src/problems/cec2009.cpp

/* Copyright 2017-2021 PaGMO development team

This file is part of the PaGMO library.

The PaGMO library is free software; you can redistribute it and/or modify
it under the terms of either:

  * the GNU Lesser General Public License as published by the Free
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or

  * the GNU General Public License as published by the Free Software
    Foundation; either version 3 of the License, or (at your option) any
    later version.

or both in parallel, as here.

The PaGMO library is distributed in the hope that it will be useful, but
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for more details.

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#include <cmath>
#include <initializer_list>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>

#include <pagmo/detail/constants.hpp>
#include <pagmo/exceptions.hpp>
#include <pagmo/problem.hpp>
#include <pagmo/problems/cec2009.hpp>
#include <pagmo/s11n.hpp>
#include <pagmo/types.hpp>

// MINGW-specific warnings.
#if defined(__GNUC__) && defined(__MINGW32__)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wsuggest-attribute=pure"
#endif

namespace pagmo
{

namespace detail
{

namespace cec2009_data
{

namespace
{

// Number of objectives
const std::vector<unsigned short> nobj = {2, 2, 2, 2, 2, 2, 2, 3, 3, 3};

// Inequality constraints dimension
const std::vector<unsigned short> nic = {1, 1, 1, 1, 1, 2, 2, 1, 1, 1};

} // namespace

} // namespace cec2009_data

} // namespace detail

// Pointers to the member functions to be used in fitness
const std::vector<detail::cec2009_data::func_ptr> cec2009::s_u_ptr
    = {&cec2009::UF1, &cec2009::UF2, &cec2009::UF3, &cec2009::UF4, &cec2009::UF5,
       &cec2009::UF6, &cec2009::UF7, &cec2009::UF8, &cec2009::UF9, &cec2009::UF10};

const std::vector<detail::cec2009_data::func_ptr> cec2009::s_c_ptr
    = {&cec2009::CF1, &cec2009::CF2, &cec2009::CF3, &cec2009::CF4, &cec2009::CF5,
       &cec2009::CF6, &cec2009::CF7, &cec2009::CF8, &cec2009::CF9, &cec2009::CF10};

cec2009::cec2009(unsigned prob_id, bool is_constrained, unsigned dim)
    : m_prob_id(prob_id), m_is_constrained(is_constrained), m_dim(dim)
{
    if (prob_id < 1u || prob_id > 10u) {
        pagmo_throw(std::invalid_argument,
                    "Error: CEC2009 Test functions are only defined for prob_id in [1, 10], a prob_id of "
                        + std::to_string(prob_id) + " was requested.");
    }
    if (dim < 1u) {
        pagmo_throw(std::invalid_argument,
                    "Error: CEC2009 Test functions must have a non zero dimension: a dimension of "
                        + std::to_string(dim) + " was requested.");
    }
}

/// Inequality constraint dimension
/**
 * Returns the number of inequality constraints
 *
 * @return the number of inequality constraints
 */
vector_double::size_type cec2009::get_nic() const
{
    if (m_is_constrained) {
        return detail::cec2009_data::nic[m_prob_id - 1u];
    } else {
        return 0u;
    }
}

/// Number of objectives
/**
 * Returns the number of objectives
 *
 * @return the number of objectives
 */
vector_double::size_type cec2009::get_nobj() const
{
    return detail::cec2009_data::nobj[m_prob_id - 1u];
}

/// Box-bounds
/**
 * It returns the box-bounds for this UDP.
 *
 * @return the lower and upper bounds for each of the decision vector components
 */
std::pair<vector_double, vector_double> cec2009::get_bounds() const
{
    vector_double lb(m_dim, 0), ub(m_dim, 0);

