LZ8.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Multi-objective optimization benchmark function LZ8.
 * 
 * The function is described in
 * 
 * H. Li and Q. Zhang. 
 * Multiobjective Optimization Problems with Complicated Pareto Sets, MOEA/D and NSGA-II, 
 * IEEE Trans on Evolutionary Computation, 2(12):284-302, April 2009. 
 * 
 * 
 *
 * \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_LZ8_H
#define SHARK_OBJECTIVEFUNCTIONS_BENCHMARK_LZ8_H

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


namespace shark {
/*! \brief Multi-objective optimization benchmark function LZ8.
*
*  The function is described in
*
*  H. Li and Q. Zhang. 
*  Multiobjective Optimization Problems with Complicated Pareto Sets, MOEA/D and NSGA-II, 
*  IEEE Trans on Evolutionary Computation, 2(12):284-302, April 2009. 
*/
struct LZ8 : public MultiObjectiveFunction
{
    LZ8(std::size_t numVariables = 0) : m_handler(SearchPointType(numVariables,0),SearchPointType(numVariables,1) ){
        announceConstraintHandler(&m_handler);
    }

    /// \brief From INameable: return the class name.
    std::string name() const
    { return "LZ8"; }
    
    std::size_t numberOfObjectives()const{
        return 2;
    }
    
    std::size_t numberOfVariables()const{
        return m_handler.dimensions();
    }
    
    bool hasScalableDimensionality()const{
        return true;
    }

    /// \brief Adjusts the number of variables if the function is scalable.
    /// \param [in] numberOfVariables The new dimension.
    void setNumberOfVariables( std::size_t numberOfVariables ){
        m_handler.setBounds(
            SearchPointType(numberOfVariables,0),
            SearchPointType(numberOfVariables,1)
        );
    }

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

        ResultType value( 2, 0 );

        std::size_t counter1 = 0, counter2 = 0;
        for( std::size_t i = 1; i < x.size(); i++ ) {
            double y = x(i) - ::pow( x(0), 0.5*(1.0 + 3*(i-1)/(x.size()-1) ) );
            if( i % 2 == 0 ) {
                counter2++;
                value[1] += sqr( y );// - ::cos( 8*y*M_PI) + 1.;
                double product = 2.;
                for( std::size_t j = 0; j < x.size(); j++ )
                    if( j%2 == 0 )
                        product *= ::cos( 20 * y * M_PI / ::sqrt( static_cast<double>( j ) ) );
                value[1] -= product + 2.;
            } else {
                counter1++;
                value[0] += sqr( y );// - ::cos( 8*y*M_PI) + 1.;
                double product = 2.;
                for( std::size_t j = 0; j < x.size(); j++ )
                    if( j%2 == 1 )
                        product *= ::cos( 20 * y * M_PI / ::sqrt( static_cast<double>( j ) ) );
                value[0] -= product + 2.;
            }
        }

        value[0] *= 8./counter1;
        value[0] += x( 0 );

        value[1] *= 8./counter2;
        value[1] += 1 - ::sqrt( x( 0 ) );

        return( value );
    }
private:
    BoxConstraintHandler<SearchPointType> m_handler;
};

}
#endif