boost/libs/graph/example/r_c_shortest_paths_example.cpp

// Copyright Michael Drexl 2005, 2006.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://boost.org/LICENSE_1_0.txt)

// Example use of the resource-constrained shortest paths algorithm.
#include <boost/config.hpp>

#ifdef BOOST_MSVC
#pragma warning(disable : 4267)
#endif

#include <boost/graph/adjacency_list.hpp>

#include <boost/graph/r_c_shortest_paths.hpp>
#include <iostream>

using namespace boost;

struct SPPRC_Example_Graph_Vert_Prop
{
    SPPRC_Example_Graph_Vert_Prop(int n = 0, int e = 0, int l = 0)
    : num(n), eat(e), lat(l)
    {
    }
    int num;
    // earliest arrival time
    int eat;
    // latest arrival time
    int lat;
};

struct SPPRC_Example_Graph_Arc_Prop
{
    SPPRC_Example_Graph_Arc_Prop(int n = 0, int c = 0, int t = 0)
    : num(n), cost(c), time(t)
    {
    }
    int num;
    // traversal cost
    int cost;
    // traversal time
    int time;
};

typedef adjacency_list< vecS, vecS, directedS, SPPRC_Example_Graph_Vert_Prop,
    SPPRC_Example_Graph_Arc_Prop >
    SPPRC_Example_Graph;

// data structures for spp without resource constraints:
// ResourceContainer model
struct spp_no_rc_res_cont
{
    spp_no_rc_res_cont(int c = 0) : cost(c) {};
    spp_no_rc_res_cont& operator=(const spp_no_rc_res_cont& other)
    {
        if (this == &other)
            return *this;
        this->~spp_no_rc_res_cont();
        new (this) spp_no_rc_res_cont(other);
        return *this;
    }
    int cost;
};

bool operator==(
    const spp_no_rc_res_cont& res_cont_1, const spp_no_rc_res_cont& res_cont_2)
{
    return (res_cont_1.cost == res_cont_2.cost);
}

bool operator<(
    const spp_no_rc_res_cont& res_cont_1, const spp_no_rc_res_cont& res_cont_2)
{
    return (res_cont_1.cost < res_cont_2.cost);
}

// ResourceExtensionFunction model
class ref_no_res_cont
{
public:
    inline bool operator()(const SPPRC_Example_Graph& g,
        spp_no_rc_res_cont& new_cont, const spp_no_rc_res_cont& old_cont,
        graph_traits< SPPRC_Example_Graph >::edge_descriptor ed) const
    {
        new_cont.cost = old_cont.cost + g[ed].cost;
        return true;
    }
};

// DominanceFunction model
class dominance_no_res_cont
{
public:
    inline bool operator()(const spp_no_rc_res_cont& res_cont_1,
        const spp_no_rc_res_cont& res_cont_2) const
    {
        // must be "<=" here!!!
        // must NOT be "<"!!!
        return res_cont_1.cost <= res_cont_2.cost;
        // this is not a contradiction to the documentation
        // the documentation says:
        // "A label $l_1$ dominates a label $l_2$ if and only if both are
        // resident at the same vertex, and if, for each resource, the resource
        // consumption of $l_1$ is less than or equal to the resource
        // consumption of $l_2$, and if there is at least one resource where
        // $l_1$ has a lower resource consumption than $l_2$." one can think of
        // a new label with a resource consumption equal to that of an old label
        // as being dominated by that old label, because the new one will have a
        // higher number and is created at a later point in time, so one can
        // implicitly use the number or the creation time as a resource for
        // tie-breaking
    }
};
// end data structures for spp without resource constraints:

// data structures for shortest path problem with time windows (spptw)
// ResourceContainer model
struct spp_spptw_res_cont
{
    spp_spptw_res_cont(int c = 0, int t = 0) : cost(c), time(t) {}
    spp_spptw_res_cont& operator=(const spp_spptw_res_cont& other)
    {
        if (this == &other)
            return *this;
        this->~spp_spptw_res_cont();
        new (this) spp_spptw_res_cont(other);
        return *this;
    }
    int cost;
    int time;
};

bool operator==(
    const spp_spptw_res_cont& res_cont_1, const spp_spptw_res_cont& res_cont_2)
{
    return (res_cont_1.cost == res_cont_2.cost
        && res_cont_1.time == res_cont_2.time);
}

bool operator<(
    const spp_spptw_res_cont& res_cont_1, const spp_spptw_res_cont& res_cont_2)
{
    if (res_cont_1.cost > res_cont_2.cost)
        return false;
    if (res_cont_1.cost == res_cont_2.cost)
        return res_cont_1.time < res_cont_2.time;
    return true;
}

