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_spptw.size()) << std::endl;
for (int i = 0; i < static_cast< int >(opt_solutions_spptw.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;
}