IHR6.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Multi-objective optimization benchmark function IHR 6.
 * 
 * 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_IHR6_H
#define SHARK_OBJECTIVEFUNCTIONS_BENCHMARK_IHR6_H

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

#include <shark/LinAlg/rotations.h>

#include <vector>

namespace shark{
/*! \brief Multi-objective optimization benchmark function IHR 6.
*
*  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 IHR6 : public MultiObjectiveFunction{

    IHR6(std::size_t numVariables = 0) 
    : m_handler(numVariables,-1,1 ){
        announceConstraintHandler(&m_handler);
    }

    /// \brief From INameable: return the class name.
    std::string name() const
    { return "IHR6"; }

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

    void setNumberOfVariables( std::size_t numberOfVariables ){
        m_handler.setBounds(
            SearchPointType(numberOfVariables,-1),
            SearchPointType(numberOfVariables,1)
        );
    }

    void init() {
        m_rotationMatrix = blas::randomRotationMatrix(*mep_rng, numberOfVariables());
        m_ymax = 1.0/norm_inf(row(m_rotationMatrix,0));
    }

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

        ResultType value( 2 );

        SearchPointType y = prod(m_rotationMatrix,x);

        value[0] = 1 - std::exp(-4 * std::abs(y(0))) * std::pow(std::sin(6 * M_PI * y(0)), 6);

        double g = 0;
        for (std::size_t i = 1; i < numberOfVariables(); i++)
            g += hg( y(i) );
        g = 1 + 9 * std::pow(g / (numberOfVariables() - 1.0), 0.25);

        value[1] = g * hf(1. - sqr( value[0] / g ), y( 0 ));

        return value;
    }

    double h( double x )const {
        return 1 / ( 1 + std::exp( -x / std::sqrt( double(numberOfVariables()) ) ) );
    }

    double hf(double x, double y0)const {
        if( std::abs(y0) <= m_ymax )
            return x;
        return std::abs( y0 ) + 1.;
    }

    double hg(double x)const {
        return sqr(x) / ( std::abs(x) + 0.1 );
    }
private:
    double m_ymax;
    BoxConstraintHandler<SearchPointType> m_handler;
    RealMatrix m_rotationMatrix;
};

}
#endif