pricer_vrp.cpp

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/*         SCIP --- Solving Constraint Integer Programs                      */
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/**@file pricer_vrp.cpp
 * @brief VRP pricer plugin
 * @author Andreas Bley
 * @author Marc Pfetsch
 */

#include "pricer_vrp.h"
#include "pqueue.h"

#include <iostream>
#include <map>
#include <vector>

#include "scip/cons_linear.h"

using namespace std;
using namespace scip;




/** Constructs the pricer object with the data needed
 *
 *  An alternative is to have a problem data class which allows to access the data.
 */
ObjPricerVRP::ObjPricerVRP(
   SCIP*                                scip,          /**< SCIP pointer */
   const char*                          p_name,        /**< name of pricer */
   const int                            p_num_nodes,   /**< number of nodes */
   const int                            p_capacity,    /**< vehicle capacity */
   const vector< int >&                 p_demand,      /**< demand array */
   const vector< vector<int> >&         p_distance,    /**< matrix of distances */
   const vector< vector<SCIP_VAR*> >&   p_arc_var,     /**< matrix of arc variables */
   const vector< vector<SCIP_CONS*> >&  p_arc_con,     /**< matrix of arc constraints */
   const vector<SCIP_CONS* >&           p_part_con     /**< array of partitioning constraints */
   ):
   ObjPricer(scip, p_name, "Finds tour with negative reduced cost.", 0, TRUE),
   _num_nodes(p_num_nodes),
   _capacity(p_capacity),
   _demand(p_demand),
   _distance(p_distance),
   _arc_var(p_arc_var),
   _arc_con(p_arc_con),
   _part_con(p_part_con)
{}


/** Destructs the pricer object. */
ObjPricerVRP::~ObjPricerVRP()
{}


/** initialization method of variable pricer (called after problem was transformed)
 *
 *  Because SCIP transformes the original problem in preprocessing, we need to get the references to
 *  the variables and constraints in the transformed problem from the references in the original
 *  problem.
 */
SCIP_DECL_PRICERINIT(ObjPricerVRP::scip_init)
{
   for (int i = 0; i < num_nodes(); ++i)
   {
      for (int j = 0; j < i; ++j)
      {
         SCIP_CALL( SCIPgetTransformedVar(scip, _arc_var[i][j], &_arc_var[i][j]) ); /*lint !e732 !e747*/
         SCIP_CALL( SCIPgetTransformedCons(scip, _arc_con[i][j], &_arc_con[i][j]) ); /*lint !e732 !e747*/
      }
   }
   for (int i = 1; i < num_nodes(); ++i)
   {
      SCIP_CALL( SCIPgetTransformedCons(scip, _part_con[i], &_part_con[i]) ); /*lint !e732 !e747*/
   }

   return SCIP_OKAY;
} /*lint !e715*/


/** perform pricing
 *
 *  @todo compute shortest length restricted tour w.r.t. duals
 */
SCIP_RETCODE ObjPricerVRP::pricing(
   SCIP*                 scip,               /**< SCIP data structure */
   bool                  isfarkas            /**< whether we perform Farkas pricing */
   ) const
{
   /* allocate array for reduced costs */
   vector< vector<SCIP_Real> > red_length(num_nodes());  /*lint !e732 !e747*/
   for (int i = 0; i < num_nodes(); ++i)
      red_length[i].resize(i, 0.0); /*lint !e732 !e747*/

   /* compute reduced-cost arc lengths store only lower triangualar matrix, i.e., red_length[i][j] only for i > j */
   if ( isfarkas )
   {
      for (int i = 0; i < num_nodes(); ++i)
      {
         assert( i == 0 || part_con(i) != 0 );
         for (int j = 0; j < i; ++j)
         {
            SCIP_Real r = 0.0;
            assert( arc_con(i,j) != 0 );

            r -= SCIPgetDualfarkasLinear(scip, arc_con(i,j));
            if ( j != 0 )
               r -= 0.5 * SCIPgetDualfarkasLinear(scip, part_con(j));
            if ( i != 0 )
               r -= 0.5 * SCIPgetDualfarkasLinear(scip, part_con(i));
            red_length[i][j] = r;  /*lint !e732 !e747*/
         }
      }
   }
   else
   {
      for (int i = 0; i < num_nodes(); ++i)
      {
         assert( i == 0 || part_con(i) != 0 );
         for (int j = 0; j < i; ++j)
         {
            SCIP_Real r = 0.0;
            assert( arc_con(i,j) != 0 );

            r -= SCIPgetDualsolLinear(scip, arc_con(i,j));
            if ( j != 0 )
               r -= 0.5 * SCIPgetDualsolLinear(scip, part_con(j));
            if ( i != 0 )
               r -= 0.5 * SCIPgetDualsolLinear(scip, part_con(i));
            red_length[i][j] = r; /*lint !e732 !e747*/
         }
      }
   }

