556 lines
22 KiB
C++
556 lines
22 KiB
C++
// Copyright 2010-2014 Google
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "ortools/sat/lp_utils.h"
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#include <stdlib.h>
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#include <algorithm>
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#include <cmath>
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#include <limits>
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#include <string>
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#include <vector>
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#include "ortools/base/integral_types.h"
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#include "ortools/base/logging.h"
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#include "ortools/base/int_type.h"
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#include "ortools/base/int_type_indexed_vector.h"
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#include "ortools/glop/lp_solver.h"
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#include "ortools/glop/parameters.pb.h"
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#include "ortools/lp_data/lp_types.h"
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#include "ortools/sat/boolean_problem.h"
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#include "ortools/sat/sat_base.h"
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#include "ortools/util/fp_utils.h"
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namespace operations_research {
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namespace sat {
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using glop::ColIndex;
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using glop::Fractional;
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using glop::RowIndex;
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using glop::kInfinity;
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using operations_research::MPConstraintProto;
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using operations_research::MPModelProto;
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using operations_research::MPVariableProto;
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bool ConvertMPModelProtoToCpModelProto(const MPModelProto& mp_model,
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CpModelProto* cp_model) {
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const double kInfinity = std::numeric_limits<double>::infinity();
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CHECK(cp_model != nullptr);
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cp_model->Clear();
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cp_model->set_name(mp_model.name());
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// To make sure we cannot have integer overflow, we use this bound for any
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// unbounded variable.
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//
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// TODO(user): This could be made larger if needed, so be smarter if we have
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// MIP problem that we cannot "convert" because of this. Note however than we
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// cannot go that much further because we need to make sure we will not run
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// into overflow if we add a big linear combination of such variables. It
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// should always be possible for an user to scale its problem so that all
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// relevant quantities are a couple of millions. A LP/MIP solver have a
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// similar condition in disguise because problem with a difference of more
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// than 6 magnitudes between the variable values will likely run into numeric
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// trouble.
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const int64 kMaxVariableBound = static_cast<int64>(1e7);
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int num_truncated_bounds = 0;
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int num_small_domains = 0;
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const int64 kSmallDomainSize = 1000;
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// Add the variables.
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const int num_variables = mp_model.variable_size();
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for (int i = 0; i < num_variables; ++i) {
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const MPVariableProto& mp_var = mp_model.variable(i);
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IntegerVariableProto* cp_var = cp_model->add_variables();
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cp_var->set_name(mp_var.name());
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// Note that we must process the lower bound first.
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for (const bool lower : {true, false}) {
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const double bound = lower ? mp_var.lower_bound() : mp_var.upper_bound();
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if (std::abs(bound) >= kMaxVariableBound) {
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if (std::abs(bound) != kInfinity) ++num_truncated_bounds;
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cp_var->add_domain(lower ? -kMaxVariableBound : kMaxVariableBound);
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continue;
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}
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// Note that the cast is "perfect" because we forbid large values.
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cp_var->add_domain(
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static_cast<int64>(lower ? std::ceil(bound) : std::floor(bound)));
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}
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// Notify if a continuous variable has a small domain as this is likely to
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// make an all integer solution far from a continuous one.
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if (!mp_var.is_integer() &&
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cp_var->domain(1) - cp_var->domain(0) < kSmallDomainSize) {
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++num_small_domains;
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}
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}
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LOG_IF(WARNING, num_truncated_bounds > 0)
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<< num_truncated_bounds << " bounds where truncated to "
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<< kMaxVariableBound << ".";
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LOG_IF(WARNING, num_small_domains > 0)
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<< num_small_domains << " continuous variable domain with less than "
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<< kSmallDomainSize << " values.";
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// Variables needed to scale the double coefficients into int64.
