a7f49a2585
* rename swig files .i in .swig * update constraint_solver and routing * backport math_opt changes * move dynamic loading to ortools/third_party_solvers
1245 lines
54 KiB
C++
1245 lines
54 KiB
C++
// Copyright 2010-2025 Google LLC
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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 <algorithm>
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#include <atomic>
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#include <cstdint>
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#include <functional>
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#include <limits>
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#include <memory>
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#include <ostream>
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#include <utility>
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#include <vector>
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#include "absl/container/btree_map.h"
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#include "absl/container/flat_hash_map.h"
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#include "absl/log/check.h"
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#include "absl/time/time.h"
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#include "absl/types/span.h"
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#include "ortools/base/map_util.h"
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#include "ortools/constraint_solver/constraint_solver.h"
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#include "ortools/constraint_solver/routing.h"
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#include "ortools/constraint_solver/routing_parameters.pb.h"
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#include "ortools/constraint_solver/routing_types.h"
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#include "ortools/sat/cp_model.pb.h"
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#include "ortools/sat/cp_model_solver.h"
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#include "ortools/sat/integer_base.h"
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#include "ortools/sat/model.h"
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#include "ortools/sat/sat_parameters.pb.h"
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#include "ortools/util/bitset.h"
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#include "ortools/util/optional_boolean.pb.h"
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#include "ortools/util/saturated_arithmetic.h"
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#include "ortools/util/time_limit.h"
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namespace operations_research {
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namespace sat {
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namespace {
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using operations_research::sat::BoolArgumentProto;
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using operations_research::sat::CircuitConstraintProto;
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using operations_research::sat::ConstraintProto;
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using operations_research::sat::CpModelProto;
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using operations_research::sat::CpObjectiveProto;
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using operations_research::sat::CpSolverResponse;
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using operations_research::sat::CpSolverStatus;
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using operations_research::sat::IntegerVariableProto;
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using operations_research::sat::kMaxIntegerValue;
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using operations_research::sat::kMinIntegerValue;
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using operations_research::sat::LinearConstraintProto;
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using operations_research::sat::Model;
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using operations_research::sat::NewSatParameters;
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using operations_research::sat::PartialVariableAssignment;
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using operations_research::sat::RoutesConstraintProto;
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using operations_research::sat::SatParameters;
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// As of 07/2019, TSPs and VRPs with homogeneous fleets of vehicles are
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// supported.
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// TODO(user): Support any type of constraints.
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// TODO(user): Make VRPs properly support optional nodes.
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bool RoutingModelCanBeSolvedBySat(const RoutingModel& model) {
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return model.GetVehicleClassesCount() == 1;
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}
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// Adds an integer variable to a CpModelProto, returning its index in the proto.
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int AddVariable(CpModelProto* cp_model, int64_t lb, int64_t ub) {
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const int index = cp_model->variables_size();
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IntegerVariableProto* const var = cp_model->add_variables();
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var->add_domain(lb);
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var->add_domain(ub);
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return index;
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}
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// Adds a linear constraint, enforcing
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// enforcement_literals -> lower_bound <= sum variable * coeff <= upper_bound.
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void AddLinearConstraint(
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CpModelProto* cp_model, int64_t lower_bound, int64_t upper_bound,
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absl::Span<const std::pair<int, double>> variable_coeffs,
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absl::Span<const int> enforcement_literals) {
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CHECK_LE(lower_bound, upper_bound);
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ConstraintProto* ct = cp_model->add_constraints();
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for (const int enforcement_literal : enforcement_literals) {
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ct->add_enforcement_literal(enforcement_literal);
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}
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LinearConstraintProto* arg = ct->mutable_linear();
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arg->add_domain(lower_bound);
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arg->add_domain(upper_bound);
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for (const auto [var, coeff] : variable_coeffs) {
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arg->add_vars(var);
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arg->add_coeffs(coeff);
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}
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}
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// Adds a linear constraint, enforcing
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// lower_bound <= sum variable * coeff <= upper_bound.
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void AddLinearConstraint(
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CpModelProto* cp_model, int64_t lower_bound, int64_t upper_bound,
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absl::Span<const std::pair<int, double>> variable_coeffs) {
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AddLinearConstraint(cp_model, lower_bound, upper_bound, variable_coeffs, {});
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}
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// Returns the unique depot node used in the CP-SAT models (as of 01/2020).
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int64_t GetDepotFromModel(const RoutingModel& model) { return model.Start(0); }
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// Structure to keep track of arcs created.
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struct Arc {
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int tail;
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int head;
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friend bool operator==(const Arc& a, const Arc& b) {
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return a.tail == b.tail && a.head == b.head;
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}
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friend bool operator!=(const Arc& a, const Arc& b) { return !(a == b); }
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friend bool operator<(const Arc& a, const Arc& b) {
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return a.tail == b.tail ? a.head < b.head : a.tail < b.tail;
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}
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friend std::ostream& operator<<(std::ostream& strm, const Arc& arc) {
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return strm << "{" << arc.tail << ", " << arc.head << "}";
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}
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template <typename H>
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friend H AbslHashValue(H h, const Arc& a) {
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return H::combine(std::move(h), a.tail, a.head);
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}
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};
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using ArcVarMap =
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absl::btree_map<Arc, int>; // needs to be stable when iterating
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void AddSoftCumulBounds(const RoutingDimension* dimension, int index, int cumul,
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int64_t cumul_min, int64_t cumul_max,
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CpModelProto* cp_model) {
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{
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const int64_t soft_ub_coef =
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dimension->GetCumulVarSoftUpperBoundCoefficient(index);
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if (soft_ub_coef != 0) {
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const int64_t soft_ub = dimension->GetCumulVarSoftUpperBound(index);
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const int soft_ub_var =
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AddVariable(cp_model, 0, CapSub(cumul_max, soft_ub));
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// soft_ub_var >= cumul - soft_ub
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AddLinearConstraint(cp_model, std::numeric_limits<int64_t>::min(),
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soft_ub, {{cumul, 1}, {soft_ub_var, -1}});
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cp_model->mutable_objective()->add_vars(soft_ub_var);
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cp_model->mutable_objective()->add_coeffs(soft_ub_coef);
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}
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}
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{
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const int64_t soft_lb_coef =
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dimension->GetCumulVarSoftLowerBoundCoefficient(index);
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if (soft_lb_coef != 0) {
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const int64_t soft_lb = dimension->GetCumulVarSoftLowerBound(index);
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const int soft_lb_var =
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AddVariable(cp_model, 0, CapSub(soft_lb, cumul_min));
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// soft_lb_var >= soft_lb - cumul
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AddLinearConstraint(cp_model, soft_lb,
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std::numeric_limits<int64_t>::max(),
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{{cumul, 1}, {soft_lb_var, 1}});
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cp_model->mutable_objective()->add_vars(soft_lb_var);
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cp_model->mutable_objective()->add_coeffs(soft_lb_coef);
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}
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}
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}
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// Adds all dimensions to a CpModelProto. Only adds path cumul constraints and
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// cumul bounds.
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void AddDimensions(const RoutingModel& model, const ArcVarMap& arc_vars,
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CpModelProto* cp_model) {
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for (const RoutingDimension* dimension : model.GetDimensions()) {
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// Only a single vehicle class.
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const RoutingModel::TransitCallback2& transit =
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dimension->transit_evaluator(0);
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const int num_cumuls = dimension->cumuls().size();
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std::vector<int> cumuls(num_cumuls, -1);
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const int64_t min_start = dimension->cumuls()[model.Start(0)]->Min();
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const int64_t max_end = std::min(dimension->cumuls()[model.End(0)]->Max(),
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dimension->vehicle_capacities()[0]);
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for (int i = 0; i < cumuls.size(); ++i) {
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if (model.IsStart(i) || model.IsEnd(i)) continue;
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// Reducing bounds supposing the triangular inequality.