    if (!m_is_constrained) { // For UF
        if (m_prob_id == 1u || m_prob_id == 2u || m_prob_id == 5u || m_prob_id == 6u || m_prob_id == 7u) {
            // [0,1] x [-1,1]^{n-1}
            lb[0] = 0.0;
            ub[0] = 1.0;
            for (decltype(m_dim) i = 1u; i < m_dim; ++i) {
                lb[i] = -1.0;
                ub[i] = 1.0;
            }
        } else if (m_prob_id == 3u) {
            // [0,1]^{n}
            for (decltype(m_dim) i = 0u; i < m_dim; ++i) {
                lb[i] = 0.0;
                ub[i] = 1.0;
            }
        } else if (m_prob_id == 4u) {
            // [0,1] x [-2,2]^{n-1}
            lb[0] = 0.0;
            ub[0] = 1.0;
            for (decltype(m_dim) i = 1u; i < m_dim; ++i) {
                lb[i] = -2.0;
                ub[i] = 2.0;
            }
        } else if (m_prob_id == 8u || m_prob_id == 9u || m_prob_id == 10u) {
            // [0,1]^{2} x [-2,2]^{n-2}
            lb[0] = 0.0;
            ub[0] = 1.0;
            lb[1] = 0.0;
            ub[1] = 1.0;
            for (decltype(m_dim) i = 2u; i < m_dim; ++i) {
                lb[i] = -2.0;
                ub[i] = 2.0;
            }
        }
    } else { // For CF
        if (m_prob_id == 2u) {
            // [0,1] x [-1,1]^{n-1}
            lb[0] = 0.0;
            ub[0] = 1.0;
            for (decltype(m_dim) i = 1u; i < m_dim; ++i) {
                lb[i] = -1.0;
                ub[i] = 1.0;
            }
        } else if (m_prob_id == 1u) {
            // [0,1]^{n}
            for (decltype(m_dim) i = 0u; i < m_dim; ++i) {
                lb[i] = 0.0;
                ub[i] = 1.0;
            }
        } else if (m_prob_id == 3u || m_prob_id == 4u || m_prob_id == 5u || m_prob_id == 6u || m_prob_id == 7u) {
            // [0,1] x [-2,2]^{n-1}
            lb[0] = 0.0;
            ub[0] = 1.0;
            for (decltype(m_dim) i = 1u; i < m_dim; ++i) {
                lb[i] = -2.0;
                ub[i] = 2.0;
            }
        } else if (m_prob_id == 8u) {
            // [0,1]^{2} x [-4,4]^{n-2}
            lb[0] = 0.0;
            ub[0] = 1.0;
            lb[1] = 0.0;
            ub[1] = 1.0;
            for (decltype(m_dim) i = 2u; i < m_dim; ++i) {
                lb[i] = -4.0;
                ub[i] = 4.0;
            }
        } else if (m_prob_id == 9u || m_prob_id == 10u) {
            // [0,1]^{2} x [-2,2]^{n-2}
            lb[0] = 0.0;
            ub[0] = 1.0;
            lb[1] = 0.0;
            ub[1] = 1.0;
            for (decltype(m_dim) i = 2u; i < m_dim; ++i) {
                lb[i] = -2.0;
                ub[i] = 2.0;
            }
        }
    }
    return std::make_pair(std::move(lb), std::move(ub));
}

/// Fitness computation
/**
 * Computes the fitness for this UDP
 *
 * @param x the decision vector.
 *
 * @return the fitness of \p x.
 */
vector_double cec2009::fitness(const vector_double &x) const
{
    if (m_is_constrained) {
        return fitness_impl(s_c_ptr[m_prob_id - 1], x);
    } else {
        return fitness_impl(s_u_ptr[m_prob_id - 1], x);
    }
}

/// Problem name
/**
 * @return a string containing the problem name
 */
std::string cec2009::get_name() const
{
    std::string retval("CEC2009 - ");
    if (!m_is_constrained) {
        retval.append("UF");
    } else {
        retval.append("CF");
    }
    retval.append(std::to_string(m_prob_id));
    return retval;
}

// Object serialization
template <typename Archive>
void cec2009::serialize(Archive &ar, unsigned)
{
    detail::archive(ar, m_prob_id, m_is_constrained, m_dim);
}

namespace
{

// Small helper for getting the sign of
// a double.
double sgn(double val)
{
    return ((val) > 0 ? 1.0 : -1.0);
}

} // namespace

// Pointers to member functions are used
vector_double cec2009::fitness_impl(detail::cec2009_data::func_ptr f, const vector_double &x) const
{
    const auto nic = m_is_constrained ? detail::cec2009_data::nic[m_prob_id - 1u] : 0u;
    vector_double retval(nic + detail::cec2009_data::nobj[m_prob_id - 1u], 0.);
    // Syntax is ugly as these are member function pointers.
    ((*this).*(f))(retval, x); // calls f
    return retval;
}

// Let's disable a few compiler warnings emitted by the cec2009 code.
#if defined(__clang__) || defined(__GNUC__)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wold-style-cast"
#endif