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double max_relative_coeff_error = 0.0;
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double max_scaled_sum_error = 0.0;
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double max_scaling_factor = 0.0;
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double relative_coeff_error = 0.0;
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double scaled_sum_error = 0.0;
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double scaling_factor = 0.0;
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std::vector<double> coefficients;
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std::vector<double> lower_bounds;
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std::vector<double> upper_bounds;
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// Add the constraints. We scale each of them individually.
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for (const MPConstraintProto& mp_constraint : mp_model.constraint()) {
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auto* constraint = cp_model->add_constraints();
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constraint->set_name(mp_constraint.name());
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auto* arg = constraint->mutable_linear();
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// First scale the coefficients of the constraints so that the constraint
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// sum can always be computed without integer overflow.
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coefficients.clear();
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lower_bounds.clear();
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upper_bounds.clear();
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const int num_coeffs = mp_constraint.coefficient_size();
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for (int i = 0; i < num_coeffs; ++i) {
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coefficients.push_back(mp_constraint.coefficient(i));
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const auto& var_proto = cp_model->variables(mp_constraint.var_index(i));
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lower_bounds.push_back(var_proto.domain(0));
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upper_bounds.push_back(var_proto.domain(var_proto.domain_size() - 1));
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}
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// TODO(user): we could use kint64max directly here if our constraint
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// propagation code was a bit more careful about integer overflow.
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GetBestScalingOfDoublesToInt64(coefficients, lower_bounds, upper_bounds,
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kint64max / 2, &scaling_factor,
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&relative_coeff_error, &scaled_sum_error);
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const int64 gcd = ComputeGcdOfRoundedDoubles(coefficients, scaling_factor);
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max_relative_coeff_error =
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std::max(relative_coeff_error, max_relative_coeff_error);
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max_scaling_factor = std::max(scaling_factor / gcd, max_scaling_factor);
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for (int i = 0; i < num_coeffs; ++i) {
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const double scaled_value = mp_constraint.coefficient(i) * scaling_factor;
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const int64 value = static_cast<int64>(std::round(scaled_value)) / gcd;
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if (value != 0) {
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arg->add_vars(mp_constraint.var_index(i));
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arg->add_coeffs(value);
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}
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}
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max_scaled_sum_error =
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std::max(max_scaled_sum_error, scaled_sum_error / scaling_factor);
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// Add the constraint bounds. Because we are sure the scaled constraint fit
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// on an int64, if the scaled bounds are too large, the constraint is either
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// always true or always false.
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const Fractional lb = mp_constraint.lower_bound();
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const Fractional scaled_lb =
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std::round(lb * scaling_factor - scaled_sum_error);
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if (lb == -kInfinity || scaled_lb <= kint64min) {
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arg->add_domain(kint64min);
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} else {
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arg->add_domain(static_cast<int64>(scaled_lb) / gcd);
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}
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const Fractional ub = mp_constraint.upper_bound();
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const Fractional scaled_ub =
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std::round(ub * scaling_factor + scaled_sum_error);
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if (ub == kInfinity || scaled_ub >= kint64max) {
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arg->add_domain(kint64max);
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} else {
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arg->add_domain(static_cast<int64>(scaled_ub) / gcd);
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}
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// TODO(user): checks feasibility (contains zero) or support that in the
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// solver!
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if (arg->vars_size() == 0) constraint->Clear();
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}
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// Display the error/scaling without taking into account the objective first.
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VLOG(1) << "Maximum constraint coefficient relative error: "
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<< max_relative_coeff_error;
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VLOG(1) << "Maximum constraint worst-case sum absolute error: "
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<< max_scaled_sum_error;
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VLOG(1) << "Maximum constraint scaling factor: " << max_scaling_factor;
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// Add the objective. We use kint64max / 2 because the objective_var will
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// also be added to the objective constraint.