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const int64_t cumul_min = std::max<int64_t>(
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std::numeric_limits<int64_t>::min() / num_cumuls,
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std::max(dimension->cumuls()[i]->Min(),
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CapAdd(transit(model.Start(0), i), min_start)));
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const int64_t cumul_max = std::min<int64_t>(
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std::numeric_limits<int64_t>::max() / num_cumuls,
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std::min(dimension->cumuls()[i]->Max(),
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CapSub(max_end, transit(i, model.End(0)))));
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cumuls[i] = AddVariable(cp_model, cumul_min, cumul_max);
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AddSoftCumulBounds(dimension, i, cumuls[i], cumul_min, cumul_max,
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cp_model);
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}
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for (const auto arc_var : arc_vars) {
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const int tail = arc_var.first.tail;
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const int head = arc_var.first.head;
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if (tail == head || model.IsStart(tail) || model.IsStart(head)) continue;
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// arc[tail][head] -> cumuls[head] >= cumuls[tail] + transit.
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// This is a relaxation of the model as it does not consider slack max.
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AddLinearConstraint(
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cp_model, transit(tail, head), std::numeric_limits<int64_t>::max(),
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{{cumuls[head], 1}, {cumuls[tail], -1}}, {arc_var.second});
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}
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}
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}
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std::vector<int> CreateRanks(const RoutingModel& model,
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const ArcVarMap& arc_vars,
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CpModelProto* cp_model) {
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const int depot = GetDepotFromModel(model);
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const int size = model.Size() + model.vehicles();
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const int rank_size = model.Size() - model.vehicles();
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std::vector<int> ranks(size, -1);
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for (int i = 0; i < size; ++i) {
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if (model.IsStart(i) || model.IsEnd(i)) continue;
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ranks[i] = AddVariable(cp_model, 0, rank_size);
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}
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ranks[depot] = AddVariable(cp_model, 0, 0);
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for (const auto arc_var : arc_vars) {
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const int tail = arc_var.first.tail;
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const int head = arc_var.first.head;
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if (tail == head || head == depot) continue;
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// arc[tail][head] -> ranks[head] == ranks[tail] + 1.
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AddLinearConstraint(cp_model, 1, 1, {{ranks[head], 1}, {ranks[tail], -1}},
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{arc_var.second});
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}
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return ranks;
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}
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// Vehicle variables do not actually represent the index of the vehicle
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// performing a node, but we ensure that the values of two vehicle variables
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// are the same if and only if the corresponding nodes are served by the same
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// vehicle.
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std::vector<int> CreateVehicleVars(const RoutingModel& model,
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const ArcVarMap& arc_vars,
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CpModelProto* cp_model) {
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const int depot = GetDepotFromModel(model);
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const int size = model.Size() + model.vehicles();
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std::vector<int> vehicles(size, -1);
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for (int i = 0; i < size; ++i) {
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if (model.IsStart(i) || model.IsEnd(i)) continue;
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vehicles[i] = AddVariable(cp_model, 0, size - 1);
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}
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for (const auto arc_var : arc_vars) {
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const int tail = arc_var.first.tail;
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const int head = arc_var.first.head;
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if (tail == head || head == depot) continue;
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if (tail == depot) {
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// arc[depot][head] -> vehicles[head] == head.
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AddLinearConstraint(cp_model, head, head, {{vehicles[head], 1}},
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{arc_var.second});
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continue;
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}
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// arc[tail][head] -> vehicles[head] == vehicles[tail].
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AddLinearConstraint(cp_model, 0, 0,
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{{vehicles[head], 1}, {vehicles[tail], -1}},
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{arc_var.second});
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}
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return vehicles;
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}
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void AddPickupDeliveryConstraints(const RoutingModel& model,
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const ArcVarMap& arc_vars,
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CpModelProto* cp_model) {
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if (model.GetPickupAndDeliveryPairs().empty()) return;
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const std::vector<int> ranks = CreateRanks(model, arc_vars, cp_model);
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const std::vector<int> vehicles =
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CreateVehicleVars(model, arc_vars, cp_model);
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for (const auto& [pickups, deliveries] : model.GetPickupAndDeliveryPairs()) {
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const int64_t pickup = pickups[0];
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const int64_t delivery = deliveries[0];
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// ranks[pickup] + 1 <= ranks[delivery].
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AddLinearConstraint(cp_model, 1, std::numeric_limits<int64_t>::max(),
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{{ranks[delivery], 1}, {ranks[pickup], -1}});
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// vehicles[pickup] == vehicles[delivery]
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AddLinearConstraint(cp_model, 0, 0,
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{{vehicles[delivery], 1}, {vehicles[pickup], -1}});
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}
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}
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// Converts a RoutingModel to CpModelProto for models with multiple vehicles.
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// All non-start/end nodes have the same index in both models. Start/end nodes
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// map to a single depot index; its value is arbitrarly the index of the start
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// node of the first vehicle in the RoutingModel.
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// The map between CPModelProto arcs and their corresponding arc variable is
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// returned.
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ArcVarMap PopulateMultiRouteModelFromRoutingModel(const RoutingModel& model,
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CpModelProto* cp_model) {
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ArcVarMap arc_vars;
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const int num_nodes = model.Nexts().size();
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const int depot = GetDepotFromModel(model);
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// Create "arc" variables and set their cost.
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for (int tail = 0; tail < num_nodes; ++tail) {
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const int tail_index = model.IsStart(tail) ? depot : tail;
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std::unique_ptr<IntVarIterator> iter(
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model.NextVar(tail)->MakeDomainIterator(false));
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for (int head : InitAndGetValues(iter.get())) {
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// Vehicle start and end nodes are represented as a single node in the
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// CP-SAT model. We choose the start index of the first vehicle to
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// represent both. We can also skip any head representing a vehicle start
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// as the CP solver will reject those.
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if (model.IsStart(head)) continue;
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const int head_index = model.IsEnd(head) ? depot : head;
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if (head_index == tail_index && head_index == depot) continue;
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const int64_t cost = tail != head ? model.GetHomogeneousCost(tail, head)
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: model.UnperformedPenalty(tail);
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if (cost == std::numeric_limits<int64_t>::max()) continue;
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const Arc arc = {tail_index, head_index};
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if (arc_vars.contains(arc)) continue;
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const int index = AddVariable(cp_model, 0, 1);
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gtl::InsertOrDie(&arc_vars, arc, index);
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cp_model->mutable_objective()->add_vars(index);
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cp_model->mutable_objective()->add_coeffs(cost);
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}
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}
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// Limit the number of routes to the maximum number of vehicles.
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{
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std::vector<std::pair<int, double>> variable_coeffs;
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for (int node = 0; node < num_nodes; ++node) {
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if (model.IsStart(node) || model.IsEnd(node)) continue;
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int* const var = gtl::FindOrNull(arc_vars, {depot, node});
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if (var == nullptr) continue;
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variable_coeffs.push_back({*var, 1});
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}
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AddLinearConstraint(
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cp_model, 0,
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std::min(model.vehicles(), model.GetMaximumNumberOfActiveVehicles()),
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variable_coeffs);
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}
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AddPickupDeliveryConstraints(model, arc_vars, cp_model);
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AddDimensions(model, arc_vars, cp_model);
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// Create Routes constraint, ensuring circuits from and to the depot.
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// This one is a bit tricky, because we need to remap the depot to zero.
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// TODO(user): Make Routes constraints support optional nodes.
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RoutesConstraintProto* routes_ct =
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cp_model->add_constraints()->mutable_routes();
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for (const auto arc_var : arc_vars) {
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const int tail = arc_var.first.tail;
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const int head = arc_var.first.head;
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routes_ct->add_tails(tail == 0 ? depot : tail == depot ? 0 : tail);
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routes_ct->add_heads(head == 0 ? depot : head == depot ? 0 : head);
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routes_ct->add_literals(arc_var.second);
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}
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// Add demands and capacities to improve the LP relaxation and cuts. These are
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// based on the first "unary" dimension in the model if it exists.
