test_functions.h

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/* Copyright (C) 2000-2013 CEA
 *
 * This software and supporting documentation were developed by
 *     bioPICSEL
 *     CEA/DSV/I²BM/MIRCen/LMN, Batiment 61,
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 */
 
#ifndef PRIMATOLOGIST_OPTIMIZATION_TEST_FUNCTIONS_H
#define PRIMATOLOGIST_OPTIMIZATION_TEST_FUNCTIONS_H
 
#include <primatologist/math/matrix.h>
#include <primatologist/math/constants.h>
#include <cmath>
 
// This file defines and implements classic test functions for optimization
// algorithms. They are described at:
// http://en.wikipedia.org/wiki/Test_functions_for_optimization
// where one can visualize their shape.
 
namespace aims {
namespace math {
 
  //==========================================================================
  //   RASTRIGIN
  //==========================================================================

  class Rastrigin
  {
  public:
    Rastrigin( int n = 2, float A = 10. );
    ~Rastrigin();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
 
  protected:
    float _A;
    float _n;
  };
 
  //==========================================================================
  //   ACKLEY
  //==========================================================================

  class Ackley
  {
  public:
    Ackley( int n = 2, float a = 20, float b = 0.2, float c = TWO_PI );
    ~Ackley();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
 
  protected:
    int _n;
    float _a;
    float _b;
    float _c;
    float term_poly( const Vector & ) const;
    float term_cos( const Vector & ) const;
    float g_poly( const Vector &, int ) const;
    float g_cos( const Vector &, int ) const;
    float gg_poly( const Vector &, int, int ) const;
    float gg_cos( const Vector &, int, int ) const;
  };
 
  //==========================================================================
  //   SPHERE
  //==========================================================================

  class SphereF
  {
  public:
    SphereF( int n = 2 );
    ~SphereF();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
 
  protected:
    float _n;
  };
 
  //==========================================================================
  //   ROSENBROCK
  //==========================================================================

  class Rosenbrock
  {
  public:
    Rosenbrock( int n = 2 );
    ~Rosenbrock();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
 
  protected:
    float _n;
  };
 
  //==========================================================================
  //   Beale
  //==========================================================================

  class Beale
  {
  public:
    Beale();
    ~Beale();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Goldstein-Price
  //==========================================================================

  class GoldsteinPrice
  {
  public:
    GoldsteinPrice();
    ~GoldsteinPrice();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Booth
  //==========================================================================
 
  class Booth
  {
  public:
    Booth();
    ~Booth();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Bukin n°6
  //==========================================================================

  class Bukin6
  {
  public:
    Bukin6();
    ~Bukin6();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Matyas
  //==========================================================================

  class Matyas
  {
  public:
    Matyas();
    ~Matyas();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Levi n°13
  //==========================================================================

  class Levi13
  {
  public:
    Levi13();
    ~Levi13();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Three-hump camel
  //==========================================================================

  class ThreeHumpCamel
  {
  public:
    ThreeHumpCamel();
    ~ThreeHumpCamel();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Easom
  //==========================================================================

  class Easom
  {
  public:
    Easom();
    ~Easom();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Cross-in-tray
  //==========================================================================

  class CrossInTray
  {
  public:
    CrossInTray();
    ~CrossInTray();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Eggholder
  //==========================================================================

  class Eggholder
  {
  public:
    Eggholder();
    ~Eggholder();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Hoelder table
  //==========================================================================

  class HolderTable
  {
  public:
    HolderTable();
    ~HolderTable();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   McCormick
  //==========================================================================
 
  class McCormick
  {
  public:
    McCormick();
    ~McCormick();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Schaffer n°2
  //==========================================================================
 
  class Schaffer2
  {
  public:
    Schaffer2();
    ~Schaffer2();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Schaffer n°4
  //==========================================================================
 
  class Schaffer4
  {
  public:
    Schaffer4();
    ~Schaffer4();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
  };
 
  //==========================================================================
  //   Styblinski–Tang
  //==========================================================================
 
  class StyblinskiTang
  {
  public:
    StyblinskiTang( int n = 2 );
    ~StyblinskiTang();
 
    float value( const Vector & x ) const;
    Vector derivative( const Vector & x ) const;
    Matrix hessian( const Vector & x ) const;
 
    Vector exactMin() const;
    float exactMinValue() const;
 
  protected:
    int _n;
  };
 
} // math
} // aims
 
#endif // PRIMATOLOGIST_OPTIMIZATION_TEST_FUNCTIONS_H