osrm-backend/routing_algorithms/tsp_farthest_insertion.hpp

/*

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#ifndef TSP_FARTHEST_INSERTION_HPP
#define TSP_FARTHEST_INSERTION_HPP


#include "../data_structures/search_engine.hpp"
#include "../util/string_util.hpp"

#include <osrm/json_container.hpp>

#include <cstdlib>

#include <algorithm>
#include <string>
#include <vector>
#include <limits>


namespace osrm
{
namespace tsp
{

void FarthestInsertion(const RouteParameters & route_parameters,
                       const PhantomNodeArray & phantom_node_vector,
                       const std::vector<EdgeWeight> & dist_table,
                       InternalRouteResult & min_route,
                       std::vector<int> & min_loc_permutation) {
    //////////////////////////////////////////////////////////////////////////////////////////////////
    // START FARTHEST INSERTION HERE
    // 1. start at a random round trip of 2 locations
    // 2. find the location that is the farthest away from the visited locations and whose insertion will make the round trip the longest
    // 3. add the found location to the current round trip such that round trip is the shortest
    // 4. repeat 2-3 until all locations are visited
    // 5. DONE!
    //////////////////////////////////////////////////////////////////////////////////////////////////

    const auto number_of_locations = phantom_node_vector.size();
    // list of the trip that will be found incrementally
    std::list<int> current_trip;
    // tracks which nodes have been already visited
    std::vector<bool> visited(number_of_locations, false);


    // find the pair of location with the biggest distance and make the pair the initial start trip
    const auto index = std::distance(dist_table.begin(), std::max_element(dist_table.begin(), dist_table.end()));
    const int max_from = index / number_of_locations;
    const int max_to = index % number_of_locations;

    visited[max_from] = true;
    visited[max_to] = true;
    current_trip.push_back(max_from);
    current_trip.push_back(max_to);

    // add all other nodes missing (two nodes are already in the initial start trip)
    for (int j = 2; j < number_of_locations; ++j) {
        auto shortest_max_tour = -1;
        int next_node = -1;
        std::list<int>::iterator min_max_insert;

        // find unvisited loc i that is the farthest away from all other visited locs
        for (int i = 0; i < number_of_locations; ++i) {
            if (!visited[i]) {
                // longest_min_tour is the distance of the longest of all insertions with the minimal distance
                auto longest_min_tour = std::numeric_limits<int>::max();
                // following_loc is the location that comes after the location that is to be inserted
                std::list<int>::iterator following_loc;

                // for all nodes in the current trip find the best insertion resulting in the shortest path
                for (auto from_node = current_trip.begin(); from_node != std::prev(current_trip.end()); ++from_node) {
                    auto to_node = std::next(from_node);

                    auto dist_from = *(dist_table.begin() + (*from_node * number_of_locations) + i);
                    auto dist_to = *(dist_table.begin() + (i * number_of_locations) + *to_node);
                    auto trip_dist = dist_from + dist_to - *(dist_table.begin() + (*from_node * number_of_locations) + *to_node);

                    // from all possible insertions to the current trip, choose the longest of all minimal insertions
                    if (trip_dist < longest_min_tour) {
                        longest_min_tour = trip_dist;
                        following_loc = to_node;
                    }
                }
                {   // check insertion between last and first location too
                    auto from_node = std::prev(current_trip.end());
                    auto to_node = current_trip.begin();

                    auto dist_from = *(dist_table.begin() + (*from_node * number_of_locations) + i);
                    auto dist_to = *(dist_table.begin() + (i * number_of_locations) + *to_node);
                    auto trip_dist = dist_from + dist_to - *(dist_table.begin() + (*from_node * number_of_locations) + *to_node);
                    if (trip_dist < longest_min_tour) {
                        longest_min_tour = trip_dist;
                        following_loc = to_node;
                    }
                }

                // add the location to the current trip such that it results in the shortest total tour
                if (longest_min_tour > shortest_max_tour) {
                    shortest_max_tour = longest_min_tour;
                    next_node = i;
                    min_max_insert = following_loc;
                }
            }
        }
        // mark as visited and insert node
        visited[next_node] = true;
        current_trip.insert(min_max_insert, next_node);
    }

    // given he final trip, compute total distance and return the route and location permutation
    PhantomNodes viapoint;
    int perm = 0;
    for (auto it = current_trip.begin(); it != std::prev(current_trip.end()); ++it) {
        auto from_node = *it;
        auto to_node = *std::next(it);

        viapoint = PhantomNodes{phantom_node_vector[from_node][0], phantom_node_vector[to_node][0]};
        min_route.segment_end_coordinates.emplace_back(viapoint);

        min_loc_permutation[from_node] = perm;
        ++perm;
    }
    {   // check dist between last and first location too
        viapoint = PhantomNodes{phantom_node_vector[*std::prev(current_trip.end())][0], phantom_node_vector[current_trip.front()][0]};
        min_route.segment_end_coordinates.emplace_back(viapoint);
        min_loc_permutation[*std::prev(current_trip.end())] = perm;
    }
}


}
}

#endif // TSP_FARTHEST_INSERTION_HPP