412 lines
18 KiB
C++
412 lines
18 KiB
C++
// Copyright 2010-2022 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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//
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// Pickup and Delivery Problem with Time Windows.
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// The overall objective is to minimize the length of the routes delivering
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// quantities of goods between pickup and delivery locations, taking into
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// account vehicle capacities and node time windows.
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// Given a set of pairs of pickup and delivery nodes, find the set of routes
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// visiting all the nodes, such that
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// - corresponding pickup and delivery nodes are visited on the same route,
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// - the pickup node is visited before the corresponding delivery node,
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// - the quantity picked up at the pickup node is the same as the quantity
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// delivered at the delivery node,
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// - the total quantity carried by a vehicle at any time is less than its
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// capacity,
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// - each node must be visited within its time window (time range during which
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// the node is accessible).
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// The maximum number of vehicles used (i.e. the number of routes used) is
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// specified in the data but can be overridden using the --pdp_force_vehicles
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// flag.
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//
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// A further description of the problem can be found here:
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// http://en.wikipedia.org/wiki/Vehicle_routing_problem
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// http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.123.9965&rep=rep1&type=pdf.
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// Reads data in the format defined by Li & Lim
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// (https://www.sintef.no/projectweb/top/pdptw/li-lim-benchmark/documentation/).
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#include <cmath>
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#include <cstdint>
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#include <utility>
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#include <vector>
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#include "absl/flags/flag.h"
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#include "absl/strings/numbers.h"
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#include "absl/strings/str_format.h"
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#include "absl/strings/str_split.h"
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#include "google/protobuf/text_format.h"
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#include "ortools/base/commandlineflags.h"
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#include "ortools/base/file.h"
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#include "ortools/base/init_google.h"
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#include "ortools/base/mathutil.h"
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#include "ortools/base/timer.h"
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#include "ortools/constraint_solver/routing.h"
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#include "ortools/constraint_solver/routing_enums.pb.h"
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#include "ortools/constraint_solver/routing_index_manager.h"
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#include "ortools/constraint_solver/routing_parameters.h"
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#include "ortools/constraint_solver/routing_parameters.pb.h"
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ABSL_FLAG(std::string, pdp_file, "",
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"File containing the Pickup and Delivery Problem to solve.");
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ABSL_FLAG(int, pdp_force_vehicles, 0,
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"Force the number of vehicles used (maximum number of routes.");
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ABSL_FLAG(bool, reduce_vehicle_cost_model, true,
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"Overrides the homonymous field of "
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"DefaultRoutingModelParameters().");
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ABSL_FLAG(std::string, routing_search_parameters,
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"first_solution_strategy:ALL_UNPERFORMED",
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"Text proto RoutingSearchParameters (possibly partial) that will "
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"override the DefaultRoutingSearchParameters()");
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namespace operations_research {
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// Scaling factor used to scale up distances, allowing a bit more precision
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// from Euclidean distances.
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const int64_t kScalingFactor = 1000;
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// Vector of (x,y) node coordinates, *unscaled*, in some imaginary planar,
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// metric grid.
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typedef std::vector<std::pair<int, int> > Coordinates;
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// Returns the scaled Euclidean distance between two nodes, coords holding the
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// coordinates of the nodes.
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int64_t Travel(const Coordinates* const coords,
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RoutingIndexManager::NodeIndex from,
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RoutingIndexManager::NodeIndex to) {
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DCHECK(coords != nullptr);
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const int xd = coords->at(from.value()).first - coords->at(to.value()).first;
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const int yd =
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coords->at(from.value()).second - coords->at(to.value()).second;
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return static_cast<int64_t>(kScalingFactor *
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std::sqrt(1.0L * xd * xd + yd * yd));
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}
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// Returns the scaled service time at a given node, service_times holding the
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// service times.
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int64_t ServiceTime(const std::vector<int64_t>* const service_times,
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RoutingIndexManager::NodeIndex node) {
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return kScalingFactor * service_times->at(node.value());
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}
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// Returns the scaled (distance plus service time) between two indices, coords
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// holding the coordinates of the nodes and service_times holding the service
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// times.
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// The service time is the time spent to execute a delivery or a pickup.
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int64_t TravelPlusServiceTime(const RoutingIndexManager& manager,
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const Coordinates* const coords,
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const std::vector<int64_t>* const service_times,
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int64_t from_index, int64_t to_index) {
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const RoutingIndexManager::NodeIndex from = manager.IndexToNode(from_index);
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const RoutingIndexManager::NodeIndex to = manager.IndexToNode(to_index);
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return ServiceTime(service_times, from) + Travel(coords, from, to);
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}
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// Returns the list of variables to use for the Tabu metaheuristic.