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// TODO(user): We might want to try to get demand lower bounds from
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// non-unary dimensions if no unary exist.
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const RoutingDimension* primary_dimension = nullptr;
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for (const RoutingDimension* dimension : model.GetDimensions()) {
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// Only a single vehicle class is supported.
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if (dimension->GetUnaryTransitEvaluator(0) != nullptr) {
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primary_dimension = dimension;
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break;
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}
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}
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if (primary_dimension != nullptr) {
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const RoutingModel::TransitCallback1& transit =
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primary_dimension->GetUnaryTransitEvaluator(0);
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for (int node = 0; node < num_nodes; ++node) {
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// Tricky: demand is added for all nodes in the sat model; this means
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// start/end nodes other than the one used for the depot must be ignored.
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if (!model.IsEnd(node) && (!model.IsStart(node) || node == depot)) {
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routes_ct->add_demands(transit(node));
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}
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}
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DCHECK_EQ(routes_ct->demands_size(), num_nodes + 1 - model.vehicles());
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routes_ct->set_capacity(primary_dimension->vehicle_capacities()[0]);
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}
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return arc_vars;
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}
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// Converts a RoutingModel with a single vehicle to a CpModelProto.
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// The mapping between CPModelProto arcs and their corresponding arc variables
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// is returned.
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ArcVarMap PopulateSingleRouteModelFromRoutingModel(const RoutingModel& model,
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CpModelProto* cp_model) {
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ArcVarMap arc_vars;
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const int num_nodes = model.Nexts().size();
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CircuitConstraintProto* circuit =
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cp_model->add_constraints()->mutable_circuit();
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for (int tail = 0; tail < num_nodes; ++tail) {
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std::unique_ptr<IntVarIterator> iter(
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model.NextVar(tail)->MakeDomainIterator(false));
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for (int head : InitAndGetValues(iter.get())) {
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// Vehicle start and end nodes are represented as a single node in the
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// CP-SAT model. We choose the start index to represent both. We can also
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// skip any head representing a vehicle start as the CP solver will reject
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// those.
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if (model.IsStart(head)) continue;
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if (model.IsEnd(head)) head = model.Start(0);
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const int64_t cost = tail != head ? model.GetHomogeneousCost(tail, head)
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: model.UnperformedPenalty(tail);
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if (cost == std::numeric_limits<int64_t>::max()) continue;
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const int index = AddVariable(cp_model, 0, 1);
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circuit->add_literals(index);
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circuit->add_tails(tail);
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circuit->add_heads(head);
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cp_model->mutable_objective()->add_vars(index);
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cp_model->mutable_objective()->add_coeffs(cost);
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gtl::InsertOrDie(&arc_vars, {tail, head}, index);
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}
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}
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AddPickupDeliveryConstraints(model, arc_vars, cp_model);
|
|
AddDimensions(model, arc_vars, cp_model);
|
|
return arc_vars;
|
|
}
|
|
|
|
// Converts a RoutingModel to a CpModelProto.
|
|
// The mapping between CPModelProto arcs and their corresponding arc variables
|
|
// is returned.
|
|
ArcVarMap PopulateModelFromRoutingModel(const RoutingModel& model,
|
|
CpModelProto* cp_model) {
|
|
if (model.vehicles() == 1) {
|
|
return PopulateSingleRouteModelFromRoutingModel(model, cp_model);
|
|
}
|
|
return PopulateMultiRouteModelFromRoutingModel(model, cp_model);
|
|
}
|
|
|
|
void ConvertObjectiveToSolution(const CpSolverResponse& response,
|
|
const CpObjectiveProto& objective,
|
|
const RoutingModel& model,
|
|
Assignment* solution) {
|
|
if (response.status() == CpSolverStatus::OPTIMAL) {
|
|
// If the solution was proven optimal by CP-SAT, add the objective value to
|
|
// the solution; it will be a proper lower bound of the routing objective.
|
|
// Recomputing the objective value to avoid rounding errors due to scaling.
|
|
// Note: We could use inner_objective_lower_bound if we were sure
|
|
// absolute_gap_limit was 0 (which is not guaranteed).
|
|
int64_t cost_value = 0;
|
|
for (int i = 0; i < objective.coeffs_size(); ++i) {
|
|
cost_value = CapAdd(
|
|
cost_value,
|
|
CapProd(objective.coeffs(i), response.solution(objective.vars(i))));
|
|
}
|
|
solution->AddObjective(model.CostVar());
|
|
solution->SetObjectiveValue(cost_value);
|
|
} else if (response.status() == CpSolverStatus::FEASIBLE) {
|
|
// If the solution is feasible only, add the lower bound of the objective to
|
|
// the solution; it will be a proper lower bound of the routing objective.
|
|
solution->AddObjective(model.CostVar());
|
|
solution->SetObjectiveValue(response.inner_objective_lower_bound());
|
|
}
|
|
}
|
|
|
|
// Converts a CpSolverResponse to an Assignment containing next variables.
|
|
bool ConvertToSolution(const CpSolverResponse& response,
|
|
const CpObjectiveProto& objective,
|
|
const RoutingModel& model, const ArcVarMap& arc_vars,
|
|
Assignment* solution) {
|
|
solution->Clear();
|
|
if (response.status() != CpSolverStatus::OPTIMAL &&
|
|
response.status() != CpSolverStatus::FEASIBLE) {
|
|
return false;
|
|
}
|
|
const int depot = GetDepotFromModel(model);
|
|
int vehicle = 0;
|
|
for (const auto& arc_var : arc_vars) {
|
|
if (response.solution(arc_var.second) != 0) {
|
|
const int tail = arc_var.first.tail;
|
|
const int head = arc_var.first.head;
|
|
if (head == depot) continue;
|
|
if (tail != depot) {
|
|
solution->Add(model.NextVar(tail))->SetValue(head);
|
|
} else {
|
|
solution->Add(model.NextVar(model.Start(vehicle)))->SetValue(head);
|
|
++vehicle;
|
|
}
|
|
}
|
|
}
|
|
// Close open routes.
|
|
for (int v = 0; v < model.vehicles(); ++v) {
|
|
int current = model.Start(v);
|
|
while (!model.IsEnd(current) &&
|
|
solution->Contains(model.NextVar(current))) {
|
|
current = solution->Value(model.NextVar(current));
|
|
}
|
|
if (model.IsEnd(current)) continue;
|
|
solution->Add(model.NextVar(current))->SetValue(model.End(v));
|
|
}
|
|
ConvertObjectiveToSolution(response, objective, model, solution);
|
|
return true;
|
|
}
|
|
|
|
// Adds dimensions to a CpModelProto for heterogeneous fleet. Adds path
|
|
// cumul constraints and cumul bounds.
|
|
void AddGeneralizedDimensions(
|
|
const RoutingModel& model, const ArcVarMap& arc_vars,
|
|
absl::Span<const absl::flat_hash_map<int, int>> vehicle_performs_node,
|
|
absl::Span<const absl::flat_hash_map<int, int>> vehicle_class_performs_arc,
|
|
CpModelProto* cp_model) {
|
|
const int num_cp_nodes = model.Nexts().size() + model.vehicles() + 1;
|
|
for (const RoutingDimension* dimension : model.GetDimensions()) {
|
|
// Initialize cumuls.
|
|
std::vector<int> cumuls(num_cp_nodes, -1);
|
|
for (int cp_node = 1; cp_node < num_cp_nodes; ++cp_node) {
|
|
const int node = cp_node - 1;
|
|
int64_t cumul_min = dimension->cumuls()[node]->Min();
|
|
int64_t cumul_max =
|
|
std::min(dimension->cumuls()[node]->Max(),
|
|
std::numeric_limits<int64_t>::max() / (2 * num_cp_nodes));
|
|
if (model.IsStart(node) || model.IsEnd(node)) {
|
|
const int vehicle = model.VehicleIndex(node);
|
|
cumul_max =
|
|
std::min(cumul_max, dimension->vehicle_capacities()[vehicle]);
|
|
}
|
|
cumuls[cp_node] = AddVariable(cp_model, cumul_min, cumul_max);
|
|
AddSoftCumulBounds(dimension, node, cumuls[cp_node], cumul_min, cumul_max,
|
|
cp_model);
|
|
}
|
|
|
|
// Constrain cumuls with vehicle capacities.
