HypervolumeIndicator.h

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/*!
 * 
 *
 * \brief       Calculates the hypervolume covered by a front of non-dominated points.
 * 
 * 
 *
 * \author      T.Voss
 * \date        2010
 *
 *
 * \par Copyright 1995-2017 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <http://shark-ml.org/>
 * 
 * Shark is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published 
 * by the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * Shark is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with Shark.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
#ifndef SHARK_ALGORITHMS_DIRECTSEARCH_INDICATORS_HYPERVOLUMEINDICATOR_H
#define SHARK_ALGORITHMS_DIRECTSEARCH_INDICATORS_HYPERVOLUMEINDICATOR_H

#include <shark/Core/Exception.h>
#include <shark/Core/OpenMP.h>
#include <shark/Algorithms/DirectSearch/Operators/Hypervolume/HypervolumeContribution.h>

#include <algorithm>
#include <vector>
#include <numeric>

namespace shark {

///  \brief Calculates the hypervolume covered by a front of non-dominated points.
///
/// If given, the Indicator uses a provided reference value that can be set via setReference. 
/// Otherwise, it is computed from the data by using the maximum value in the set. As this usually
/// gives 0 contribution to the extremum points (i.e. the ones with best function value), those
/// points are skipped when computing the contribution (i.e. extremum points are never selected).
/// Note, that for boundary points that are not extrema, this does not hold and they are selected.
///
/// for problems with many objectives, an approximative algorithm can be used.
struct HypervolumeIndicator {
    /// \brief Determines the point contributing the least hypervolume to the overall front of points.
    ///
    /// \param [in] front pareto front of points
    template<typename ParetoFrontType, typename ParetoArchive>
    std::size_t leastContributor( ParetoFrontType const& front, ParetoArchive const& /*archive*/)const{
        HypervolumeContribution algorithm;
        if(m_reference.size() != 0)
            return m_algorithm.smallest(front,1,m_reference)[0].value;
        else    
            return m_algorithm.smallest(front,1)[0].value;
    }
    
    template<typename ParetoFrontType, typename ParetoArchive>
    std::vector<std::size_t> leastContributors( ParetoFrontType const& front, ParetoArchive const& archive, std::size_t K)const{
        std::vector<std::size_t> indices;
        std::vector<RealVector> points(front.begin(),front.end());
        std::vector<std::size_t> activeIndices(points.size());
        std::iota(activeIndices.begin(),activeIndices.end(),0);
        for(std::size_t k=0; k != K; ++k){
            std::size_t index = leastContributor(points,archive);
            
            points.erase(points.begin()+index);
            indices.push_back(activeIndices[index]);
            activeIndices.erase(activeIndices.begin()+index);
        }
        return indices;
    }
    
    template<class random>
    void init(std::size_t /*numOfObjectives*/, std::size_t /*mu*/, random& /*rng*/){}
    
    /// \brief Sets the reference point. 
    ///
    /// If no point is set, it is estimated from the current front and the extremum points are never selected.
    void setReference(RealVector const& newReference){
        m_reference = newReference;
    }
    
    /// \brief Whether the approximtive algorithm should be used on large problems
    void useApproximation(bool useApproximation){
        m_algorithm.useApproximation(useApproximation);
    }
    
    ///\brief Error bound for the approximative algorithm
    double approximationEpsilon()const{
        return m_algorithm.approximationEpsilon();
    }
    ///\brief Error bound for the approximative algorithm
    double& approximationEpsilon(){
        return m_algorithm.approximationEpsilon();
    }
    
    ///\brief Error probability for the approximative algorithm
    double approximationDelta()const{
        return m_algorithm.approximationDelta();
    }
    
    ///\brief Error probability for the approximative algorithm
    double& approximationDelta(){
        return m_algorithm.approximationDelta();
    }

    template<typename Archive>
    void serialize( Archive & archive, const unsigned int version ) {
        archive & BOOST_SERIALIZATION_NVP( m_reference );
        archive & BOOST_SERIALIZATION_NVP( m_algorithm );
    }

private:
    RealVector m_reference;
    HypervolumeContribution m_algorithm;
};
}

#endif