// For the coverage analysis we do not cover the code below as its derived from a third party source
// LCOV_EXCL_START

// -------------------------------------------
void cec2009::UF1(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, yj;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        yj = x[j - 1] - std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        yj = yj * yj;
        if (j % 2 == 0u) {
            sum2 += yj;
            count2++;
        } else {
            sum1 += yj;
            count1++;
        }
    }
    f[0] = x[0] + 2.0 * sum1 / count1;
    f[1] = 1.0 - std::sqrt(x[0]) + 2.0 * sum2 / count2;
}

void cec2009::UF2(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, yj;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        if (j % 2 == 0u) {
            yj = x[j - 1]
                 - 0.3 * x[0]
                       * (x[0] * std::cos(24.0 * detail::pi() * x[0] + 4.0 * j * detail::pi() / (double)m_dim) + 2.0)
                       * std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            sum2 += yj * yj;
            count2++;
        } else {
            yj = x[j - 1]
                 - 0.3 * x[0]
                       * (x[0] * std::cos(24.0 * detail::pi() * x[0] + 4.0 * j * detail::pi() / (double)m_dim) + 2.0)
                       * std::cos(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            sum1 += yj * yj;
            count1++;
        }
    }
    f[0] = x[0] + 2.0 * sum1 / count1;
    f[1] = 1.0 - std::sqrt(x[0]) + 2.0 * sum2 / count2;
}

void cec2009::UF3(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, prod1, prod2, yj, pj;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    prod1 = prod2 = 1.0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        yj = x[j - 1] - std::pow(x[0], 0.5 * (1.0 + 3.0 * (j - 2.0) / ((double)m_dim - 2.0)));
        pj = std::cos(20.0 * yj * detail::pi() / std::sqrt(j + 0.0));
        if (j % 2 == 0u) {
            sum2 += yj * yj;
            prod2 *= pj;
            count2++;
        } else {
            sum1 += yj * yj;
            prod1 *= pj;
            count1++;
        }
    }
    f[0] = x[0] + 2.0 * (4.0 * sum1 - 2.0 * prod1 + 2.0) / count1;
    f[1] = 1.0 - std::sqrt(x[0]) + 2.0 * (4.0 * sum2 - 2.0 * prod2 + 2.0) / count2;
}

void cec2009::UF4(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, yj, hj;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        yj = x[j - 1] - std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        hj = std::abs(yj) / (1.0 + std::exp(2.0 * std::abs(yj)));
        if (j % 2 == 0u) {
            sum2 += hj;
            count2++;
        } else {
            sum1 += hj;
            count1++;
        }
    }
    f[0] = x[0] + 2.0 * sum1 / count1;
    f[1] = 1.0 - x[0] * x[0] + 2.0 * sum2 / count2;
}

void cec2009::UF5(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, yj, hj, N, E;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    N = 10.0;
    E = 0.1;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        yj = x[j - 1] - std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        hj = 2.0 * yj * yj - std::cos(4.0 * detail::pi() * yj) + 1.0;
        if (j % 2 == 0u) {
            sum2 += hj;
            count2++;
        } else {
            sum1 += hj;
            count1++;
        }
    }
    hj = (0.5 / N + E) * std::abs(std::sin(2.0 * N * detail::pi() * x[0]));
    f[0] = x[0] + hj + 2.0 * sum1 / count1;
    f[1] = 1.0 - x[0] + hj + 2.0 * sum2 / count2;
}

void cec2009::UF6(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, prod1, prod2, yj, hj, pj, N, E;
    N = 2.0;
    E = 0.1;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    prod1 = prod2 = 1.0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        yj = x[j - 1] - std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        pj = std::cos(20.0 * yj * detail::pi() / std::sqrt(j + 0.0));
        if (j % 2 == 0u) {
            sum2 += yj * yj;
            prod2 *= pj;
            count2++;
        } else {
            sum1 += yj * yj;
            prod1 *= pj;
            count1++;
        }
    }

    hj = 2.0 * (0.5 / N + E) * std::sin(2.0 * N * detail::pi() * x[0]);
    if (hj < 0.0) hj = 0.0;
    f[0] = x[0] + hj + 2.0 * (4.0 * sum1 - 2.0 * prod1 + 2.0) / count1;
    f[1] = 1.0 - x[0] + hj + 2.0 * (4.0 * sum2 - 2.0 * prod2 + 2.0) / count2;
}