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const int64 kMaxObjective = kint64max / 2;
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coefficients.clear();
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lower_bounds.clear();
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upper_bounds.clear();
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for (int i = 0; i < num_variables; ++i) {
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const MPVariableProto& mp_var = mp_model.variable(i);
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if (mp_var.objective_coefficient() == 0.0) continue;
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coefficients.push_back(mp_var.objective_coefficient());
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const auto& var_proto = cp_model->variables(i);
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lower_bounds.push_back(var_proto.domain(0));
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upper_bounds.push_back(var_proto.domain(var_proto.domain_size() - 1));
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}
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if (!coefficients.empty() || mp_model.objective_offset() != 0.0) {
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GetBestScalingOfDoublesToInt64(coefficients, lower_bounds, upper_bounds,
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kMaxObjective, &scaling_factor,
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&relative_coeff_error, &scaled_sum_error);
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const int64 gcd = ComputeGcdOfRoundedDoubles(coefficients, scaling_factor);
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max_relative_coeff_error =
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std::max(relative_coeff_error, max_relative_coeff_error);
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// Display the objective error/scaling.
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VLOG(1) << "objective coefficient relative error: " << relative_coeff_error;
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VLOG(1) << "objective worst-case absolute error: "
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<< scaled_sum_error / scaling_factor;
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VLOG(1) << "objective scaling factor: " << scaling_factor / gcd;
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// Note that here we set the scaling factor for the inverse operation of
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// getting the "true" objective value from the scaled one. Hence the
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// inverse.
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auto* objective = cp_model->mutable_objective();
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const int mult = mp_model.maximize() ? -1 : 1;
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objective->set_offset(mp_model.objective_offset() * scaling_factor / gcd *
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mult);
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objective->set_scaling_factor(1.0 / scaling_factor * gcd * mult);
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for (int i = 0; i < num_variables; ++i) {
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const MPVariableProto& mp_var = mp_model.variable(i);
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const int64 value =
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static_cast<int64>(
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std::round(mp_var.objective_coefficient() * scaling_factor)) /
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gcd;
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if (value != 0) {
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objective->add_vars(i);
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objective->add_coeffs(value * mult);
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}
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}
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}
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// Test the precision of the conversion.
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const double kRelativeTolerance = 1e-2;
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if (max_relative_coeff_error > kRelativeTolerance) {
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LOG(WARNING) << "The relative error during double -> int64 conversion "
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<< "is too high!";
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return false;
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}
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return true;
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}
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bool ConvertBinaryMPModelProtoToBooleanProblem(const MPModelProto& mp_model,
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LinearBooleanProblem* problem) {
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CHECK(problem != nullptr);
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problem->Clear();
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problem->set_name(mp_model.name());
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const int num_variables = mp_model.variable_size();
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problem->set_num_variables(num_variables);
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// Test if the variables are binary variables.
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// Add constraints for the fixed variables.
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for (int var_id(0); var_id < num_variables; ++var_id) {
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const MPVariableProto& mp_var = mp_model.variable(var_id);
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problem->add_var_names(mp_var.name());
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// This will be changed to false as soon as we detect the variable to be
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// non-binary. This is done this way so we can display a nice error message
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// before aborting the function and returning false.
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bool is_binary = mp_var.is_integer();
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const Fractional lb = mp_var.lower_bound();
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const Fractional ub = mp_var.upper_bound();
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if (lb <= -1.0) is_binary = false;
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if (ub >= 2.0) is_binary = false;
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if (is_binary) {
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// 4 cases.
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if (lb <= 0.0 && ub >= 1.0) {
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// Binary variable. Ok.
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} else if (lb <= 1.0 && ub >= 1.0) {
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// Fixed variable at 1.
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LinearBooleanConstraint* constraint = problem->add_constraints();
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constraint->set_lower_bound(1);
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constraint->set_upper_bound(1);
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constraint->add_literals(var_id + 1);
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constraint->add_coefficients(1);
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} else if (lb <= 0.0 && ub >= 0.0) {
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// Fixed variable at 0.
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LinearBooleanConstraint* constraint = problem->add_constraints();
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constraint->set_lower_bound(0);
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constraint->set_upper_bound(0);
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constraint->add_literals(var_id + 1);
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constraint->add_coefficients(1);
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} else {
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// No possible integer value!