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// The current list is:
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// - Total cost of the solution,
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// - Number of used vehicles,
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// - Total schedule duration.
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// TODO(user): add total waiting time.
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std::vector<IntVar*> GetTabuVars(std::vector<IntVar*> existing_vars,
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operations_research::RoutingModel* routing) {
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Solver* const solver = routing->solver();
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std::vector<IntVar*> vars(std::move(existing_vars));
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vars.push_back(routing->CostVar());
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IntVar* used_vehicles = solver->MakeIntVar(0, routing->vehicles());
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std::vector<IntVar*> is_used_vars;
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// Number of vehicle used
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is_used_vars.reserve(routing->vehicles());
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for (int v = 0; v < routing->vehicles(); v++) {
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is_used_vars.push_back(solver->MakeIsDifferentCstVar(
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routing->NextVar(routing->Start(v)), routing->End(v)));
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}
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solver->AddConstraint(
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solver->MakeEquality(solver->MakeSum(is_used_vars), used_vehicles));
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vars.push_back(used_vehicles);
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return vars;
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}
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// Outputs a solution to the current model in a string.
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std::string VerboseOutput(const RoutingModel& routing,
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const RoutingIndexManager& manager,
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const Assignment& assignment,
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const Coordinates& coords,
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const std::vector<int64_t>& service_times) {
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std::string output;
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const RoutingDimension& time_dimension = routing.GetDimensionOrDie("time");
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const RoutingDimension& load_dimension = routing.GetDimensionOrDie("demand");
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for (int i = 0; i < routing.vehicles(); ++i) {
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absl::StrAppendFormat(&output, "Vehicle %d: ", i);
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int64_t index = routing.Start(i);
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if (routing.IsEnd(assignment.Value(routing.NextVar(index)))) {
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output.append("empty");
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} else {
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while (!routing.IsEnd(index)) {
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absl::StrAppendFormat(&output, "%d ",
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manager.IndexToNode(index).value());
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const IntVar* vehicle = routing.VehicleVar(index);
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absl::StrAppendFormat(&output, "Vehicle(%d) ",
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assignment.Value(vehicle));
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const IntVar* arrival = time_dimension.CumulVar(index);
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absl::StrAppendFormat(&output, "Time(%d..%d) ", assignment.Min(arrival),
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assignment.Max(arrival));
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const IntVar* load = load_dimension.CumulVar(index);
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absl::StrAppendFormat(&output, "Load(%d..%d) ", assignment.Min(load),
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assignment.Max(load));
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const int64_t next_index = assignment.Value(routing.NextVar(index));
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absl::StrAppendFormat(
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&output, "Transit(%d) ",
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TravelPlusServiceTime(manager, &coords, &service_times, index,
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next_index));
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index = next_index;
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}
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output.append("Route end ");
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const IntVar* vehicle = routing.VehicleVar(index);
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absl::StrAppendFormat(&output, "Vehicle(%d) ", assignment.Value(vehicle));
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const IntVar* arrival = time_dimension.CumulVar(index);
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absl::StrAppendFormat(&output, "Time(%d..%d) ", assignment.Min(arrival),
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assignment.Max(arrival));
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const IntVar* load = load_dimension.CumulVar(index);
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absl::StrAppendFormat(&output, "Load(%d..%d) ", assignment.Min(load),
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assignment.Max(load));
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}
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output.append("\n");
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}
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return output;
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}
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namespace {
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// An inefficient but convenient method to parse a whitespace-separated list
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// of integers. Returns true iff the input string was entirely valid and parsed.
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bool SafeParseInt64Array(const std::string& str,
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std::vector<int64_t>* parsed_int) {
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std::istringstream input(str);
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int64_t x;
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parsed_int->clear();
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while (input >> x) parsed_int->push_back(x);
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return input.eof();
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}
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} // namespace
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// Builds and solves a model from a file in the format defined by Li & Lim
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// (https://www.sintef.no/projectweb/top/pdptw/li-lim-benchmark/documentation/).
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bool LoadAndSolve(const std::string& pdp_file,
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const RoutingModelParameters& model_parameters,
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const RoutingSearchParameters& search_parameters) {
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// Load all the lines of the file in RAM (it shouldn't be too large anyway).
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std::vector<std::string> lines;
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{
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std::string contents;
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CHECK_OK(file::GetContents(pdp_file, &contents, file::Defaults()));
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const int64_t kMaxInputFileSize = 1 << 30; // 1GB
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if (contents.size() >= kMaxInputFileSize) {
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LOG(WARNING) << "Input file '" << pdp_file << "' is too large (>"
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<< kMaxInputFileSize << " bytes).";
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return false;
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}
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lines = absl::StrSplit(contents, '\n', absl::SkipEmpty());
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}
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// Reading header.