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
for (int cp_node = 1; cp_node < num_cp_nodes; cp_node++) {
|
|
if (!vehicle_performs_node[vehicle].contains(cp_node)) continue;
|
|
const int64_t vehicle_capacity =
|
|
dimension->vehicle_capacities()[vehicle];
|
|
AddLinearConstraint(cp_model, std::numeric_limits<int64_t>::min(),
|
|
vehicle_capacity, {{cumuls[cp_node], 1}},
|
|
{vehicle_performs_node[vehicle].at(cp_node)});
|
|
}
|
|
}
|
|
|
|
for (auto vehicle_class = RoutingVehicleClassIndex(0);
|
|
vehicle_class < model.GetVehicleClassesCount(); vehicle_class++) {
|
|
std::vector<int> slack(num_cp_nodes, -1);
|
|
const int64_t slack_cost = CapAdd(
|
|
dimension->GetSpanCostCoefficientForVehicleClass(vehicle_class),
|
|
dimension->GetSlackCostCoefficientForVehicleClass(vehicle_class));
|
|
for (const auto [arc, arc_var] : arc_vars) {
|
|
const auto [cp_tail, cp_head] = arc;
|
|
if (cp_tail == cp_head || cp_tail == 0 || cp_head == 0) continue;
|
|
if (!vehicle_class_performs_arc[vehicle_class.value()].contains(
|
|
arc_var)) {
|
|
continue;
|
|
}
|
|
// Create slack variable and add span cost to the objective.
|
|
if (slack[cp_tail] == -1) {
|
|
const int64_t slack_max =
|
|
cp_tail - 1 < dimension->slacks().size()
|
|
? dimension->slacks()[cp_tail - 1]->Max()
|
|
: 0;
|
|
slack[cp_tail] = AddVariable(
|
|
cp_model, 0,
|
|
std::min(slack_max, std::numeric_limits<int64_t>::max() /
|
|
(2 * num_cp_nodes)));
|
|
if (slack_max > 0 && slack_cost > 0) {
|
|
cp_model->mutable_objective()->add_vars(slack[cp_tail]);
|
|
cp_model->mutable_objective()->add_coeffs(slack_cost);
|
|
}
|
|
}
|
|
const int64_t transit = dimension->class_transit_evaluator(
|
|
vehicle_class)(cp_tail - 1, cp_head - 1);
|
|
// vehicle_class_performs_arc[vehicle][arc_var] = 1 ->
|
|
// cumuls[cp_head] - cumuls[cp_tail] - slack[cp_tail] = transit
|
|
AddLinearConstraint(
|
|
cp_model, transit, transit,
|
|
{{cumuls[cp_head], 1}, {cumuls[cp_tail], -1}, {slack[cp_tail], -1}},
|
|
{vehicle_class_performs_arc[vehicle_class.value()].at(arc_var)});
|
|
}
|
|
}
|
|
|
|
// Constrain cumuls with span limits.
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
const int64_t span_limit =
|
|
dimension->vehicle_span_upper_bounds()[vehicle];
|
|
if (span_limit == std::numeric_limits<int64_t>::max()) continue;
|
|
int cp_start = model.Start(vehicle) + 1;
|
|
int cp_end = model.End(vehicle) + 1;
|
|
AddLinearConstraint(cp_model, std::numeric_limits<int64_t>::min(),
|
|
span_limit,
|
|
{{cumuls[cp_end], 1}, {cumuls[cp_start], -1}});
|
|
}
|
|
|
|
// Set soft span upper bound costs.
|
|
if (dimension->HasSoftSpanUpperBounds()) {
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
const auto [bound, cost] =
|
|
dimension->GetSoftSpanUpperBoundForVehicle(vehicle);
|
|
const int cp_start = model.Start(vehicle) + 1;
|
|
const int cp_end = model.End(vehicle) + 1;
|
|
const int extra =
|
|
AddVariable(cp_model, 0,
|
|
std::min(dimension->cumuls()[model.End(vehicle)]->Max(),
|
|
dimension->vehicle_capacities()[vehicle]));
|
|
// -inf <= cumuls[cp_end] - cumuls[cp_start] - extra <= bound
|
|
AddLinearConstraint(
|
|
cp_model, std::numeric_limits<int64_t>::min(), bound,
|
|
{{cumuls[cp_end], 1}, {cumuls[cp_start], -1}, {extra, -1}});
|
|
// Add extra * cost to objective.
|
|
cp_model->mutable_objective()->add_vars(extra);
|
|
cp_model->mutable_objective()->add_coeffs(cost);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
std::vector<int> CreateGeneralizedRanks(const RoutingModel& model,
|
|
const ArcVarMap& arc_vars,
|
|
absl::Span<const int> is_unperformed,
|
|
CpModelProto* cp_model) {
|
|
const int depot = 0;
|
|
const int num_cp_nodes = model.Nexts().size() + model.vehicles() + 1;
|
|
// Maximum length of a single route (excluding the depot & vehicle end nodes).
|
|
const int max_rank = num_cp_nodes - 2 * model.vehicles();
|
|
std::vector<int> ranks(num_cp_nodes, -1);
|
|
ranks[depot] = AddVariable(cp_model, 0, 0);
|
|
for (int cp_node = 1; cp_node < num_cp_nodes; cp_node++) {
|
|
if (model.IsEnd(cp_node - 1)) continue;
|
|
ranks[cp_node] = AddVariable(cp_model, 0, max_rank);
|
|
// For unperformed nodes rank is 0.
|
|
AddLinearConstraint(cp_model, 0, 0, {{ranks[cp_node], 1}},
|
|
{is_unperformed[cp_node]});
|
|
}
|
|
for (const auto [arc, arc_var] : arc_vars) {
|
|
const auto [cp_tail, cp_head] = arc;
|
|
if (cp_head == 0 || model.IsEnd(cp_head - 1)) continue;
|
|
if (cp_tail == cp_head || cp_head == depot) continue;
|
|
// arc[tail][head] -> ranks[head] == ranks[tail] + 1.
|
|
AddLinearConstraint(cp_model, 1, 1,
|
|
{{ranks[cp_head], 1}, {ranks[cp_tail], -1}}, {arc_var});
|
|
}
|
|
return ranks;
|
|
}
|
|
|
|
void AddGeneralizedPickupDeliveryConstraints(
|
|
const RoutingModel& model, const ArcVarMap& arc_vars,
|
|
absl::Span<const absl::flat_hash_map<int, int>> vehicle_performs_node,
|
|
absl::Span<const int> is_unperformed, CpModelProto* cp_model) {
|
|
if (model.GetPickupAndDeliveryPairs().empty()) return;
|
|
const std::vector<int> ranks =
|
|
CreateGeneralizedRanks(model, arc_vars, is_unperformed, cp_model);
|
|
for (const auto& [pickups, deliveries] : model.GetPickupAndDeliveryPairs()) {
|
|
for (const int delivery : deliveries) {
|
|
const int cp_delivery = delivery + 1;
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
const Arc vehicle_start_delivery_arc = {
|
|
static_cast<int>(model.Start(vehicle) + 1), cp_delivery};
|
|
if (arc_vars.contains(vehicle_start_delivery_arc)) {
|
|
// Forbid vehicle_start -> delivery arc.
|
|
AddLinearConstraint(cp_model, 0, 0,
|
|
{{arc_vars.at(vehicle_start_delivery_arc), 1}});
|
|
}
|
|
}
|
|
|
|
for (const int pickup : pickups) {
|
|
const int cp_pickup = pickup + 1;
|
|
const Arc delivery_pickup_arc = {cp_delivery, cp_pickup};
|
|
if (arc_vars.contains(delivery_pickup_arc)) {
|
|
// Forbid delivery -> pickup arc.
|
|
AddLinearConstraint(cp_model, 0, 0,
|
|
{{arc_vars.at(delivery_pickup_arc), 1}});
|
|
}
|
|
|
|
DCHECK_GE(is_unperformed[cp_delivery], 0);
|
|
DCHECK_GE(is_unperformed[cp_pickup], 0);
|
|
// A negative index i refers to NOT the literal at index -i - 1.
|
|
// -i - 1 ~ NOT i, if value of i in [0, 1] (boolean).
|
|
const int delivery_performed = -is_unperformed[cp_delivery] - 1;
|
|
const int pickup_performed = -is_unperformed[cp_pickup] - 1;
|
|
// The same vehicle performs pickup and delivery.