void cec2009::UF7(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, yj;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        yj = x[j - 1] - std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        if (j % 2 == 0u) {
            sum2 += yj * yj;
            count2++;
        } else {
            sum1 += yj * yj;
            count1++;
        }
    }
    yj = std::pow(x[0], 0.2);
    f[0] = yj + 2.0 * sum1 / count1;
    f[1] = 1.0 - yj + 2.0 * sum2 / count2;
}

void cec2009::UF8(vector_double &f, const vector_double &x) const
{
    double count1, count2, count3;
    double sum1, sum2, sum3, yj;

    sum1 = sum2 = sum3 = 0.0;
    count1 = count2 = count3 = 0;
    for (decltype(m_dim) j = 3u; j <= m_dim; ++j) {
        yj = x[j - 1] - 2.0 * x[1] * std::sin(2.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        if (j % 3 == 1u) {
            sum1 += yj * yj;
            count1++;
        } else if (j % 3 == 2u) {
            sum2 += yj * yj;
            count2++;
        } else {
            sum3 += yj * yj;
            count3++;
        }
    }
    f[0] = std::cos(0.5 * detail::pi() * x[0]) * std::cos(0.5 * detail::pi() * x[1]) + 2.0 * sum1 / count1;
    f[1] = std::cos(0.5 * detail::pi() * x[0]) * std::sin(0.5 * detail::pi() * x[1]) + 2.0 * sum2 / count2;
    f[2] = std::sin(0.5 * detail::pi() * x[0]) + 2.0 * sum3 / count3;
}

void cec2009::UF9(vector_double &f, const vector_double &x) const
{
    double count1, count2, count3;
    double sum1, sum2, sum3, yj, E;

    E = 0.1;
    sum1 = sum2 = sum3 = 0.0;
    count1 = count2 = count3 = 0;
    for (decltype(m_dim) j = 3u; j <= m_dim; ++j) {
        yj = x[j - 1] - 2.0 * x[1] * std::sin(2.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        if (j % 3 == 1u) {
            sum1 += yj * yj;
            count1++;
        } else if (j % 3 == 2u) {
            sum2 += yj * yj;
            count2++;
        } else {
            sum3 += yj * yj;
            count3++;
        }
    }
    yj = (1.0 + E) * (1.0 - 4.0 * (2.0 * x[0] - 1.0) * (2.0 * x[0] - 1.0));
    if (yj < 0.0) yj = 0.0;
    f[0] = 0.5 * (yj + 2 * x[0]) * x[1] + 2.0 * sum1 / count1;
    f[1] = 0.5 * (yj - 2 * x[0] + 2.0) * x[1] + 2.0 * sum2 / count2;
    f[2] = 1.0 - x[1] + 2.0 * sum3 / count3;
}

void cec2009::UF10(vector_double &f, const vector_double &x) const
{
    double count1, count2, count3;
    double sum1, sum2, sum3, yj, hj;

    sum1 = sum2 = sum3 = 0.0;
    count1 = count2 = count3 = 0;
    for (decltype(m_dim) j = 3u; j <= m_dim; ++j) {
        yj = x[j - 1] - 2.0 * x[1] * std::sin(2.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        hj = 4.0 * yj * yj - std::cos(8.0 * detail::pi() * yj) + 1.0;
        if (j % 3 == 1u) {
            sum1 += hj;
            count1++;
        } else if (j % 3 == 2u) {
            sum2 += hj;
            count2++;
        } else {
            sum3 += hj;
            count3++;
        }
    }
    f[0] = std::cos(0.5 * detail::pi() * x[0]) * std::cos(0.5 * detail::pi() * x[1]) + 2.0 * sum1 / count1;
    f[1] = std::cos(0.5 * detail::pi() * x[0]) * std::sin(0.5 * detail::pi() * x[1]) + 2.0 * sum2 / count2;
    f[2] = std::sin(0.5 * detail::pi() * x[0]) + 2.0 * sum3 / count3;
}