#ifdef SCIP_OUTPUT
   if ( isfarkas )
   {
      SCIPinfoMessage(scip, NULL, "dual ray solution:\n");
      for (int i = 0; i < num_nodes(); ++i)
      {
         for (int j = 0; j < i; ++j)
            SCIPinfoMessage(scip, NULL, "arc_%d_%d:  %g\n", i, j, SCIPgetDualfarkasLinear(scip, arc_con(i,j)));
      }

      for (int i = 1; i < num_nodes(); ++i)
         SCIPinfoMessage(scip, NULL, "part_%d:  %g\n", i, SCIPgetDualfarkasLinear(scip, part_con(i)));

      for (int i = 0; i < num_nodes(); ++i)
      {
         for (int j = 0; j < i; ++j)
            SCIPinfoMessage(scip, NULL, "length_%d_%d:  %g\n", i, j, red_length[i][j]);
      }
   }
   else
   {
      SCIPinfoMessage(scip, NULL, "dual solution:\n");
      for (int i = 0; i < num_nodes(); ++i)
      {
         for (int j = 0; j < i; ++j)
            SCIPinfoMessage(scip, NULL, "arc_%d_%d:  %g\n", i, j, SCIPgetDualsolLinear(scip, arc_con(i,j)));
      }

      for (int i = 1; i < num_nodes(); ++i)
         SCIPinfoMessage(scip, NULL, "part_%d:  %g\n", i, SCIPgetDualsolLinear(scip, part_con(i)));

      for (int i = 0; i < num_nodes(); ++i)
      {
         for (int j = 0; j < i; ++j)
            SCIPinfoMessage(scip, NULL, "length_%d_%d:  %g\n", i, j, red_length[i][j]);
      }
   }
#endif

   /* compute shortest length restricted tour w.r.t. reduced-cost arc length */
   list<int> tour;
   SCIP_Real reduced_cost = find_shortest_tour(red_length, tour);

   /* add tour variable */
   if ( SCIPisNegative(scip, reduced_cost) )
   {
      return add_tour_variable(scip, tour);
   }

#ifdef SCIP_OUTPUT
   SCIP_CALL( SCIPwriteTransProblem(scip, "vrp.lp", "lp", FALSE) );
#endif

   return SCIP_OKAY;
}



/** Pricing of additional variables if LP is feasible.
 *
 *  - get the values of the dual variables you need
 *  - construct the reduced-cost arc lengths from these values
 *  - find the shortest admissible tour with respect to these lengths
 *  - if this tour has negative reduced cost, add it to the LP
 *
 *  possible return values for *result:
 *  - SCIP_SUCCESS    : at least one improving variable was found, or it is ensured that no such variable exists
 *  - SCIP_DIDNOTRUN  : the pricing process was aborted by the pricer, there is no guarantee that the current LP solution is optimal
 */
SCIP_DECL_PRICERREDCOST(ObjPricerVRP::scip_redcost)
{
   SCIPdebugMsg(scip, "call scip_redcost ...\n");

   /* set result pointer, see above */
   *result = SCIP_SUCCESS;

   /* call pricing routine */
   SCIP_CALL( pricing(scip, false) );

   return SCIP_OKAY;
} /*lint !e715*/


/** Pricing of additional variables if LP is infeasible.
 *
 *  - get the values of the dual Farks multipliers you need
 *  - construct the reduced-cost arc lengths from these values
 *  - find the shortest admissible tour with respect to these lengths
 *  - if this tour has negative reduced cost, add it to the LP
 */
SCIP_DECL_PRICERFARKAS(ObjPricerVRP::scip_farkas)
{
   SCIPdebugMsg(scip, "call scip_farkas ...\n");