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
// delivery_performed & pickup_performed ->
|
|
// vehicle_performs_node[vehicle][cp_delivery] -
|
|
// vehicle_performs_node[vehicle][cp_pickup] = 0
|
|
AddLinearConstraint(
|
|
cp_model, 0, 0,
|
|
{{vehicle_performs_node[vehicle].at(cp_delivery), 1},
|
|
{vehicle_performs_node[vehicle].at(cp_pickup), -1}},
|
|
{delivery_performed, pickup_performed});
|
|
}
|
|
}
|
|
}
|
|
|
|
std::vector<std::pair<int, double>> ranks_difference;
|
|
// -SUM(pickup)ranks[pickup].
|
|
for (const int pickup : pickups) {
|
|
const int cp_pickup = pickup + 1;
|
|
ranks_difference.push_back({ranks[cp_pickup], -1});
|
|
}
|
|
// SUM(delivery)ranks[delivery].
|
|
for (const int delivery : deliveries) {
|
|
const int cp_delivery = delivery + 1;
|
|
ranks_difference.push_back({ranks[cp_delivery], 1});
|
|
}
|
|
// SUM(delivery)ranks[delivery] - SUM(pickup)ranks[pickup] >= 1
|
|
AddLinearConstraint(cp_model, 1, std::numeric_limits<int64_t>::max(),
|
|
ranks_difference);
|
|
}
|
|
}
|
|
|
|
// Converts a RoutingModel to CpModelProto for models with multiple
|
|
// vehicles. The node 0 is depot. All nodes in CpModel have index increased
|
|
// by 1 in comparison to the RoutingModel. Each start node has only 1
|
|
// incoming arc (from depot), each end node has only 1 outgoing arc (to
|
|
// depot). The mapping from CPModelProto arcs to their corresponding arc
|
|
// variable is returned.
|
|
ArcVarMap PopulateGeneralizedRouteModelFromRoutingModel(
|
|
const RoutingModel& model, CpModelProto* cp_model) {
|
|
ArcVarMap arc_vars;
|
|
const int depot = 0;
|
|
const int num_nodes = model.Nexts().size();
|
|
const int num_cp_nodes = num_nodes + model.vehicles() + 1;
|
|
// vehicle_performs_node[vehicle][node] equals to 1 if the vehicle performs
|
|
// the node, and 0 otherwise.
|
|
std::vector<absl::flat_hash_map<int, int>> vehicle_performs_node(
|
|
model.vehicles());
|
|
// Connect vehicles start and end nodes to depot.
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
const int cp_start = model.Start(vehicle) + 1;
|
|
const Arc start_arc = {depot, cp_start};
|
|
const int start_arc_var = AddVariable(cp_model, 1, 1);
|
|
DCHECK(!arc_vars.contains(start_arc));
|
|
arc_vars.insert({start_arc, start_arc_var});
|
|
|
|
const int cp_end = model.End(vehicle) + 1;
|
|
const Arc end_arc = {cp_end, depot};
|
|
const int end_arc_var = AddVariable(cp_model, 1, 1);
|
|
DCHECK(!arc_vars.contains(end_arc));
|
|
arc_vars.insert({end_arc, end_arc_var});
|
|
|
|
vehicle_performs_node[vehicle][cp_start] = start_arc_var;
|
|
vehicle_performs_node[vehicle][cp_end] = end_arc_var;
|
|
}
|
|
|
|
// is_unperformed[node] variable equals to 1 if visit is unperformed, and 0
|
|
// otherwise.
|
|
std::vector<int> is_unperformed(num_cp_nodes, -1);
|
|
// Initialize is_unperformed variables for nodes that must be performed.
|
|
for (int node = 0; node < num_nodes; node++) {
|
|
const int cp_node = node + 1;
|
|
// Forced active and nodes that are not involved in any disjunctions are
|
|
// always performed.
|
|
const std::vector<RoutingDisjunctionIndex>& disjunction_indices =
|
|
model.GetDisjunctionIndices(node);
|
|
if (disjunction_indices.empty() || model.ActiveVar(node)->Min() == 1) {
|
|
is_unperformed[cp_node] = AddVariable(cp_model, 0, 0);
|
|
continue;
|
|
}
|
|
// Check if the node is in a forced active disjunction.
|
|
for (RoutingDisjunctionIndex disjunction_index : disjunction_indices) {
|
|
const int num_nodes =
|
|
model.GetDisjunctionNodeIndices(disjunction_index).size();
|
|
const int64_t penalty = model.GetDisjunctionPenalty(disjunction_index);
|
|
const int64_t max_cardinality =
|
|
model.GetDisjunctionMaxCardinality(disjunction_index);
|
|
if (num_nodes == max_cardinality &&
|
|
(penalty < 0 || penalty == std::numeric_limits<int64_t>::max())) {
|
|
// Nodes in this disjunction are forced active.
|
|
is_unperformed[cp_node] = AddVariable(cp_model, 0, 0);
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
// Add alternative visits. Create self-looped arc variables. Set penalty for
|
|
// not performing disjunctions.
|
|
for (RoutingDisjunctionIndex disjunction_index(0);
|
|
disjunction_index < model.GetNumberOfDisjunctions();
|
|
disjunction_index++) {
|
|
const std::vector<int64_t>& disjunction_indices =
|
|
model.GetDisjunctionNodeIndices(disjunction_index);
|
|
const int disjunction_size = disjunction_indices.size();
|
|
const int64_t penalty = model.GetDisjunctionPenalty(disjunction_index);
|
|
const int64_t max_cardinality =
|
|
model.GetDisjunctionMaxCardinality(disjunction_index);
|
|
// Case when disjunction involves only 1 node, the node is only present in
|
|
// this disjunction, and the node can be unperformed.
|
|
if (disjunction_size == 1 &&
|
|
model.GetDisjunctionIndices(disjunction_indices[0]).size() == 1 &&
|
|
is_unperformed[disjunction_indices[0] + 1] == -1) {
|
|
const int cp_node = disjunction_indices[0] + 1;
|
|
const Arc arc = {cp_node, cp_node};
|
|
DCHECK(!arc_vars.contains(arc));
|
|
is_unperformed[cp_node] = AddVariable(cp_model, 0, 1);
|
|
arc_vars.insert({arc, is_unperformed[cp_node]});
|
|
cp_model->mutable_objective()->add_vars(is_unperformed[cp_node]);
|
|
cp_model->mutable_objective()->add_coeffs(penalty);
|
|
continue;
|
|
}
|
|
// num_performed + SUM(node)is_unperformed[node] = disjunction_size
|
|
const int num_performed = AddVariable(cp_model, 0, max_cardinality);
|
|
std::vector<std::pair<int, double>> var_coeffs;
|
|
var_coeffs.push_back({num_performed, 1});
|
|
for (const int node : disjunction_indices) {
|
|
const int cp_node = node + 1;
|
|
// Node can be unperformed.