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if (lines.empty()) {
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LOG(WARNING) << "Empty file: " << pdp_file;
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return false;
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}
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// Parse file header.
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std::vector<int64_t> parsed_int;
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if (!SafeParseInt64Array(lines[0], &parsed_int) || parsed_int.size() != 3 ||
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parsed_int[0] < 0 || parsed_int[1] < 0 || parsed_int[2] < 0) {
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LOG(WARNING) << "Malformed header: " << lines[0];
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return false;
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}
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const int num_vehicles = absl::GetFlag(FLAGS_pdp_force_vehicles) > 0
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? absl::GetFlag(FLAGS_pdp_force_vehicles)
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: parsed_int[0];
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const int64_t capacity = parsed_int[1];
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// We do not care about the 'speed' field, in third position.
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// Parse order data.
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std::vector<int> customer_ids;
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std::vector<std::pair<int, int> > coords;
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std::vector<int64_t> demands;
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std::vector<int64_t> open_times;
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std::vector<int64_t> close_times;
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std::vector<int64_t> service_times;
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std::vector<RoutingIndexManager::NodeIndex> pickups;
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std::vector<RoutingIndexManager::NodeIndex> deliveries;
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int64_t horizon = 0;
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RoutingIndexManager::NodeIndex depot(0);
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for (int line_index = 1; line_index < lines.size(); ++line_index) {
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if (!SafeParseInt64Array(lines[line_index], &parsed_int) ||
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parsed_int.size() != 9 || parsed_int[0] < 0 || parsed_int[4] < 0 ||
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parsed_int[5] < 0 || parsed_int[6] < 0 || parsed_int[7] < 0 ||
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parsed_int[8] < 0) {
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LOG(WARNING) << "Malformed line #" << line_index << ": "
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<< lines[line_index];
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return false;
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}
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const int customer_id = parsed_int[0];
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const int x = parsed_int[1];
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const int y = parsed_int[2];
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const int64_t demand = parsed_int[3];
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const int64_t open_time = parsed_int[4];
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const int64_t close_time = parsed_int[5];
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const int64_t service_time = parsed_int[6];
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const int pickup = parsed_int[7];
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const int delivery = parsed_int[8];
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customer_ids.push_back(customer_id);
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coords.push_back(std::make_pair(x, y));
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demands.push_back(demand);
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open_times.push_back(open_time);
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close_times.push_back(close_time);
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service_times.push_back(service_time);
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pickups.push_back(RoutingIndexManager::NodeIndex(pickup));
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deliveries.push_back(RoutingIndexManager::NodeIndex(delivery));
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if (pickup == 0 && delivery == 0) {
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depot = RoutingIndexManager::NodeIndex(pickups.size() - 1);
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}
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horizon = std::max(horizon, close_time);
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}
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// Build pickup and delivery model.
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const int num_nodes = customer_ids.size();
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RoutingIndexManager manager(num_nodes, num_vehicles, depot);
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RoutingModel routing(manager, model_parameters);
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const int vehicle_cost = routing.RegisterTransitCallback(
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[&coords, &manager](int64_t i, int64_t j) {
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return Travel(const_cast<const Coordinates*>(&coords),
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manager.IndexToNode(i), manager.IndexToNode(j));
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});
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routing.SetArcCostEvaluatorOfAllVehicles(vehicle_cost);
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RoutingTransitCallback2 demand_evaluator = [&](int64_t from_index,
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int64_t to_index) {
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return demands[manager.IndexToNode(from_index).value()];
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};
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routing.AddDimension(routing.RegisterTransitCallback(demand_evaluator), 0,
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capacity, /*fix_start_cumul_to_zero=*/true, "demand");
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RoutingTransitCallback2 time_evaluator = [&](int64_t from_index,
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int64_t to_index) {
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return TravelPlusServiceTime(manager, &coords, &service_times, from_index,
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to_index);
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};
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routing.AddDimension(routing.RegisterTransitCallback(time_evaluator),
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kScalingFactor * horizon, kScalingFactor * horizon,
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/*fix_start_cumul_to_zero=*/true, "time");
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const RoutingDimension& time_dimension = routing.GetDimensionOrDie("time");
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Solver* const solver = routing.solver();
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for (int node = 0; node < num_nodes; ++node) {
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const int64_t index =
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manager.NodeToIndex(RoutingIndexManager::NodeIndex(node));
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if (pickups[node] == 0 && deliveries[node] != 0) {
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const int64_t delivery_index = manager.NodeToIndex(deliveries[node]);
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solver->AddConstraint(solver->MakeEquality(
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routing.VehicleVar(index), routing.VehicleVar(delivery_index)));
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solver->AddConstraint(
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solver->MakeLessOrEqual(time_dimension.CumulVar(index),
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time_dimension.CumulVar(delivery_index)));
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routing.AddPickupAndDelivery(index,
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manager.NodeToIndex(deliveries[node]));
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}
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IntVar* const cumul = time_dimension.CumulVar(index);
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cumul->SetMin(kScalingFactor * open_times[node]);
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cumul->SetMax(kScalingFactor * close_times[node]);
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}
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if (search_parameters.local_search_metaheuristic() ==
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LocalSearchMetaheuristic::GENERIC_TABU_SEARCH) {
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// Create variable for the total schedule time of the solution.