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is_binary = false;
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}
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}
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// Abort if the variable is not binary.
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if (!is_binary) {
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LOG(WARNING) << "The variable #" << var_id << " with name "
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<< mp_var.name() << " is not binary. "
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<< "lb: " << lb << " ub: " << ub;
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return false;
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}
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}
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// Variables needed to scale the double coefficients into int64.
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const int64 kInt64Max = std::numeric_limits<int64>::max();
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double max_relative_error = 0.0;
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double max_bound_error = 0.0;
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double max_scaling_factor = 0.0;
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double relative_error = 0.0;
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double scaling_factor = 0.0;
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std::vector<double> coefficients;
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// Add all constraints.
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for (const MPConstraintProto& mp_constraint : mp_model.constraint()) {
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LinearBooleanConstraint* constraint = problem->add_constraints();
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constraint->set_name(mp_constraint.name());
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// First scale the coefficients of the constraints.
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coefficients.clear();
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const int num_coeffs = mp_constraint.coefficient_size();
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for (int i = 0; i < num_coeffs; ++i) {
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coefficients.push_back(mp_constraint.coefficient(i));
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}
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GetBestScalingOfDoublesToInt64(coefficients, kInt64Max, &scaling_factor,
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&relative_error);
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const int64 gcd = ComputeGcdOfRoundedDoubles(coefficients, scaling_factor);
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max_relative_error = std::max(relative_error, max_relative_error);
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max_scaling_factor = std::max(scaling_factor / gcd, max_scaling_factor);
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double bound_error = 0.0;
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for (int i = 0; i < num_coeffs; ++i) {
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const double scaled_value = mp_constraint.coefficient(i) * scaling_factor;
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bound_error += std::abs(round(scaled_value) - scaled_value);
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const int64 value = static_cast<int64>(round(scaled_value)) / gcd;
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if (value != 0) {
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constraint->add_literals(mp_constraint.var_index(i) + 1);
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constraint->add_coefficients(value);
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}
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}
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max_bound_error = std::max(max_bound_error, bound_error);
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// Add the bounds. Note that we do not pass them to
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// GetBestScalingOfDoublesToInt64() because we know that the sum of absolute
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// coefficients of the constraint fit on an int64. If one of the scaled
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// bound overflows, we don't care by how much because in this case the
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// constraint is just trivial or unsatisfiable.
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const Fractional lb = mp_constraint.lower_bound();
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if (lb != -kInfinity) {
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if (lb * scaling_factor > static_cast<double>(kInt64Max)) {
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LOG(WARNING) << "A constraint is trivially unsatisfiable.";
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return false;
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}
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if (lb * scaling_factor > -static_cast<double>(kInt64Max)) {
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// Otherwise, the constraint is not needed.
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constraint->set_lower_bound(
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static_cast<int64>(round(lb * scaling_factor - bound_error)) / gcd);
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}
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}
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const Fractional ub = mp_constraint.upper_bound();
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if (ub != kInfinity) {
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if (ub * scaling_factor < -static_cast<double>(kInt64Max)) {
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LOG(WARNING) << "A constraint is trivially unsatisfiable.";
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return false;
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}
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if (ub * scaling_factor < static_cast<double>(kInt64Max)) {
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// Otherwise, the constraint is not needed.
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constraint->set_upper_bound(
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static_cast<int64>(round(ub * scaling_factor + bound_error)) / gcd);
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}
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}
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}
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// Display the error/scaling without taking into account the objective first.
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LOG(INFO) << "Maximum constraint relative error: " << max_relative_error;
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LOG(INFO) << "Maximum constraint bound error: " << max_bound_error;
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LOG(INFO) << "Maximum constraint scaling factor: " << max_scaling_factor;
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// Add the objective.