   /* call pricing routine */
   SCIP_CALL( pricing(scip, true) );

   return SCIP_OKAY;
} /*lint !e715*/


/** add tour variable to problem */
SCIP_RETCODE ObjPricerVRP::add_tour_variable(
   SCIP*                 scip,               /**< SCIP data structure */
   const list<int>&      tour                /**< list of nodes in tour */
   ) const
{
   /* create meaningful variable name */
   char tmp_name[255];
   char var_name[255];
   (void) SCIPsnprintf(var_name, 255, "T");
   for (list<int>::const_iterator it = tour.begin(); it != tour.end(); ++it)  /*lint !e1702*/
   {
      strncpy(tmp_name, var_name, 255);
      (void) SCIPsnprintf(var_name, 255, "%s_%d", tmp_name, *it);
   }
   SCIPdebugMsg(scip, "new variable <%s>\n", var_name);

   /* create the new variable: Use upper bound of infinity such that we do not have to care about
    * the reduced costs of the variable in the pricing. The upper bound of 1 is implicitly satisfied
    * due to the set partitioning constraints.
    */
   SCIP_VAR* var;
   SCIP_CALL( SCIPcreateVar(scip, &var, var_name,
                            0.0,                     // lower bound
                            SCIPinfinity(scip),      // upper bound
                            0.0,                     // objective
                            SCIP_VARTYPE_CONTINUOUS, // variable type
                            false, false, NULL, NULL, NULL, NULL, NULL) );

   /* add new variable to the list of variables to price into LP (score: leave 1 here) */
   SCIP_CALL( SCIPaddPricedVar(scip, var, 1.0) );

   /* add coefficient into the set partition constraints */
   for (list<int>::const_iterator it = tour.begin(); it != tour.end(); ++it) /*lint !e1702*/
   {
      assert( 0 <= *it && *it < num_nodes() );
      SCIP_CALL( SCIPaddCoefLinear(scip, part_con(*it), var, 1.0) );
   }

   /* add coefficient into arc routing constraints */
   int last = 0;
   for (list<int>::const_iterator it = tour.begin(); it != tour.end(); ++it) /*lint !e1702*/
   {
      assert( 0 <= *it && *it < num_nodes() );
      SCIP_CALL( SCIPaddCoefLinear(scip, arc_con(last, *it), var, 1.0) );
      last = *it;
   }
   SCIP_CALL( SCIPaddCoefLinear(scip, arc_con(last, 0), var, 1.0 ) );

   /* cleanup */
   SCIP_CALL( SCIPreleaseVar(scip, &var) );

   return SCIP_OKAY;
}


/** Computes a shortest admissible tour with respect to the given lengths. The function must return
 *  the computed tour via the parameter tour and the length (w.r.t. given lengths) of this tour as
 *  return parameter. The returned tour must be the ordered list of customer nodes contained in the
 *  tour (i.e., 2-5-7 for the tour 0-2-5-7-0).
 */
namespace
{

/* types needed for prioity queue -------------------- */
static const SCIP_Real   eps = 1e-9;

struct PQUEUE_KEY
{
   int       demand;
   SCIP_Real length;

   PQUEUE_KEY() : demand(0), length(0.0) {}
};

bool operator< (const PQUEUE_KEY& l1, const PQUEUE_KEY& l2)
{
   if ( l1.demand < l2.demand )
      return true;
   if ( l1.demand > l2.demand )
      return false;
   if ( l1.length < l2.length-eps )
      return true;
   /* not needed, since we return false anyway:
   if ( l1.length > l2.length+eps )
      return false;
   */
   return false;
}

typedef int                                    PQUEUE_DATA; // node
typedef pqueue<PQUEUE_KEY,PQUEUE_DATA>         PQUEUE;
typedef PQUEUE::pqueue_item                    PQUEUE_ITEM;


/* types needed for dyn. programming table */
struct NODE_TABLE_DATA
{
   SCIP_Real             length;
   int                   predecessor;
   PQUEUE::pqueue_item   queue_item;

   NODE_TABLE_DATA( ) : length(0.0), predecessor(-1), queue_item( NULL ) {}
};

typedef int NODE_TABLE_KEY; // demand
typedef std::map< NODE_TABLE_KEY, NODE_TABLE_DATA > NODE_TABLE;
}


/** return negative reduced cost tour (uses restricted shortest path dynamic programming algorithm) 
 *
 *  The algorithm uses the priority queue implementation in pqueue.h. SCIP's implementation of
 *  priority queues cannot be used, since it currently does not support removal of elements that are
 *  not at the top.
 */
SCIP_Real ObjPricerVRP::find_shortest_tour(
   const vector< vector<SCIP_Real> >& length,   /**< matrix of lengths */
   list<int>&            tour                /**< list of nodes in tour */
   ) const
{
   tour.clear();