|
|
if (is_unperformed[cp_node] == -1) {
|
|
const Arc arc = {cp_node, cp_node};
|
|
DCHECK(!arc_vars.contains(arc));
|
|
is_unperformed[cp_node] = AddVariable(cp_model, 0, 1);
|
|
arc_vars.insert({arc, is_unperformed[cp_node]});
|
|
}
|
|
var_coeffs.push_back({is_unperformed[cp_node], 1});
|
|
}
|
|
AddLinearConstraint(cp_model, disjunction_size, disjunction_size,
|
|
var_coeffs);
|
|
// When penalty is negative or max int64_t (forced active), num_violated is
|
|
// 0.
|
|
if (penalty < 0 || penalty == std::numeric_limits<int64_t>::max()) {
|
|
AddLinearConstraint(cp_model, max_cardinality, max_cardinality,
|
|
{{num_performed, 1}});
|
|
continue;
|
|
}
|
|
// If number of active indices is less than max_cardinality, then for each
|
|
// violated index 'penalty' is paid.
|
|
const int num_violated = AddVariable(cp_model, 0, max_cardinality);
|
|
cp_model->mutable_objective()->add_vars(num_violated);
|
|
cp_model->mutable_objective()->add_coeffs(penalty);
|
|
// num_performed + num_violated = max_cardinality
|
|
AddLinearConstraint(cp_model, max_cardinality, max_cardinality,
|
|
{{num_performed, 1}, {num_violated, 1}});
|
|
}
|
|
// Create "arc" variables.
|
|
std::vector<std::pair<int, double>> first_to_end_arcs;
|
|
for (int tail = 0; tail < num_nodes; ++tail) {
|
|
const int cp_tail = tail + 1;
|
|
std::unique_ptr<IntVarIterator> iter(
|
|
model.NextVar(tail)->MakeDomainIterator(false));
|
|
for (int head : InitAndGetValues(iter.get())) {
|
|
const int cp_head = head + 1;
|
|
if (model.IsStart(head)) continue;
|
|
// Arcs for unperformed visits have already been created.
|
|
if (tail == head) continue;
|
|
// Direct arcs from start to end nodes should exist only if they are
|
|
// for the same vehicle.
|
|
if (model.IsStart(tail) && model.IsEnd(head) &&
|
|
model.VehicleIndex(tail) != model.VehicleIndex(head)) {
|
|
continue;
|
|
}
|
|
|
|
bool feasible = false;
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
if (model.GetArcCostForVehicle(tail, head, vehicle) !=
|
|
std::numeric_limits<int64_t>::max()) {
|
|
feasible = true;
|
|
break;
|
|
}
|
|
}
|
|
if (!feasible) continue;
|
|
|
|
const Arc arc = {cp_tail, cp_head};
|
|
DCHECK(!arc_vars.contains(arc));
|
|
const int arc_var = AddVariable(cp_model, 0, 1);
|
|
arc_vars.insert({arc, arc_var});
|
|
if (model.IsStart(tail) && model.IsEnd(head)) {
|
|
first_to_end_arcs.push_back({arc_var, 1});
|
|
}
|
|
}
|
|
}
|
|
// Limit the number of routes to the maximum number of vehicles.
|
|
{
|
|
AddLinearConstraint(
|
|
cp_model,
|
|
std::max(model.vehicles() - model.GetMaximumNumberOfActiveVehicles(),
|
|
0),
|
|
model.vehicles(), first_to_end_arcs);
|
|
}
|
|
|
|
// Set literals for vehicle performing node.
|
|
for (int cp_node = 1; cp_node < num_cp_nodes; cp_node++) {
|
|
const int routing_index = cp_node - 1;
|
|
// For starts and ends nodes vehicle_performs_node variables already set.
|
|
if (model.IsStart(routing_index) || model.IsEnd(routing_index)) continue;
|
|
// Each node should be performed by 1 vehicle, or be unperformed.
|
|
// SUM(vehicle)(vehicle_performs_node[vehicle][cp_node]) + loop(cp_node) = 1
|
|
std::vector<std::pair<int, double>> var_coeffs;
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
vehicle_performs_node[vehicle][cp_node] =
|
|
model.VehicleVar(routing_index)->Contains(vehicle)
|
|
? AddVariable(cp_model, 0, 1)
|
|
: AddVariable(cp_model, 0, 0);
|
|
var_coeffs.push_back({vehicle_performs_node[vehicle][cp_node], 1});
|
|
}
|
|
var_coeffs.push_back({is_unperformed[cp_node], 1});
|
|
AddLinearConstraint(cp_model, 1, 1, var_coeffs);
|
|
}
|
|
const int num_vehicle_classes = model.GetVehicleClassesCount();
|
|
// vehicle_class_performs_node[vehicle_class][node] equals to 1 if the
|
|
// vehicle of vehicle_class performs the node, and 0 otherwise.
|
|
std::vector<absl::flat_hash_map<int, int>> vehicle_class_performs_node(
|
|
num_vehicle_classes);
|
|
for (int cp_node = 1; cp_node < num_cp_nodes; cp_node++) {
|
|
const int node = cp_node - 1;
|
|
for (int vehicle_class = 0; vehicle_class < num_vehicle_classes;
|
|
vehicle_class++) {
|
|
if (model.IsStart(node) || model.IsEnd(node)) {
|
|
const int vehicle = model.VehicleIndex(node);
|
|
vehicle_class_performs_node[vehicle_class][cp_node] =
|
|
vehicle_class ==
|
|
model.GetVehicleClassIndexOfVehicle(vehicle).value()
|
|
? AddVariable(cp_model, 1, 1)
|
|
: AddVariable(cp_model, 0, 0);
|
|
continue;
|
|
}
|
|
vehicle_class_performs_node[vehicle_class][cp_node] =
|
|
AddVariable(cp_model, 0, 1);
|
|
std::vector<std::pair<int, double>> var_coeffs;
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
if (model.GetVehicleClassIndexOfVehicle(vehicle).value() ==
|
|
vehicle_class) {
|
|
var_coeffs.push_back({vehicle_performs_node[vehicle][cp_node], 1});
|
|
// vehicle_performs_node -> vehicle_class_performs_node
|
|
AddLinearConstraint(
|
|
cp_model, 1, 1,
|
|
{{vehicle_class_performs_node[vehicle_class][cp_node], 1}},
|
|
{vehicle_performs_node[vehicle][cp_node]});
|
|
}
|
|
}
|
|
// vehicle_class_performs_node -> exactly one vehicle from this class
|
|
// performs node.
|
|
AddLinearConstraint(
|
|
cp_model, 1, 1, var_coeffs,
|
|
{vehicle_class_performs_node[vehicle_class][cp_node]});
|
|
}
|
|
}
|
|
// vehicle_class_performs_arc[vehicle_class][arc_var] equals to 1 if the
|
|
// vehicle of vehicle_class performs the arc, and 0 otherwise.
|
|
std::vector<absl::flat_hash_map<int, int>> vehicle_class_performs_arc(
|
|
num_vehicle_classes);
|
|
// Set "arc" costs.
|
|
for (const auto [arc, arc_var] : arc_vars) {
|
|
const auto [cp_tail, cp_head] = arc;
|
|
if (cp_tail == depot || cp_head == depot) continue;
|
|
const int tail = cp_tail - 1;
|
|
const int head = cp_head - 1;
|
|
// Costs for unperformed arcs have already been set.
|
|
if (tail == head) continue;
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
// The arc can't be performed by the vehicle when vehicle can't perform
|
|
// arc nodes.
|
|
if (!vehicle_performs_node[vehicle].contains(cp_tail) ||
|
|
!vehicle_performs_node[vehicle].contains(cp_head)) {
|
|
continue;
|
|
}
|
|
int64_t cost = model.GetArcCostForVehicle(tail, head, vehicle);
|
|
// Arcs with int64_t's max cost are infeasible.