/****************************************************************************/
// constraint test instances
/****************************************************************************/
void cec2009::CF1(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, yj, N, a;
    N = 10.0;
    a = 1.0;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        yj = x[j - 1] - std::pow(x[0], 0.5 * (1.0 + 3.0 * (j - 2.0) / ((double)m_dim - 2.0)));
        if (j % 2 == 1u) {
            sum1 += yj * yj;
            count1++;
        } else {
            sum2 += yj * yj;
            count2++;
        }
    }
    f[0] = x[0] + 2.0 * sum1 / count1;
    f[1] = 1.0 - x[0] + 2.0 * sum2 / count2;
    // Inequality constraint
    f[2] = f[1] + f[0] - a * std::abs(std::sin(N * detail::pi() * (f[0] - f[1] + 1.0))) - 1.0;
    f[2] = -f[2]; // convert to g(x) <= 0 form
}

void cec2009::CF2(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, yj, N, a, t;
    N = 2.0;
    a = 1.0;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        if (j % 2 == 1) {
            yj = x[j - 1] - std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            sum1 += yj * yj;
            count1++;
        } else {
            yj = x[j - 1] - std::cos(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            sum2 += yj * yj;
            count2++;
        }
    }
    f[0] = x[0] + 2.0 * sum1 / count1;
    f[1] = 1.0 - std::sqrt(x[0]) + 2.0 * sum2 / count2;
    // Inequality constraint
    t = f[1] + std::sqrt(f[0]) - a * std::sin(N * detail::pi() * (sqrt(f[0]) - f[1] + 1.0)) - 1.0;
    f[2] = sgn(t) * std::abs(t) / (1 + std::exp(4.0 * std::abs(t)));
    f[2] = -f[2]; // convert to g(x) <= 0 form
}

void cec2009::CF3(vector_double &f, const vector_double &x) const
{
    double count1, count2;
    double sum1, sum2, prod1, prod2, yj, pj, N, a;
    N = 2.0;
    a = 1.0;

    sum1 = sum2 = 0.0;
    count1 = count2 = 0;
    prod1 = prod2 = 1.0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        yj = x[j - 1] - std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        pj = std::cos(20.0 * yj * detail::pi() / std::sqrt(j + 0.0));
        if (j % 2 == 0u) {
            sum2 += yj * yj;
            prod2 *= pj;
            count2++;
        } else {
            sum1 += yj * yj;
            prod1 *= pj;
            count1++;
        }
    }

    f[0] = x[0] + 2.0 * (4.0 * sum1 - 2.0 * prod1 + 2.0) / count1;
    f[1] = 1.0 - x[0] * x[0] + 2.0 * (4.0 * sum2 - 2.0 * prod2 + 2.0) / count2;
    // Inequality constraint
    f[2] = f[1] + f[0] * f[0] - a * std::sin(N * detail::pi() * (f[0] * f[0] - f[1] + 1.0)) - 1.0;
    f[2] = -f[2]; // convert to g(x) <= 0 form
}

void cec2009::CF4(vector_double &f, const vector_double &x) const
{
    double sum1, sum2, yj, t;

    sum1 = sum2 = 0.0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        yj = x[j - 1] - std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        if (j % 2 == 1u) {
            sum1 += yj * yj;
        } else {
            if (j == 2u)
                sum2 += yj < 1.5 - 0.75 * std::sqrt(2.0) ? std::abs(yj) : (0.125 + (yj - 1) * (yj - 1));
            else
                sum2 += yj * yj;
        }
    }
    f[0] = x[0] + sum1;
    f[1] = 1.0 - x[0] + sum2;
    // Inequality constraint
    t = x[1] - std::sin(6.0 * x[0] * detail::pi() + 2.0 * detail::pi() / (double)m_dim) - 0.5 * x[0] + 0.25;
    f[2] = sgn(t) * std::abs(t) / (1 + std::exp(4.0 * std::abs(t)));
    f[2] = -f[2]; // convert to g(x) <= 0 form
}

void cec2009::CF5(vector_double &f, const vector_double &x) const
{
    double sum1, sum2, yj;