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// This will be used as one of the Tabu criteria.
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// This is done here and not in GetTabuVarsCallback as it requires calling
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// AddVariableMinimizedByFinalizer and this method must be called early.
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std::vector<IntVar*> end_cumuls;
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std::vector<IntVar*> start_cumuls;
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for (int i = 0; i < routing.vehicles(); ++i) {
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end_cumuls.push_back(time_dimension.CumulVar(routing.End(i)));
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start_cumuls.push_back(time_dimension.CumulVar(routing.Start(i)));
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}
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IntVar* total_time = solver->MakeIntVar(0, 99999999, "total");
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solver->AddConstraint(solver->MakeEquality(
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solver->MakeDifference(solver->MakeSum(end_cumuls),
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solver->MakeSum(start_cumuls)),
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total_time));
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routing.AddVariableMinimizedByFinalizer(total_time);
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RoutingModel::GetTabuVarsCallback tabu_var_callback =
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[total_time](RoutingModel* model) {
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return GetTabuVars({total_time}, model);
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};
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routing.SetTabuVarsCallback(tabu_var_callback);
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}
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// Adding penalty costs to allow skipping orders.
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const int64_t kPenalty = 10000000;
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for (RoutingIndexManager::NodeIndex order(1); order < routing.nodes();
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++order) {
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std::vector<int64_t> orders(1, manager.NodeToIndex(order));
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routing.AddDisjunction(orders, kPenalty);
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}
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// Solve pickup and delivery problem.
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SimpleCycleTimer timer;
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timer.Start();
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const Assignment* assignment = routing.SolveWithParameters(search_parameters);
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timer.Stop();
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LOG(INFO) << routing.solver()->LocalSearchProfile();
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if (nullptr != assignment) {
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LOG(INFO) << VerboseOutput(routing, manager, *assignment, coords,
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service_times);
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LOG(INFO) << "Cost: " << assignment->ObjectiveValue();
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int skipped_nodes = 0;
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for (int node = 0; node < routing.Size(); node++) {
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if (!routing.IsEnd(node) && !routing.IsStart(node) &&
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assignment->Value(routing.NextVar(node)) == node) {
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skipped_nodes++;
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}
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}
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LOG(INFO) << "Number of skipped nodes: " << skipped_nodes;
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int num_used_vehicles = 0;
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for (int v = 0; v < routing.vehicles(); v++) {
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if (routing.IsVehicleUsed(*assignment, v)) {
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num_used_vehicles++;
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}
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}
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LOG(INFO) << "Number of used vehicles: " << num_used_vehicles;
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LOG(INFO) << "Time: " << timer.Get();
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return true;
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}
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return false;
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}
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} // namespace operations_research
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int main(int argc, char** argv) {
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absl::SetFlag(&FLAGS_logtostderr, true);
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InitGoogle(argv[0], &argc, &argv, true);
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operations_research::RoutingModelParameters model_parameters =
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operations_research::DefaultRoutingModelParameters();
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model_parameters.set_reduce_vehicle_cost_model(
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absl::GetFlag(FLAGS_reduce_vehicle_cost_model));
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operations_research::RoutingSearchParameters search_parameters =
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operations_research::DefaultRoutingSearchParameters();
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CHECK(google::protobuf::TextFormat::MergeFromString(
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absl::GetFlag(FLAGS_routing_search_parameters), &search_parameters));
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if (!operations_research::LoadAndSolve(absl::GetFlag(FLAGS_pdp_file),
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model_parameters, search_parameters)) {
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LOG(INFO) << "Error solving " << absl::GetFlag(FLAGS_pdp_file);
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}
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return EXIT_SUCCESS;
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}
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