DTLZ4.h

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//===========================================================================
/*!
 * 
 *
 * \brief       Objective function DTLZ4
 * 
 * 
 *
 * \author      T.Voss, T. Glasmachers, O.Krause
 * \date        2010-2011
 *
 *
 * \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_OBJECTIVEFUNCTIONS_BENCHMARK_DTLZ4_H
#define SHARK_OBJECTIVEFUNCTIONS_BENCHMARK_DTLZ4_H
 
#include <shark/ObjectiveFunctions/AbstractObjectiveFunction.h>
#include <shark/ObjectiveFunctions/BoxConstraintHandler.h>
 
namespace shark {namespace benchmarks{
/**
 * \brief Implements the benchmark function DTLZ4.
 *
 * See: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.18.7531&rep=rep1&type=pdf 
 * The benchmark function exposes the following features:
 *  - Scalable w.r.t. the searchspace and w.r.t. the objective space.
 *  - Highly multi-modal.
* \ingroup benchmarks
 */
struct DTLZ4 : public MultiObjectiveFunction
{
    DTLZ4(std::size_t numVariables = 0) : m_objectives(2), m_handler(SearchPointType(numVariables,0),SearchPointType(numVariables,1) ){
        announceConstraintHandler(&m_handler);
    }
 
    /// \brief From INameable: return the class name.
    std::string name() const
    { return "DTLZ4"; }
 
    std::size_t numberOfObjectives()const{
        return m_objectives;
    }
    bool hasScalableObjectives()const{
        return true;
    }
    void setNumberOfObjectives( std::size_t numberOfObjectives ){
        m_objectives = numberOfObjectives;
    }
    
    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( numberOfObjectives() );
 
        const double alpha = 10.;
        //~ const double alpha = 100.; //original, but numerically extremely difficult
        
        std::size_t k = numberOfVariables() - numberOfObjectives() + 1 ;
        double g = 0.0;
        for( std::size_t i = numberOfVariables() - k; i < numberOfVariables(); i++ )
            g += sqr( x( i ) - 0.5);
 
        for (std::size_t i = 0; i < numberOfObjectives(); i++) {
            value[i] = 1.0+g;
            for( std::size_t j = 0; j < numberOfObjectives() - i -1; ++j)
                value[i] *= std::cos(std::pow(x( j ),alpha) * M_PI / 2.0);
 
            if (i > 0)
                value[i] *= std::sin(std::pow(x(numberOfObjectives() - i -1),alpha) * M_PI / 2.0);
        }
 
        return value;
        return value;
    }
    
private:
    std::size_t m_objectives;
    BoxConstraintHandler<SearchPointType> m_handler;
};
 
}}
#endif