|
|
if (cost == std::numeric_limits<int64_t>::max()) continue;
|
|
const int vehicle_class =
|
|
model.GetVehicleClassIndexOfVehicle(vehicle).value();
|
|
if (!vehicle_class_performs_arc[vehicle_class].contains(arc_var)) {
|
|
vehicle_class_performs_arc[vehicle_class][arc_var] =
|
|
AddVariable(cp_model, 0, 1);
|
|
// Create constraints to set vehicle_class_performs_arc.
|
|
// vehicle_class_performs_arc ->
|
|
// vehicle_class_performs_tail & vehicle_class_performs_head &
|
|
// arc_is_performed
|
|
ConstraintProto* ct = cp_model->add_constraints();
|
|
ct->add_enforcement_literal(
|
|
vehicle_class_performs_arc[vehicle_class][arc_var]);
|
|
BoolArgumentProto* bool_and = ct->mutable_bool_and();
|
|
bool_and->add_literals(
|
|
vehicle_class_performs_node[vehicle_class][cp_tail]);
|
|
bool_and->add_literals(
|
|
vehicle_class_performs_node[vehicle_class][cp_head]);
|
|
bool_and->add_literals(arc_var);
|
|
// Don't add arcs with zero cost to the objective.
|
|
if (cost != 0) {
|
|
cp_model->mutable_objective()->add_vars(
|
|
vehicle_class_performs_arc[vehicle_class][arc_var]);
|
|
cp_model->mutable_objective()->add_coeffs(cost);
|
|
}
|
|
}
|
|
// (arc_is_performed & vehicle_performs_tail) ->
|
|
// (vehicle_class_performs_arc & vehicle_performs_head)
|
|
ConstraintProto* ct_arc_tail = cp_model->add_constraints();
|
|
ct_arc_tail->add_enforcement_literal(arc_var);
|
|
ct_arc_tail->add_enforcement_literal(
|
|
vehicle_performs_node[vehicle][cp_tail]);
|
|
ct_arc_tail->mutable_bool_and()->add_literals(
|
|
vehicle_class_performs_arc[vehicle_class][arc_var]);
|
|
ct_arc_tail->mutable_bool_and()->add_literals(
|
|
vehicle_performs_node[vehicle][cp_head]);
|
|
// (arc_is_performed & vehicle_performs_head) ->
|
|
// (vehicle_class_performs_arc & vehicle_performs_tail)
|
|
ConstraintProto* ct_arc_head = cp_model->add_constraints();
|
|
ct_arc_head->add_enforcement_literal(arc_var);
|
|
ct_arc_head->add_enforcement_literal(
|
|
vehicle_performs_node[vehicle][cp_head]);
|
|
ct_arc_head->mutable_bool_and()->add_literals(
|
|
vehicle_class_performs_arc[vehicle_class][arc_var]);
|
|
ct_arc_head->mutable_bool_and()->add_literals(
|
|
vehicle_performs_node[vehicle][cp_tail]);
|
|
}
|
|
}
|
|
|
|
AddGeneralizedPickupDeliveryConstraints(
|
|
model, arc_vars, vehicle_performs_node, is_unperformed, cp_model);
|
|
|
|
AddGeneralizedDimensions(model, arc_vars, vehicle_performs_node,
|
|
vehicle_class_performs_arc, cp_model);
|
|
|
|
// Create Routes constraint, ensuring circuits from and to the depot.
|
|
RoutesConstraintProto* routes_ct =
|
|
cp_model->add_constraints()->mutable_routes();
|
|
for (const auto [arc, arc_var] : arc_vars) {
|
|
const int tail = arc.tail;
|
|
const int head = arc.head;
|
|
routes_ct->add_tails(tail);
|
|
routes_ct->add_heads(head);
|
|
routes_ct->add_literals(arc_var);
|
|
}
|
|
|
|
// Add demands and capacities to improve the LP relaxation and cuts. These
|
|
// are based on the first "unary" dimension in the model if it exists.
|
|
// TODO(user): We might want to try to get demand lower bounds from
|
|
// non-unary dimensions if no unary exist.
|
|
const RoutingDimension* primary_dimension = nullptr;
|
|
for (const RoutingDimension* dimension : model.GetDimensions()) {
|
|
bool is_unary = true;
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
if (dimension->GetUnaryTransitEvaluator(vehicle) == nullptr) {
|
|
is_unary = false;
|
|
break;
|
|
}
|
|
}
|
|
if (is_unary) {
|
|
primary_dimension = dimension;
|
|
break;
|
|
}
|
|
}
|
|
if (primary_dimension != nullptr) {
|
|
for (int cp_node = 0; cp_node < num_cp_nodes; ++cp_node) {
|
|
int64_t min_transit = std::numeric_limits<int64_t>::max();
|
|
if (cp_node != 0 && !model.IsEnd(cp_node - 1)) {
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
const RoutingModel::TransitCallback1& transit =
|
|
primary_dimension->GetUnaryTransitEvaluator(vehicle);
|
|
min_transit = std::min(min_transit, transit(cp_node - 1));
|
|
}
|
|
} else {
|
|
min_transit = 0;
|
|
}
|
|
routes_ct->add_demands(min_transit);
|
|
}
|
|
DCHECK_EQ(routes_ct->demands_size(), num_cp_nodes);
|
|
int64_t max_capacity = std::numeric_limits<int64_t>::min();
|
|
for (int vehicle = 0; vehicle < model.vehicles(); vehicle++) {
|
|
max_capacity = std::max(max_capacity,
|
|
primary_dimension->vehicle_capacities()[vehicle]);
|
|
}
|
|
routes_ct->set_capacity(max_capacity);
|
|
}
|
|
return arc_vars;
|
|
}
|
|
|
|
// Converts a CpSolverResponse to an Assignment containing next variables.
|
|
bool ConvertGeneralizedResponseToSolution(const CpSolverResponse& response,
|
|
const CpObjectiveProto& objective,
|
|
const RoutingModel& model,
|
|
const ArcVarMap& arc_vars,
|
|
Assignment* solution) {
|
|
solution->Clear();
|
|
if (response.status() != CpSolverStatus::OPTIMAL &&
|
|
response.status() != CpSolverStatus::FEASIBLE) {
|
|
return false;
|
|
}
|
|
const int depot = 0;
|
|
for (const auto [arc, arc_var] : arc_vars) {
|
|
if (response.solution(arc_var) == 0) continue;
|
|
const auto [tail, head] = arc;
|
|
if (head == depot || tail == depot) continue;
|
|
solution->Add(model.NextVar(tail - 1))->SetValue(head - 1);
|
|
}
|
|
ConvertObjectiveToSolution(response, objective, model, solution);
|
|
return true;
|
|
}
|
|
|
|
// Uses CP solution as hint for CP-SAT.
|
|
void AddSolutionAsHintToGeneralizedModel(const Assignment* solution,
|
|
const RoutingModel& model,
|
|
const ArcVarMap& arc_vars,
|
|
CpModelProto* cp_model) {
|
|
if (solution == nullptr) return;
|
|
PartialVariableAssignment* const hint = cp_model->mutable_solution_hint();
|
|
hint->Clear();
|
|
const int num_nodes = model.Nexts().size();
|
|
for (int tail = 0; tail < num_nodes; ++tail) {
|
|
const int cp_tail = tail + 1;
|
|
const int cp_head = solution->Value(model.NextVar(tail)) + 1;
|
|
const int* const arc_var = gtl::FindOrNull(arc_vars, {cp_tail, cp_head});
|
|
// Arcs with a cost of max int64_t are not added to the model (considered as
|
|
// infeasible). In some rare cases CP solutions might contain such arcs in
|
|
// which case they are skipped here and a partial solution is used as a
|
|
// hint.