    sum1 = sum2 = 0.0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        if (j % 2 == 1u) {
            yj = x[j - 1] - 0.8 * x[0] * std::cos(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            sum1 += 2.0 * yj * yj - std::cos(4.0 * detail::pi() * yj) + 1.0;
        } else {
            yj = x[j - 1] - 0.8 * x[0] * std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            if (j == 2u)
                sum2 += yj < 1.5 - 0.75 * std::sqrt(2.0) ? std::abs(yj) : (0.125 + (yj - 1) * (yj - 1));
            else
                sum2 += 2.0 * yj * yj - std::cos(4.0 * detail::pi() * yj) + 1.0;
        }
    }
    f[0] = x[0] + sum1;
    f[1] = 1.0 - x[0] + sum2;
    // Inequality constraint
    f[2] = x[1] - 0.8 * x[0] * std::sin(6.0 * x[0] * detail::pi() + 2.0 * detail::pi() / (double)m_dim) - 0.5 * x[0]
           + 0.25;
    f[2] = -f[2]; // convert to g(x) <= 0 form
}

void cec2009::CF6(vector_double &f, const vector_double &x) const
{
    double sum1, sum2, yj;

    sum1 = sum2 = 0.0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        if (j % 2 == 1u) {
            yj = x[j - 1] - 0.8 * x[0] * std::cos(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            sum1 += yj * yj;
        } else {
            yj = x[j - 1] - 0.8 * x[0] * std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            sum2 += yj * yj;
        }
    }
    f[0] = x[0] + sum1;
    f[1] = (1.0 - x[0]) * (1.0 - x[0]) + sum2;
    // Inequality constraint
    f[2] = x[1] - 0.8 * x[0] * std::sin(6.0 * x[0] * detail::pi() + 2.0 * detail::pi() / (double)m_dim)
           - sgn((x[0] - 0.5) * (1.0 - x[0])) * std::sqrt(std::abs((x[0] - 0.5) * (1.0 - x[0])));
    f[3] = x[3] - 0.8 * x[0] * std::sin(6.0 * x[0] * detail::pi() + 4.0 * detail::pi() / (double)m_dim)
           - sgn(0.25 * std::sqrt(1 - x[0]) - 0.5 * (1.0 - x[0]))
                 * std::sqrt(std::abs(0.25 * std::sqrt(1 - x[0]) - 0.5 * (1.0 - x[0])));
    // convert to g(x) <= 0 form
    f[2] = -f[2];
    f[3] = -f[3];
}

void cec2009::CF7(vector_double &f, const vector_double &x) const
{
    double sum1, sum2, yj;

    sum1 = sum2 = 0.0;
    for (decltype(m_dim) j = 2u; j <= m_dim; ++j) {
        if (j % 2 == 1u) {
            yj = x[j - 1] - std::cos(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            sum1 += 2.0 * yj * yj - std::cos(4.0 * detail::pi() * yj) + 1.0;
        } else {
            yj = x[j - 1] - std::sin(6.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
            if (j == 2u || j == 4u)
                sum2 += yj * yj;
            else
                sum2 += 2.0 * yj * yj - std::cos(4.0 * detail::pi() * yj) + 1.0;
        }
    }
    f[0] = x[0] + sum1;
    f[1] = (1.0 - x[0]) * (1.0 - x[0]) + sum2;
    // Inequality constraint
    f[2] = x[1] - std::sin(6.0 * x[0] * detail::pi() + 2.0 * detail::pi() / (double)m_dim)
           - sgn((x[0] - 0.5) * (1.0 - x[0])) * std::sqrt(std::abs((x[0] - 0.5) * (1.0 - x[0])));
    f[3] = x[3] - std::sin(6.0 * x[0] * detail::pi() + 4.0 * detail::pi() / (double)m_dim)
           - sgn(0.25 * std::sqrt(1 - x[0]) - 0.5 * (1.0 - x[0]))
                 * std::sqrt(std::abs(0.25 * std::sqrt(1 - x[0]) - 0.5 * (1.0 - x[0])));
    // convert to g(x) <= 0 form
    f[2] = -f[2];
    f[3] = -f[3];
}

void cec2009::CF8(vector_double &f, const vector_double &x) const
{
    double count1, count2, count3;
    double sum1, sum2, sum3, yj, N, a;
    N = 2.0;
    a = 4.0;