// ResourceExtensionFunction model
class ref_spptw
{
public:
    inline bool operator()(const SPPRC_Example_Graph& g,
        spp_spptw_res_cont& new_cont, const spp_spptw_res_cont& old_cont,
        graph_traits< SPPRC_Example_Graph >::edge_descriptor ed) const
    {
        const SPPRC_Example_Graph_Arc_Prop& arc_prop = get(edge_bundle, g)[ed];
        const SPPRC_Example_Graph_Vert_Prop& vert_prop
            = get(vertex_bundle, g)[target(ed, g)];
        new_cont.cost = old_cont.cost + arc_prop.cost;
        int& i_time = new_cont.time;
        i_time = old_cont.time + arc_prop.time;
        i_time < vert_prop.eat ? i_time = vert_prop.eat : 0;
        return i_time <= vert_prop.lat ? true : false;
    }
};

// DominanceFunction model
class dominance_spptw
{
public:
    inline bool operator()(const spp_spptw_res_cont& res_cont_1,
        const spp_spptw_res_cont& res_cont_2) const
    {
        // must be "<=" here!!!
        // must NOT be "<"!!!
        return res_cont_1.cost <= res_cont_2.cost
            && res_cont_1.time <= res_cont_2.time;
        // this is not a contradiction to the documentation
        // the documentation says:
        // "A label $l_1$ dominates a label $l_2$ if and only if both are
        // resident at the same vertex, and if, for each resource, the resource
        // consumption of $l_1$ is less than or equal to the resource
        // consumption of $l_2$, and if there is at least one resource where
        // $l_1$ has a lower resource consumption than $l_2$." one can think of
        // a new label with a resource consumption equal to that of an old label
        // as being dominated by that old label, because the new one will have a
        // higher number and is created at a later point in time, so one can
        // implicitly use the number or the creation time as a resource for
        // tie-breaking
    }
};
// end data structures for shortest path problem with time windows (spptw)

// example graph structure and cost from
// http://www.boost.org/libs/graph/example/dijkstra-example.cpp
enum nodes
{
    A,
    B,
    C,
    D,
    E
};
char name[] = "ABCDE";

int main()
{
    SPPRC_Example_Graph g;

    add_vertex(SPPRC_Example_Graph_Vert_Prop(A, 0, 0), g);
    add_vertex(SPPRC_Example_Graph_Vert_Prop(B, 5, 20), g);
    add_vertex(SPPRC_Example_Graph_Vert_Prop(C, 6, 10), g);
    add_vertex(SPPRC_Example_Graph_Vert_Prop(D, 3, 12), g);
    add_vertex(SPPRC_Example_Graph_Vert_Prop(E, 0, 100), g);

    add_edge(A, C, SPPRC_Example_Graph_Arc_Prop(0, 1, 5), g);
    add_edge(B, B, SPPRC_Example_Graph_Arc_Prop(1, 2, 5), g);
    add_edge(B, D, SPPRC_Example_Graph_Arc_Prop(2, 1, 2), g);
    add_edge(B, E, SPPRC_Example_Graph_Arc_Prop(3, 2, 7), g);
    add_edge(C, B, SPPRC_Example_Graph_Arc_Prop(4, 7, 3), g);
    add_edge(C, D, SPPRC_Example_Graph_Arc_Prop(5, 3, 8), g);
    add_edge(D, E, SPPRC_Example_Graph_Arc_Prop(6, 1, 3), g);
    add_edge(E, A, SPPRC_Example_Graph_Arc_Prop(7, 1, 5), g);
    add_edge(E, B, SPPRC_Example_Graph_Arc_Prop(8, 1, 4), g);

    // the unique shortest path from A to E in the dijkstra-example.cpp is
    // A -> C -> D -> E
    // its length is 5
    // the following code also yields this result

    // with the above time windows, this path is infeasible
    // now, there are two shortest paths that are also feasible with respect to
    // the vertex time windows:
    // A -> C -> B -> D -> E and
    // A -> C -> B -> E
    // however, the latter has a longer total travel time and is therefore not
    // pareto-optimal, i.e., it is dominated by the former path
    // therefore, the code below returns only the former path