|
|
if (arc_var == nullptr) continue;
|
|
hint->add_vars(*arc_var);
|
|
hint->add_values(1);
|
|
}
|
|
}
|
|
|
|
void AddSolutionAsHintToModel(const Assignment* solution,
|
|
const RoutingModel& model,
|
|
const ArcVarMap& arc_vars,
|
|
CpModelProto* cp_model) {
|
|
if (solution == nullptr) return;
|
|
PartialVariableAssignment* const hint = cp_model->mutable_solution_hint();
|
|
hint->Clear();
|
|
const int depot = GetDepotFromModel(model);
|
|
const int num_nodes = model.Nexts().size();
|
|
for (int tail = 0; tail < num_nodes; ++tail) {
|
|
const int tail_index = model.IsStart(tail) ? depot : tail;
|
|
const int head = solution->Value(model.NextVar(tail));
|
|
const int head_index = model.IsEnd(head) ? depot : head;
|
|
if (tail_index == depot && head_index == depot) continue;
|
|
const int* const var_index =
|
|
gtl::FindOrNull(arc_vars, {tail_index, head_index});
|
|
// Arcs with a cost of kint64max are not added to the model (considered as
|
|
// infeasible). In some rare cases CP solutions might contain such arcs in
|
|
// which case they are skipped here and a partial solution is used as a
|
|
// hint.
|
|
if (var_index == nullptr) continue;
|
|
hint->add_vars(*var_index);
|
|
hint->add_values(1);
|
|
}
|
|
}
|
|
|
|
// Configures a CP-SAT solver and solves the given (routing) model using it.
|
|
// Returns the response of the search.
|
|
CpSolverResponse SolveRoutingModel(
|
|
const CpModelProto& cp_model, absl::Duration remaining_time,
|
|
std::atomic<bool>* interrupt_solve,
|
|
const RoutingSearchParameters& search_parameters,
|
|
const std::function<void(const CpSolverResponse& response)>& observer) {
|
|
// Copying to set remaining time.
|
|
SatParameters sat_parameters = search_parameters.sat_parameters();
|
|
if (!sat_parameters.has_max_time_in_seconds()) {
|
|
sat_parameters.set_max_time_in_seconds(
|
|
absl::ToDoubleSeconds(remaining_time));
|
|
} else {
|
|
sat_parameters.set_max_time_in_seconds(
|
|
std::min(absl::ToDoubleSeconds(remaining_time),
|
|
sat_parameters.max_time_in_seconds()));
|
|
}
|
|
Model model;
|
|
model.Add(NewSatParameters(sat_parameters));
|
|
model.GetOrCreate<TimeLimit>()->RegisterExternalBooleanAsLimit(
|
|
interrupt_solve);
|
|
if (observer != nullptr) {
|
|
model.Add(NewFeasibleSolutionObserver(observer));
|
|
}
|
|
// TODO(user): Add an option to dump the CP-SAT model or check if the
|
|
// cp_model_dump_file flag in cp_model_solver.cc is good enough.
|
|
return SolveCpModel(cp_model, &model);
|
|
}
|
|
|
|
// Check if all the nodes are present in arcs. Otherwise, CP-SAT solver may
|
|
// fail.
|
|
bool IsFeasibleArcVarMap(const ArcVarMap& arc_vars, int max_node_index) {
|
|
Bitset64<> present_in_arcs(max_node_index + 1);
|
|
for (const auto [arc, _] : arc_vars) {
|
|
present_in_arcs.Set(arc.head);
|
|
present_in_arcs.Set(arc.tail);
|
|
}
|
|
for (int i = 0; i <= max_node_index; i++) {
|
|
if (!present_in_arcs[i]) return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
} // namespace
|
|
} // namespace sat
|
|
|
|
// Solves a RoutingModel using the CP-SAT solver. Returns false if no solution
|
|
// was found.
|
|
bool SolveModelWithSat(RoutingModel* model, RoutingSearchStats* search_stats,
|
|
const RoutingSearchParameters& search_parameters,
|
|
const Assignment* initial_solution,
|
|
Assignment* solution) {
|
|
// Adding a bit of slack to the time limit for the CP-SAT solver.
|
|
const absl::Duration remaining_time = model->RemainingTime() * 0.95;
|
|
const absl::Time deadline = model->solver()->Now() + remaining_time;
|
|
sat::CpModelProto cp_model;
|
|
cp_model.mutable_objective()->set_scaling_factor(
|
|
search_parameters.log_cost_scaling_factor());
|
|
cp_model.mutable_objective()->set_offset(search_parameters.log_cost_offset());
|
|
const sat::CpObjectiveProto& objective = cp_model.objective();
|
|
const std::function<void(const sat::CpSolverResponse& response)>
|
|
null_observer;
|
|
if (search_parameters.use_generalized_cp_sat() == BOOL_TRUE ||
|
|
!sat::RoutingModelCanBeSolvedBySat(*model)) {
|
|
const sat::ArcVarMap arc_vars =
|
|
sat::PopulateGeneralizedRouteModelFromRoutingModel(*model, &cp_model);
|
|
const int max_node_index = model->Nexts().size() + model->vehicles();
|
|
if (!sat::IsFeasibleArcVarMap(arc_vars, max_node_index)) return false;
|
|
sat::AddSolutionAsHintToGeneralizedModel(initial_solution, *model, arc_vars,
|
|
&cp_model);
|
|
const std::function<void(const sat::CpSolverResponse& response)> observer =
|
|
search_parameters.report_intermediate_cp_sat_solutions() ?
|
|
[model, &objective, &arc_vars, solution, deadline]
|
|
(const sat::CpSolverResponse& response) {
|
|
// TODO(user): Check that performance is acceptable.
|
|
sat::ConvertGeneralizedResponseToSolution(
|
|
response, objective, *model, arc_vars, solution);
|
|
const absl::Duration remaining_time =
|
|
deadline - model->solver()->Now();
|
|
if (remaining_time < absl::ZeroDuration()) return;
|
|
model->UpdateTimeLimit(remaining_time);
|
|
model->CheckIfAssignmentIsFeasible(
|
|
*solution,
|
|
/*call_at_solution_monitors=*/true);
|
|
} : null_observer;
|
|
if (search_stats) search_stats->num_generalized_cp_sat_calls_in_routing++;
|
|
return sat::ConvertGeneralizedResponseToSolution(
|
|
sat::SolveRoutingModel(cp_model, remaining_time,
|
|
model->GetMutableCPSatInterrupt(),
|
|
search_parameters, observer),
|
|
objective, *model, arc_vars, solution);
|
|
}
|
|
DCHECK(sat::RoutingModelCanBeSolvedBySat(*model));
|
|
const sat::ArcVarMap arc_vars =
|
|
sat::PopulateModelFromRoutingModel(*model, &cp_model);
|
|
sat::AddSolutionAsHintToModel(initial_solution, *model, arc_vars, &cp_model);
|
|
const std::function<void(const sat::CpSolverResponse& response)> observer =
|
|
search_parameters.report_intermediate_cp_sat_solutions() ?
|
|
[model, &objective, &arc_vars, solution, deadline]
|
|
(const sat::CpSolverResponse& response) {
|
|
// TODO(user): Check that performance is acceptable.
|
|
sat::ConvertToSolution(response, objective, *model, arc_vars, solution);
|
|
const absl::Duration remaining_time = deadline - model->solver()->Now();
|
|
if (remaining_time < absl::ZeroDuration()) return;
|
|
model->UpdateTimeLimit(remaining_time);
|
|
|
|
model->CheckIfAssignmentIsFeasible(*solution,
|
|
/*call_at_solution_monitors=*/true);
|
|
} : null_observer;
|
|
if (search_stats) search_stats->num_cp_sat_calls_in_routing++;
|
|
return sat::ConvertToSolution(
|
|
sat::SolveRoutingModel(cp_model, remaining_time,
|
|
model->GetMutableCPSatInterrupt(),
|
|
search_parameters, observer),
|
|
objective, *model, arc_vars, solution);
|
|
}
|
|
|
|
} // namespace operations_research
|