    sum1 = sum2 = sum3 = 0.0;
    count1 = count2 = count3 = 0;
    for (decltype(m_dim) j = 3u; j <= m_dim; ++j) {
        yj = x[j - 1] - 2.0 * x[1] * std::sin(2.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        if (j % 3 == 1u) {
            sum1 += yj * yj;
            count1++;
        } else if (j % 3 == 2u) {
            sum2 += yj * yj;
            count2++;
        } else {
            sum3 += yj * yj;
            count3++;
        }
    }
    f[0] = std::cos(0.5 * detail::pi() * x[0]) * std::cos(0.5 * detail::pi() * x[1]) + 2.0 * sum1 / count1;
    f[1] = std::cos(0.5 * detail::pi() * x[0]) * std::sin(0.5 * detail::pi() * x[1]) + 2.0 * sum2 / count2;
    f[2] = std::sin(0.5 * detail::pi() * x[0]) + 2.0 * sum3 / count3;
    // Inequality constraint
    f[3] = (f[0] * f[0] + f[1] * f[1]) / (1 - f[2] * f[2])
           - a * std::abs(sin(N * detail::pi() * ((f[0] * f[0] - f[1] * f[1]) / (1 - f[2] * f[2]) + 1.0))) - 1.0;
    f[3] = -f[3]; // convert to g(x) <= 0 form
}

void cec2009::CF9(vector_double &f, const vector_double &x) const
{
    double count1, count2, count3;
    double sum1, sum2, sum3, yj, N, a;
    N = 2.0;
    a = 3.0;

    sum1 = sum2 = sum3 = 0.0;
    count1 = count2 = count3 = 0;
    for (decltype(m_dim) j = 3u; j <= m_dim; ++j) {
        yj = x[j - 1] - 2.0 * x[1] * std::sin(2.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        if (j % 3 == 1u) {
            sum1 += yj * yj;
            count1++;
        } else if (j % 3 == 2u) {
            sum2 += yj * yj;
            count2++;
        } else {
            sum3 += yj * yj;
            count3++;
        }
    }
    f[0] = std::cos(0.5 * detail::pi() * x[0]) * std::cos(0.5 * detail::pi() * x[1]) + 2.0 * sum1 / count1;
    f[1] = std::cos(0.5 * detail::pi() * x[0]) * std::sin(0.5 * detail::pi() * x[1]) + 2.0 * sum2 / count2;
    f[2] = std::sin(0.5 * detail::pi() * x[0]) + 2.0 * sum3 / count3;
    // Inequality constraint
    f[3] = (f[0] * f[0] + f[1] * f[1]) / (1 - f[2] * f[2])
           - a * std::sin(N * detail::pi() * ((f[0] * f[0] - f[1] * f[1]) / (1 - f[2] * f[2]) + 1.0)) - 1.0;
    f[3] = -f[3]; // convert to g(x) <= 0 form
}

void cec2009::CF10(vector_double &f, const vector_double &x) const
{
    double count1, count2, count3;
    double sum1, sum2, sum3, yj, hj, N, a;
    N = 2.0;
    a = 1.0;

    sum1 = sum2 = sum3 = 0.0;
    count1 = count2 = count3 = 0;
    for (decltype(m_dim) j = 3u; j <= m_dim; ++j) {
        yj = x[j - 1] - 2.0 * x[1] * std::sin(2.0 * detail::pi() * x[0] + j * detail::pi() / (double)m_dim);
        hj = 4.0 * yj * yj - std::cos(8.0 * detail::pi() * yj) + 1.0;
        if (j % 3 == 1u) {
            sum1 += hj;
            count1++;
        } else if (j % 3 == 2u) {
            sum2 += hj;
            count2++;
        } else {
            sum3 += hj;
            count3++;
        }
    }
    f[0] = std::cos(0.5 * detail::pi() * x[0]) * std::cos(0.5 * detail::pi() * x[1]) + 2.0 * sum1 / count1;
    f[1] = std::cos(0.5 * detail::pi() * x[0]) * std::sin(0.5 * detail::pi() * x[1]) + 2.0 * sum2 / count2;
    f[2] = std::sin(0.5 * detail::pi() * x[0]) + 2.0 * sum3 / count3;
    // Inequality constraint
    f[3] = (f[0] * f[0] + f[1] * f[1]) / (1 - f[2] * f[2])
           - a * std::sin(N * detail::pi() * ((f[0] * f[0] - f[1] * f[1]) / (1 - f[2] * f[2]) + 1.0)) - 1.0;
    f[3] = -f[3]; // convert to g(x) <= 0 form
}
// -------------------------------------------
// LCOV_EXCL_STOP

#if defined(__clang__) || defined(__GNUC__)
#pragma GCC diagnostic pop
#endif

} // namespace pagmo

PAGMO_S11N_PROBLEM_IMPLEMENT(pagmo::cec2009)