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coefficients.clear();
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for (int var_id = 0; var_id < num_variables; ++var_id) {
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const MPVariableProto& mp_var = mp_model.variable(var_id);
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coefficients.push_back(mp_var.objective_coefficient());
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}
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GetBestScalingOfDoublesToInt64(coefficients, kInt64Max, &scaling_factor,
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&relative_error);
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const int64 gcd = ComputeGcdOfRoundedDoubles(coefficients, scaling_factor);
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max_relative_error = std::max(relative_error, max_relative_error);
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// Display the objective error/scaling.
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LOG(INFO) << "objective relative error: " << relative_error;
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LOG(INFO) << "objective scaling factor: " << scaling_factor / gcd;
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LinearObjective* objective = problem->mutable_objective();
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objective->set_offset(mp_model.objective_offset() * scaling_factor / gcd);
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// Note that here we set the scaling factor for the inverse operation of
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// getting the "true" objective value from the scaled one. Hence the inverse.
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objective->set_scaling_factor(1.0 / scaling_factor * gcd);
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for (int var_id = 0; var_id < num_variables; ++var_id) {
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const MPVariableProto& mp_var = mp_model.variable(var_id);
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const int64 value = static_cast<int64>(round(
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mp_var.objective_coefficient() * scaling_factor)) /
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gcd;
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if (value != 0) {
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objective->add_literals(var_id + 1);
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objective->add_coefficients(value);
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}
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}
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// If the problem was a maximization one, we need to modify the objective.
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if (mp_model.maximize()) ChangeOptimizationDirection(problem);
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// Test the precision of the conversion.
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const double kRelativeTolerance = 1e-8;
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if (max_relative_error > kRelativeTolerance) {
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LOG(WARNING) << "The relative error during double -> int64 conversion "
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<< "is too high!";
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return false;
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}
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return true;
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}
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void ConvertBooleanProblemToLinearProgram(const LinearBooleanProblem& problem,
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glop::LinearProgram* lp) {
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lp->Clear();
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for (int i = 0; i < problem.num_variables(); ++i) {
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const ColIndex col = lp->CreateNewVariable();
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lp->SetVariableType(col, glop::LinearProgram::VariableType::INTEGER);
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lp->SetVariableBounds(col, 0.0, 1.0);
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}
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// Variables name are optional.
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if (problem.var_names_size() != 0) {
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CHECK_EQ(problem.var_names_size(), problem.num_variables());
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for (int i = 0; i < problem.num_variables(); ++i) {
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lp->SetVariableName(ColIndex(i), problem.var_names(i));
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}
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}
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for (const LinearBooleanConstraint& constraint : problem.constraints()) {
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|
const RowIndex constraint_index = lp->CreateNewConstraint();
|
|
lp->SetConstraintName(constraint_index, constraint.name());
|
|
double sum = 0.0;
|
|
for (int i = 0; i < constraint.literals_size(); ++i) {
|
|
const int literal = constraint.literals(i);
|
|
const double coeff = constraint.coefficients(i);
|
|
const ColIndex variable_index = ColIndex(abs(literal) - 1);
|
|
if (literal < 0) {
|
|
sum += coeff;
|
|
lp->SetCoefficient(constraint_index, variable_index, -coeff);
|
|
} else {
|
|
lp->SetCoefficient(constraint_index, variable_index, coeff);
|
|
}
|
|
}
|
|
lp->SetConstraintBounds(
|
|
constraint_index,
|
|
constraint.has_lower_bound() ? constraint.lower_bound() - sum
|
|
: -kInfinity,
|
|
constraint.has_upper_bound() ? constraint.upper_bound() - sum
|
|
: kInfinity);
|
|
}
|
|
|
|
// Objective.