    // spp without resource constraints
    graph_traits< SPPRC_Example_Graph >::vertex_descriptor s = A;
    graph_traits< SPPRC_Example_Graph >::vertex_descriptor t = E;

    std::vector<
        std::vector< graph_traits< SPPRC_Example_Graph >::edge_descriptor > >
        opt_solutions;
    std::vector< spp_no_rc_res_cont > pareto_opt_rcs_no_rc;

    r_c_shortest_paths(g, get(&SPPRC_Example_Graph_Vert_Prop::num, g),
        get(&SPPRC_Example_Graph_Arc_Prop::num, g), s, t, opt_solutions,
        pareto_opt_rcs_no_rc, spp_no_rc_res_cont(0), ref_no_res_cont(),
        dominance_no_res_cont(),
        std::allocator< r_c_shortest_paths_label< SPPRC_Example_Graph,
            spp_no_rc_res_cont > >(),
        default_r_c_shortest_paths_visitor());

    std::cout << "SPP without resource constraints:" << std::endl;
    std::cout << "Number of optimal solutions: ";
    std::cout << static_cast< int >(opt_solutions.size()) << std::endl;
    for (int i = 0; i < static_cast< int >(opt_solutions.size()); ++i)
    {
        std::cout << "The " << i << "th shortest path from A to E is: ";
        std::cout << std::endl;
        for (int j = static_cast< int >(opt_solutions[i].size()) - 1; j >= 0;
             --j)
            std::cout << name[source(opt_solutions[i][j], g)] << std::endl;
        std::cout << "E" << std::endl;
        std::cout << "Length: " << pareto_opt_rcs_no_rc[i].cost << std::endl;
    }
    std::cout << std::endl;

    // spptw
    std::vector<
        std::vector< graph_traits< SPPRC_Example_Graph >::edge_descriptor > >
        opt_solutions_spptw;
    std::vector< spp_spptw_res_cont > pareto_opt_rcs_spptw;

    r_c_shortest_paths(g, get(&SPPRC_Example_Graph_Vert_Prop::num, g),
        get(&SPPRC_Example_Graph_Arc_Prop::num, g), s, t, opt_solutions_spptw,
        pareto_opt_rcs_spptw, spp_spptw_res_cont(0, 0), ref_spptw(),
        dominance_spptw(),
        std::allocator< r_c_shortest_paths_label< SPPRC_Example_Graph,
            spp_spptw_res_cont > >(),
        default_r_c_shortest_paths_visitor());

    std::cout << "SPP with time windows:" << std::endl;
    std::cout << "Number of optimal solutions: ";
    std::cout << static_cast< int >(opt_solutions.size()) << std::endl;
    for (int i = 0; i < static_cast< int >(opt_solutions.size()); ++i)
    {
        std::cout << "The " << i << "th shortest path from A to E is: ";
        std::cout << std::endl;
        for (int j = static_cast< int >(opt_solutions_spptw[i].size()) - 1;
             j >= 0; --j)
            std::cout << name[source(opt_solutions_spptw[i][j], g)]
                      << std::endl;
        std::cout << "E" << std::endl;
        std::cout << "Length: " << pareto_opt_rcs_spptw[i].cost << std::endl;
        std::cout << "Time: " << pareto_opt_rcs_spptw[i].time << std::endl;
    }

    // utility function check_r_c_path example
    std::cout << std::endl;
    bool b_is_a_path_at_all = false;
    bool b_feasible = false;
    bool b_correctly_extended = false;
    spp_spptw_res_cont actual_final_resource_levels(0, 0);
    graph_traits< SPPRC_Example_Graph >::edge_descriptor ed_last_extended_arc;
    check_r_c_path(g, opt_solutions_spptw[0], spp_spptw_res_cont(0, 0), true,
        pareto_opt_rcs_spptw[0], actual_final_resource_levels, ref_spptw(),
        b_is_a_path_at_all, b_feasible, b_correctly_extended,
        ed_last_extended_arc);
    if (!b_is_a_path_at_all)
        std::cout << "Not a path." << std::endl;
    if (!b_feasible)
        std::cout << "Not a feasible path." << std::endl;
    if (!b_correctly_extended)
        std::cout << "Not correctly extended." << std::endl;
    if (b_is_a_path_at_all && b_feasible && b_correctly_extended)
    {
        std::cout << "Actual final resource levels:" << std::endl;
        std::cout << "Length: " << actual_final_resource_levels.cost
                  << std::endl;
        std::cout << "Time: " << actual_final_resource_levels.time << std::endl;
        std::cout << "OK." << std::endl;
    }

    return 0;
}