}
}
// For maximum precision, and also to simplify the postsolve, we choose
// a representative for each class of proportional columns that has at least
// one of the two tightest bounds.
for (RowIndex row(0); row < num_rows; ++row) {
if (!is_a_representative[row]) continue;
const RowIndex lower_source = lower_bound_sources_[row];
const RowIndex upper_source = upper_bound_sources_[row];
lower_bound_sources_[row] = kInvalidRow;
upper_bound_sources_[row] = kInvalidRow;
DCHECK_NE(lower_source, kInvalidRow);
DCHECK_NE(upper_source, kInvalidRow);
if (lower_source == upper_source) {
// In this case, a simple change of representative is enough.
// The constraint bounds of the representative will not change.
DCHECK_NE(lower_source, kInvalidRow);
row_deletion_helper_.UnmarkRow(lower_source);
} else {
// Report ProblemStatus::PRIMAL_INFEASIBLE if the new lower bound is not
// lower than the new upper bound modulo the default tolerance.
if (!IsSmallerWithinFeasibilityTolerance(lower_bounds[row],
upper_bounds[row])) {
status_ = ProblemStatus::PRIMAL_INFEASIBLE;
return false;
}
// Special case for fixed rows.
if (lp->constraint_lower_bounds()[lower_source] ==
lp->constraint_upper_bounds()[lower_source]) {
row_deletion_helper_.UnmarkRow(lower_source);
continue;
}
if (lp->constraint_lower_bounds()[upper_source] ==
lp->constraint_upper_bounds()[upper_source]) {
row_deletion_helper_.UnmarkRow(upper_source);
continue;
}
// This is the only case where a more complex postsolve is needed.
// To maximize precision, the class representative is changed to either
// upper_source or lower_source depending of which row has the largest
// proportionality factor.
RowIndex new_representative = lower_source;
RowIndex other = upper_source;
if (std::abs(row_factors_[new_representative]) <
std::abs(row_factors_[other])) {
std::swap(new_representative, other);
}
// Initialize the new bounds with the implied ones.
const Fractional factor =
row_factors_[new_representative] / row_factors_[other];
Fractional new_lb = factor * lp->constraint_lower_bounds()[other];
Fractional new_ub = factor * lp->constraint_upper_bounds()[other];
if (factor < 0.0) {
std::swap(new_lb, new_ub);
}
lower_bound_sources_[new_representative] = new_representative;
upper_bound_sources_[new_representative] = new_representative;
if (new_lb > lp->constraint_lower_bounds()[new_representative]) {
lower_bound_sources_[new_representative] = other;
} else {
new_lb = lp->constraint_lower_bounds()[new_representative];
}
if (new_ub < lp->constraint_upper_bounds()[new_representative]) {
upper_bound_sources_[new_representative] = other;
} else {
new_ub = lp->constraint_upper_bounds()[new_representative];
}
const RowIndex new_lower_source =
lower_bound_sources_[new_representative];
if (new_lower_source == upper_bound_sources_[new_representative]) {
row_deletion_helper_.UnmarkRow(new_lower_source);
lower_bound_sources_[new_representative] = kInvalidRow;
upper_bound_sources_[new_representative] = kInvalidRow;
continue;
}
// Take care of small numerical imprecision by making sure that lb <= ub.
// Note that if the imprecision was greater than the tolerance, the code
// at the beginning of this block would have reported
// ProblemStatus::PRIMAL_INFEASIBLE.
DCHECK(IsSmallerWithinFeasibilityTolerance(new_lb, new_ub));
if (new_lb > new_ub) {
if (lower_bound_sources_[new_representative] == new_representative) {
new_ub = lp->constraint_lower_bounds()[new_representative];
} else {