ReferenceVectorGuidedSelection.h

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//===========================================================================
/*!
 *
 *
 * \brief       Implements the reference vector selection for RVEA
 *
 * \author      Bjoern Bugge Grathwohl
 * \date        March 2017
 *
 * \par Copyright 1995-2017 Shark Development Team
 *
 * <BR><HR>
 * This file is part of Shark.
 * <https://shark-ml.github.io/Shark/>
 *
 * 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_DIRECT_SEARCH_OPERATORS_SELECTION_REFERENCE_VECTOR_GUIDED_SELECTION_H
#define SHARK_ALGORITHMS_DIRECT_SEARCH_OPERATORS_SELECTION_REFERENCE_VECTOR_GUIDED_SELECTION_H
 
#include <shark/LinAlg/Base.h>
#include <shark/Algorithms/DirectSearch/Individual.h>
 
namespace shark {
 
/**
 * \brief Implements the reference vector selection for the RVEA algorithm.
 *
 * This selector uses a set of unit reference vectors to partition the search
 * space by assigning to each reference vector the individual that is "closest"
 * to it, as measured by the angle-penalized distance.
 * See below paper for details:
 * R. Cheng, Y. Jin, M. Olhofer, and B. Sendhoff, “A reference vector guided
 * evolutionary algorithm for many-objective optimization,” IEEE Transactions on
 * Evolutionary Computation, Vol 20, Issue 5, October 2016
 * http://dx.doi.org/10.1109/TEVC.2016.2519378
 */
template <typename IndividualType>
struct ReferenceVectorGuidedSelection
{
    typedef std::set<std::size_t> bag_t;
 
    /**
     * \brief Select individuals by marking them as "selected".
     *
     * The selection operator requires the set of reference vectors, the set of
     * least angles between reference vectors (the gammas), as well as the
     * current iteration number.
     */
    void operator()(
        std::vector<IndividualType> & population,
        RealMatrix const & referenceVectors,
        RealVector const & gammas,
        std::size_t const curIteration)
    {
        if(population.empty())
        {
            return;
        }
        RealMatrix fitness = extractPopulationFitness(population);
        SIZE_CHECK(fitness.size2() == referenceVectors.size2());
        const std::size_t groupCount = referenceVectors.size1();
        // Objective value translation
        // line 4
        const RealVector minFitness = minCol(fitness);
        // line 5-7
        fitness -= repeat(minFitness, fitness.size1());
 
        // Population partition
        // line 9-13
        const RealMatrix cosA = cosAngles(fitness, referenceVectors);
        const RealMatrix angles = acos(cosA);
        // line 14-17
        const std::vector<bag_t> subGroups = populationPartition(cosA);
        SIZE_CHECK(subGroups.size() == groupCount);
        // Elitism selection
        for(auto & p : population)
        {
            p.selected() = false;
        }
        const double theta = fitness.size2()
            * std::pow(static_cast<double>(curIteration) /
                       static_cast<double>(m_maxIters), m_alpha);
        // line 25-28
        for(std::size_t j = 0; j < groupCount; ++j)
        {
            if(subGroups[j].size() == 0)
            {
                continue;
            }
            std::size_t selected_idx = 0;
            double min = 1e5;
            for(std::size_t i : subGroups[j])
            {
                // Angle-penalized distance (APD) calculation
                double apd = 1 + theta * angles(i, j) / gammas[j];
                apd *= norm_2(row(fitness, i));
                if(apd < min)
                {
                    selected_idx = i;
                    min = apd;
                }
            }
            population[selected_idx].selected() = true;
        }
    }
 
    /**
     * \brief Associates a population to a set of reference vectors.
     *
     * The parameter is an N-by-M matrix where N is the population size and M is
     * the number of reference vectors.  Entry (i,j) is the cosine of the angle
     * between population i and reference vector j.
     */
    static std::vector<bag_t> populationPartition(
        RealMatrix const & cosAngles)
    {
        std::vector<std::set<std::size_t>> subGroups(cosAngles.size2());
        for(std::size_t i = 0; i < cosAngles.size1(); ++i)
        {
            const std::size_t k = std::distance(
                row(cosAngles, i).begin(),
                std::max_element(row(cosAngles, i).begin(),
                                 row(cosAngles, i).end()));
            subGroups[k].insert(i);
        }
        return subGroups;
    }
 
    static RealMatrix extractPopulationFitness(
        std::vector<IndividualType> const & population)
    {
        RealMatrix fitness(population.size(),
                           population[0].unpenalizedFitness().size());
        for(std::size_t i = 0; i < population.size(); ++i)
        {
            row(fitness, i) = population[i].unpenalizedFitness();
        }
        return fitness;
    }
 
    static RealVector minCol(RealMatrix const & m)
    {
        RealVector minColumns(m.size2());
        for(std::size_t i = 0; i < m.size2(); ++i)
        {
            minColumns[i] = min(column(m, i));
        }
        return minColumns;
    }
 
    /**
     * \brief Compute cosine of angles between all row vectors in two matrices.
     */
    static RealMatrix cosAngles(RealMatrix const & m1, RealMatrix const & m2)
    {
        RealMatrix c = prod(m1, trans(m2));
        for(std::size_t i = 0; i < c.size1(); ++i)
        {
            row(c, i) /= norm_2(row(m1, i));
        }
        return c;
    }
 
    template <typename Archive>
    void serialize(Archive & archive)
    {
        archive & BOOST_SERIALIZATION_NVP(m_alpha);
        archive & BOOST_SERIALIZATION_NVP(m_maxIters);
    }
 
    double m_alpha;
    std::size_t m_maxIters;
};
 
} // namespace shark
 
#endif // SHARK_ALGORITHMS_DIRECT_SEARCH_OPERATORS_SELECTION_REFERENCE_VECTOR_GUIDED_SELECTION_H