ELLI2.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Multi-objective optimization benchmark function ELLI 2.
 * 
 * The function is described in
 * 
 * Christian Igel, Nikolaus Hansen, and Stefan Roth. 
 * Covariance Matrix Adaptation for Multi-objective Optimization. 
 * Evolutionary Computation 15(1), pp. 1-28, 2007
 * 
 * 
 *
 * \author      -
 * \date        -
 *
 *
 * \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_OBJECTIVEFUNCTIONS_BENCHMARK_ELLI2_H
#define SHARK_OBJECTIVEFUNCTIONS_BENCHMARK_ELLI2_H

#include <shark/ObjectiveFunctions/AbstractObjectiveFunction.h>
#include <shark/ObjectiveFunctions/BoxConstraintHandler.h>
#include <shark/Core/Random.h>

#include <shark/LinAlg/rotations.h>

namespace shark {
/*! \brief Multi-objective optimization benchmark function ELLI2.
*
*  The function is described in
*
*  Christian Igel, Nikolaus Hansen, and Stefan Roth. 
*  Covariance Matrix Adaptation for Multi-objective Optimization. 
*  Evolutionary Computation 15(1), pp. 1-28, 2007 
*/
struct ELLI2 : public MultiObjectiveFunction{

    ELLI2(std::size_t numVariables = 0) : m_a( 1E6 ){
        m_features |= CAN_PROPOSE_STARTING_POINT;
        setNumberOfVariables(numVariables);
    }

    /// \brief From INameable: return the class name.
    std::string name() const
    { return "ELLI2"; }

    std::size_t numberOfObjectives()const{
        return 2;
    }
    
    std::size_t numberOfVariables()const{
        return m_coefficients.size();
    }
    
    bool hasScalableDimensionality()const{
        return true;
    }

    void setNumberOfVariables( std::size_t numVariables ){
        m_coefficients.resize(numVariables);
        for(std::size_t i = 0; i != numVariables; ++i){
            m_coefficients(i) = std::pow(m_a, 2.0 * (i / (numVariables - 1.0)));
        }
    }

    void init() {
        m_rotationMatrix1 = blas::randomRotationMatrix(*mep_rng, numberOfVariables() );
        m_rotationMatrix2 = blas::randomRotationMatrix(*mep_rng, numberOfVariables() );
    }

    ResultType eval( const SearchPointType & x ) const {
        m_evaluationCounter++;

        ResultType value( 2 );

        SearchPointType y = prod( m_rotationMatrix1, x );
        SearchPointType z = prod( m_rotationMatrix2, x );

        double sum1 = 0.0;
        double sum2 = 0.0;
        for (unsigned i = 0; i < numberOfVariables(); i++) {
            sum1 += m_coefficients(i) * sqr( y(i) );
            sum2 += m_coefficients(i) * sqr( z(i) - 2.0 );
        }

        value[0] = sum1 / ( sqr(m_a) * numberOfVariables() );
        value[1] = sum2 / ( sqr(m_a) * numberOfVariables() );

        return value;
    }

    SearchPointType proposeStartingPoint() const {
        RealVector x(numberOfVariables());

        for (std::size_t i = 0; i < x.size(); i++) {
            x(i) = random::uni(*mep_rng, -10,10);
        }
        return x;
    }

private:
    double m_a;
    RealMatrix m_rotationMatrix1;
    RealMatrix m_rotationMatrix2;
    RealVector m_coefficients;
};

}
#endif