|
|
{
|
|
double sum = 0.0;
|
|
const LinearObjective& objective = problem.objective();
|
|
const double scaling_factor = objective.scaling_factor();
|
|
for (int i = 0; i < objective.literals_size(); ++i) {
|
|
const int literal = objective.literals(i);
|
|
const double coeff =
|
|
static_cast<double>(objective.coefficients(i)) * scaling_factor;
|
|
const ColIndex variable_index = ColIndex(abs(literal) - 1);
|
|
if (literal < 0) {
|
|
sum += coeff;
|
|
lp->SetObjectiveCoefficient(variable_index, -coeff);
|
|
} else {
|
|
lp->SetObjectiveCoefficient(variable_index, coeff);
|
|
}
|
|
}
|
|
lp->SetObjectiveOffset((sum + objective.offset()) * scaling_factor);
|
|
lp->SetMaximizationProblem(scaling_factor < 0);
|
|
}
|
|
|
|
lp->CleanUp();
|
|
}
|
|
|
|
int FixVariablesFromSat(const SatSolver& solver, glop::LinearProgram* lp) {
|
|
int num_fixed_variables = 0;
|
|
const Trail& trail = solver.LiteralTrail();
|
|
for (int i = 0; i < trail.Index(); ++i) {
|
|
const BooleanVariable var = trail[i].Variable();
|
|
const int value = trail[i].IsPositive() ? 1.0 : 0.0;
|
|
if (trail.Info(var).level == 0) {
|
|
++num_fixed_variables;
|
|
lp->SetVariableBounds(ColIndex(var.value()), value, value);
|
|
}
|
|
}
|
|
return num_fixed_variables;
|
|
}
|
|
|
|
bool SolveLpAndUseSolutionForSatAssignmentPreference(
|
|
const glop::LinearProgram& lp, SatSolver* sat_solver,
|
|
double max_time_in_seconds) {
|
|
glop::LPSolver solver;
|
|
glop::GlopParameters glop_parameters;
|
|
glop_parameters.set_max_time_in_seconds(max_time_in_seconds);
|
|
solver.SetParameters(glop_parameters);
|
|
const glop::ProblemStatus& status = solver.Solve(lp);
|
|
if (status != glop::ProblemStatus::OPTIMAL &&
|
|
status != glop::ProblemStatus::IMPRECISE &&
|
|
status != glop::ProblemStatus::PRIMAL_FEASIBLE) {
|
|
return false;
|
|
}
|
|
for (ColIndex col(0); col < lp.num_variables(); ++col) {
|
|
const Fractional& value = solver.variable_values()[col];
|
|
sat_solver->SetAssignmentPreference(
|
|
Literal(BooleanVariable(col.value()), round(value) == 1),
|
|
1 - std::abs(value - round(value)));
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool SolveLpAndUseIntegerVariableToStartLNS(const glop::LinearProgram& lp,
|
|
LinearBooleanProblem* problem) {
|
|
glop::LPSolver solver;
|
|
const glop::ProblemStatus& status = solver.Solve(lp);
|
|
if (status != glop::ProblemStatus::OPTIMAL &&
|
|
status != glop::ProblemStatus::PRIMAL_FEASIBLE) return false;
|
|
int num_variable_fixed = 0;
|
|
for (ColIndex col(0); col < lp.num_variables(); ++col) {
|
|
const Fractional tolerance = 1e-5;
|
|
const Fractional& value = solver.variable_values()[col];
|
|
if (value > 1 - tolerance) {
|
|
++num_variable_fixed;
|
|
LinearBooleanConstraint* constraint = problem->add_constraints();
|
|
constraint->set_lower_bound(1);
|
|
constraint->set_upper_bound(1);
|
|
constraint->add_coefficients(1);
|
|
constraint->add_literals(col.value() + 1);
|
|
} else if (value < tolerance) {
|
|
++num_variable_fixed;
|
|
LinearBooleanConstraint* constraint = problem->add_constraints();
|
|
constraint->set_lower_bound(0);
|
|
constraint->set_upper_bound(0);
|
|
constraint->add_coefficients(1);
|
|
constraint->add_literals(col.value() + 1);
|
|
}
|
|
}
|
|
LOG(INFO) << "LNS with " << num_variable_fixed << " fixed variables.";
|
|
return true;
|
|
}
|
|
|
|
} // namespace sat
|
|
} // namespace operations_research
|