   SCIPdebugMessage("Enter RSP - capacity: %d\n", capacity());

   /* begin algorithm */
   PQUEUE               PQ;
   vector< NODE_TABLE > table(num_nodes()); /*lint !e732 !e747*/

   /* insert root node (start at node 0) */
   PQUEUE_KEY       queue_key;
   PQUEUE_DATA      queue_data = 0;
   PQUEUE_ITEM      queue_item = PQ.insert(queue_key, queue_data);

   NODE_TABLE_KEY   table_key = 0;
   NODE_TABLE_DATA  table_entry;

   /* run Dijkstra-like updates */
   while ( ! PQ.empty() )
   {
      /* get front queue entry */
      queue_item = PQ.top();
      queue_key  = PQ.get_key (queue_item);
      queue_data = PQ.get_data(queue_item);
      PQ.pop();

      /* get corresponding node and node-table key */
      const int       curr_node   = queue_data;
      const SCIP_Real curr_length = queue_key.length;
      const int       curr_demand = queue_key.demand;

      /* stop as soon as some negative length tour was found */
      if ( curr_node == 0 && curr_length < -eps )
         break;

      /* stop as soon don't create multi-tours  */
      if ( curr_node == 0 && curr_demand != 0 )
         continue;

      /* update all active neighbors */
      for (int next_node = 0; next_node < num_nodes(); ++next_node)
      {
         if ( next_node == curr_node )
            continue;
         if ( have_edge( next_node, curr_node ) == false )
            continue;

         const int next_demand = curr_demand + demand(next_node);

         if ( next_demand > capacity() )
            continue;

         const SCIP_Real next_length = curr_length + ( curr_node > next_node ?      /*lint !e732 !e747*/
                                                    length[curr_node][next_node] :  /*lint !e732 !e747*/
                                                    length[next_node][curr_node] ); /*lint !e732 !e747*/

         NODE_TABLE& next_table = table[next_node]; /*lint !e732 !e747*/

         /* check if new table entry would be dominated */
         bool skip = false;
         list<NODE_TABLE::iterator> dominated;

         for (NODE_TABLE::iterator it = next_table.begin(); it != next_table.end() && ! skip; ++it) /*lint !e1702*/
         {
            if ( next_demand >= it->first && next_length >= it->second.length - eps )
               skip = true;

            if ( next_demand <= it->first && next_length <= it->second.length + eps )
               dominated.push_front( it );
         }
         if ( skip )
            continue;

         /* remove dominated table and queue entries */
         for (list<NODE_TABLE::iterator>::iterator it = dominated.begin(); it != dominated.end(); ++it) /*lint !e1702*/
         {
            PQ.remove( (*it)->second.queue_item );
            next_table.erase( *it );
         }

         /* insert new table and queue entry  */
         queue_key.demand = next_demand;
         queue_key.length = next_length;
         queue_data       = next_node;

         queue_item = PQ.insert(queue_key, queue_data);

         table_key               = next_demand;
         table_entry.length      = next_length;
         table_entry.predecessor = curr_node;
         table_entry.queue_item  = queue_item;

         next_table[table_key] = table_entry;

#ifdef SCIP_OUTPUT
         printf("new entry  node = %d  demand = %d  length = %g  pref = %d\n", next_node, next_demand, next_length, curr_node);
#endif
      }
   }

   SCIPdebugMessage("Done RSP DP.\n");

   table_entry.predecessor = -1;
   table_entry.length      = 0;
   int curr_node = 0;

   /* find most negative tour */
   for (NODE_TABLE::iterator it = table[0].begin(); it != table[0].end(); ++it) /*lint !e1702 !e732 !e747*/
   {
      if ( it->second.length < table_entry.length )
      {
         table_key   = it->first;
         table_entry = it->second;
      }
   }
   SCIP_Real tour_length = table_entry.length;

   while ( table_entry.predecessor > 0 )
   {
      table_key -= demand(curr_node);
      curr_node  = table_entry.predecessor;
      tour.push_front(curr_node);
      table_entry = table[curr_node][table_key]; /*lint !e732 !e747*/
   }

   SCIPdebugMessage("Leave RSP  tour length = %g\n", tour_length);

   return tour_length;
}