CrowdingDistance.h

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/*!
 *
 *
 * \brief       Algorithm selecting points based on their crowding distance
 *
 * \author      O.Krause
 * \date        2017
 *
 *
 * \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_CROWDING_DISTANCE_H
#define SHARK_ALGORITHMS_DIRECTSEARCH_INDICATORS_CROWDING_DISTANCE_H

#include <shark/LinAlg/Base.h>
#include <limits>

namespace shark {

/// \brief Implements the Crowding Distance of a pareto front
///
/// The Crowding distance is an estimate of the perimeter of the cuboid formed by
/// using the nearest neighbors of a given point as the vertices. 
/// The point with the smallest crowding distance is removed from the set.
///
/// See the following reference for further details:
/// Deb, Kalyanmoy, et al. "A fast and elitist multiobjective genetic algorithm: NSGA-II."
/// IEEE transactions on evolutionary computation 6.2 (2002): 182-197.
struct CrowdingDistance {
    /// \brief Selects the point with the smallest crowding distance
    ///
    /// Crowding distance is computed wrt the union of the set front and the archive of points dominating the front
    template<typename ParetofrontType, typename ParetoArchive>
    std::size_t leastContributor(ParetofrontType const& front, ParetoArchive const& archive)const{
        if(front.size() < 2)
            return 0;
        std::size_t numDims = front[0].size();
        double keep = std::numeric_limits<double>::max();
        //compute the crowding distance
        std::vector<double> distances(front.size(),0.0);
        std::vector<KeyValuePair<double, unsigned int > > order(front.size() + archive.size());
        for( std::size_t i = 0; i != numDims; ++i ) {
            //create a joint set of front and archive
            for( std::size_t j = 0; j != front.size(); ++j ) {
                order[j].key = front[j][i];
                order[j].value = j;
            }
            for( std::size_t j = 0; j != archive.size(); ++j ) {
                order[j+front.size()].key = archive[j][i];
                order[j+front.size()].value = j+front.size();
            }
            //order to obtain neighbours
            std::sort(order.begin(),order.end());
            
            //check if we have to keep points because they are on the boundary
            if(order.front().value < front.size())
                distances[order.front().value] = keep;
            if(order.back().value < front.size())
                distances[order.back().value] = keep;
            double normalizer = order.back().key - order.front().key;
            for( std::size_t j = 1; j != order.size()-1; ++j ) {
                std::size_t index = order[j].value;
                //skip points which are part of the archive or which we want to keep
                if (index >= front.size() || distances[index] == keep)
                    continue;
                
                //compute crowding distance
                distances[index] += (order[j+1].key - order[j-1].key)/normalizer;
            }
        }
        
        //get index of point with least crowding distance
        return std::min_element(distances.begin(), distances.end()) - distances.begin();
    }
    
    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*/){}
        
    template<typename Archive>
    void serialize( Archive &, const unsigned int ) {}
};

}

#endif