paradiseo/moeo/src/metric/moeoHypervolumeBinaryMetric.h

/*
* <moeoHypervolumeBinaryMetric.h>
* Copyright (C) DOLPHIN Project-Team, INRIA Futurs, 2006-2007
* (C) OPAC Team, LIFL, 2002-2007
*
* Arnaud Liefooghe
*
* This software is governed by the CeCILL license under French law and
* abiding by the rules of distribution of free software.  You can  use,
* modify and/ or redistribute the software under the terms of the CeCILL
* license as circulated by CEA, CNRS and INRIA at the following URL
* "http://www.cecill.info".
*
* As a counterpart to the access to the source code and  rights to copy,
* modify and redistribute granted by the license, users are provided only
* with a limited warranty  and the software's author,  the holder of the
* economic rights,  and the successive licensors  have only  limited liability.
*
* In this respect, the user's attention is drawn to the risks associated
* with loading,  using,  modifying and/or developing or reproducing the
* software by the user in light of its specific status of free software,
* that may mean  that it is complicated to manipulate,  and  that  also
* therefore means  that it is reserved for developers  and  experienced
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*
* ParadisEO WebSite : http://paradiseo.gforge.inria.fr
* Contact: paradiseo-help@lists.gforge.inria.fr
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*/
//-----------------------------------------------------------------------------

#ifndef MOEOHYPERVOLUMEBINARYMETRIC_H_
#define MOEOHYPERVOLUMEBINARYMETRIC_H_

#include <stdexcept>
#include <comparator/moeoParetoObjectiveVectorComparator.h>
#include <metric/moeoNormalizedSolutionVsSolutionBinaryMetric.h>

/**
 * Hypervolume binary metric allowing to compare two objective vectors as proposed in
 * Zitzler E., Künzli S.: Indicator-Based Selection in Multiobjective Search. In Parallel Problem Solving from Nature (PPSN VIII).
 * Lecture Notes in Computer Science 3242, Springer, Birmingham, UK pp.832–842 (2004).
 * This indicator is based on the hypervolume concept introduced in
 * Zitzler, E., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study.
 * Parallel Problem Solving from Nature (PPSN-V), pp.292-301 (1998).
 */
template < class ObjectiveVector >
class moeoHypervolumeBinaryMetric : public moeoNormalizedSolutionVsSolutionBinaryMetric < ObjectiveVector, double >
  {
  public:

    /**
     * Ctor
     * @param _rho value used to compute the reference point from the worst values for each objective (default : 1.1)
     */
    moeoHypervolumeBinaryMetric(double _rho = 1.1) : moeoNormalizedSolutionVsSolutionBinaryMetric<ObjectiveVector, double>(), rho(_rho)
    {
      // not-a-maximization problem check
      for (unsigned int i=0; i<ObjectiveVector::Traits::nObjectives(); i++)
        {
          if (ObjectiveVector::Traits::maximizing(i))
            {
              throw std::runtime_error("Hypervolume binary metric not yet implemented for a maximization problem in moeoHypervolumeBinaryMetric");
            }
        }
      // consistency check
      if (rho < 1)
        {
          std::cout << "Warning, value used to compute the reference point rho for the hypervolume calculation must not be smaller than 1" << std::endl;
          std::cout << "Adjusted to 1" << std::endl;
          rho = 1;
        }
    }


    /**
     * Returns the volume of the space that is dominated by _o2 but not by _o1 with respect to a reference point computed using rho.
     * @warning don't forget to set the bounds for every objective before the call of this function
     * @param _o1 the first objective vector
     * @param _o2 the second objective vector
     */
    double operator()(const ObjectiveVector & _o1, const ObjectiveVector & _o2)
    {
      double result;
      // if _o2 is dominated by _o1
      if ( paretoComparator(_o2,_o1) )
        {
          result = - hypervolume(_o1, _o2, ObjectiveVector::Traits::nObjectives()-1);
        }
      else
        {
          result = hypervolume(_o2, _o1, ObjectiveVector::Traits::nObjectives()-1);
        }
      return result;
    }


  private:

    /** value used to compute the reference point from the worst values for each objective */
    double rho;
    /** the bounds for every objective */
    using moeoNormalizedSolutionVsSolutionBinaryMetric < ObjectiveVector, double > :: bounds;
    /** Functor to compare two objective vectors according to Pareto dominance relation */
    moeoParetoObjectiveVectorComparator < ObjectiveVector > paretoComparator;


    /**
     * Returns the volume of the space that is dominated by _o2 but not by _o1 with respect to a reference point computed using rho for the objective _obj.
     * @param _o1 the first objective vector
     * @param _o2 the second objective vector
     * @param _obj the objective index
     * @param _flag used for iteration, if _flag=true _o2 is not talen into account (default : false)
     */
    double hypervolume(const ObjectiveVector & _o1, const ObjectiveVector & _o2, const unsigned int _obj, const bool _flag = false)
    {
      double result;
      double range = rho * bounds[_obj].range();
      double max = bounds[_obj].minimum() + range;
      // value of _1 for the objective _obj
      double v1 = _o1[_obj];
      // value of _2 for the objective _obj (if _flag=true, v2=max)
      double v2;
      if (_flag)
        {
          v2 = max;
        }
      else
        {
          v2 = _o2[_obj];
        }
      // computation of the volume
      if (_obj == 0)
        {
          if (v1 < v2)
            {
              result = (v2 - v1) / range;
            }
          else
            {
              result = 0;
            }
        }
      else
        {
          if (v1 < v2)
            {
              result = ( hypervolume(_o1, _o2, _obj-1, true) * (v2 - v1) / range ) + ( hypervolume(_o1, _o2, _obj-1) * (max - v2) / range );
            }
          else
            {
              result = hypervolume(_o1, _o2, _obj-1) * (max - v2) / range;
            }
        }
      return result;
    }

  };

#endif /*MOEOHYPERVOLUMEBINARYMETRIC_H_*/