Utils::HJPatternSearch< Real > Class Template Reference

Class for implementing the Hooke-Jeeves Pattern Search Algorithm. More...

#include <Utils_HJPatternSearch.hh>

Public Member Functions
	HJPatternSearch (string_view name)
	Constructs a Hooke-Jeeves Pattern Search instance.
string_view	name (void) const
	Retrieves the name of the pattern search instance.
void	setup (integer dim, HJFunc &fun, Console const *console)
	Sets up the pattern search with the specified dimension and objective function.
void	change_console (Console const *console)
	Changes the console used for output messages.
void	set_verbose (integer level)
	Sets the verbosity level for output messages.
void	set_tolerance (Real tol)
	Sets the convergence tolerance.
void	set_max_iterations (integer mit)
	Sets the maximum number of iterations.
void	set_max_fun_evaluation (integer mfev)
	Sets the maximum number of function evaluations.
void	set_max_num_stagnation (integer nstg)
	Sets the maximum number of allowed stagnation iterations.
string	info () const
	Provides information about the current state of the algorithm.
void	print_info (ostream_type &stream) const
	Prints the current state information to the specified output stream.
void	best_nearby ()
	Searches for the best nearby solution.
void	search ()
	Performs the main search algorithm.
void	run (Real const x_sol[], Real h)
	Runs the optimization algorithm starting from the provided solution.
Real	get_last_solution (Real x[]) const
	Retrieves the last solution found by the algorithm.

Detailed Description

template<typename Real>
class Utils::HJPatternSearch< Real >

Class for implementing the Hooke-Jeeves Pattern Search Algorithm.

The HJPatternSearch class provides an implementation of the Hooke-Jeeves Pattern Search Algorithm, which is a direct search method for optimization problems. This method does not require the computation of gradients and is suitable for minimizing functions in arbitrary dimensions.

Template Parameters

Real	The data type used for the optimization (e.g., float, double).

References

The implementation is based on the following references:

• R. Hooke, T. A. Jeeves, "Direct Search" Solution of Numerical and Statistical Problems, Westinghouse Research Laboratories, Pittsburgh, Pennsylvania.
• Arthur Kaupe, "Algorithm 178: Direct Search," Communications of the ACM, Volume 6, Number 6, June 1963, page 313.
• M. Bell, Malcolm Pike, "Remark on Algorithm 178: Direct Search," Communications of the ACM, Volume 9, Number 9, September 1966, page 684.
• F.K. Tomlin, L.B. Smith, "Remark on Algorithm 178: Direct Search," Communications of the ACM, Volume 12, Number 11, November 1969, pages 637-638.

Using the HJPatternSearch Class for Function Minimization

The HJPatternSearch class is a powerful tool for finding the minimum of a function in an arbitrary number of dimensions using the Hooke-Jeeves Pattern Search algorithm. This tutorial will guide you through the process of using this class effectively.

Prerequisites

Before you begin, ensure you have the following:

1. C++ Compiler: A C++ compiler that supports C++11 or later.
2. Eigen Library: Make sure the Eigen library is included in your project for matrix operations.
3. Your Implementation of HJPatternSearch: Ensure you have the implementation of the HJPatternSearch class available in your project.

Step 1: Include Necessary Headers

Start by including the headers for the HJPatternSearch class and any necessary libraries.

#include "Utils_HJPatternSearch.hh" // Adjust the path according to your project structure
#include "Utils_fmt.hh" // For formatted output (optional)
 
#include <cmath>
#include <iostream>
#include <functional>
 
using namespace std;
using Utils::HJPatternSearch; // Adjust according to your namespace
using real_type = double; // Define the real type as double for precision

Step 2: Define the Objective Function

You need to define the function you want to minimize. The function should take an array of doubles as input and return a double representing the function value.

Here’s an example of a simple quadratic function:

static real_type fun3(real_type const X[]) {
  real_type x = X[0];
  real_type y = X[1];
  return 100 * pow(y - x * x, 2) + pow(1 - x, 2); // Rosenbrock function
}

Step 3: Set Up the Solver

Create a function to set up and run the HJPatternSearch solver.

template <typename FUN>
void do_solve(FUN f, real_type const X0[], real_type delta) {
  Utils::Console console(&cout, 4); // Create a console for logging
  HJPatternSearch<real_type> solver("HJPatternSearch"); // Create the solver
  solver.setup(2, f, &console); // Setup for 2D optimization
  solver.set_tolerance(1e-20); // Set the desired tolerance for convergence
  solver.run(X0, delta); // Run the optimization from initial guess X0 with step size delta
 
  real_type X[2]; // Array to store the result
  solver.get_last_solution(X); // Retrieve the best solution found
  fmt::print("X={}, Y={}\n", X[0], X[1]); // Print the results
}

Step 4: Main Function to Execute the Solver

In your main function, define your initial guess and the step size for the search. Then call the do_solve function with your defined objective function.

int main() {
  real_type X0[2]{-1, 1}; // Initial guess for [x, y]
  real_type delta = 0.1; // Initial step size for search
  std::function<real_type(real_type const[])> F(fun3); // Create a function wrapper
  do_solve(F, X0, delta); // Execute the optimization
 
  cout << "\nAll Done Folks!\n"; // Indicate completion
  return 0; // Return success
}

Step 5: Compile and Run

Compile your program using a suitable C++ compiler. For example, using g++ you can compile with:

g++ -std=c++11 -o HJPatternSearchExample your_file.cpp

Run the executable:

./HJPatternSearchExample

Constructor & Destructor Documentation

HJPatternSearch()

template<typename Real>

Utils::HJPatternSearch< Real >::HJPatternSearch ( string_view name )

inlineexplicit

Constructs a Hooke-Jeeves Pattern Search instance.

Parameters

name	The name of this instance for identification.

Member Function Documentation

best_nearby()

template<typename Real>

void Utils::HJPatternSearch< Real >::best_nearby

(

)

Searches for the best nearby solution.

This method performs a search around the current best solution to find a nearby minimum.

change_console()

template<typename Real>

void Utils::HJPatternSearch< Real >::change_console ( Console const * console )

inline

Changes the console used for output messages.

Parameters

console

Pointer to the new console for output.

get_last_solution()

template<typename Real>

Real Utils::HJPatternSearch< Real >::get_last_solution ( Real x[] ) const

inline

Retrieves the last solution found by the algorithm.

Parameters

x	Array to store the last solution.

Returns

The objective function value at the last solution.

info()

template<typename Real>

string Utils::HJPatternSearch< Real >::info

(

)

const

Provides information about the current state of the algorithm.

Returns

A string containing the current state information.

name()

template<typename Real>

string_view Utils::HJPatternSearch< Real >::name ( void ) const

inline

Retrieves the name of the pattern search instance.

Returns

The name of the instance.

print_info()

template<typename Real>

void Utils::HJPatternSearch< Real >::print_info ( ostream_type & stream ) const

inline

Prints the current state information to the specified output stream.

Parameters

stream

The output stream to which the information will be printed.

run()

template<typename Real>

void Utils::HJPatternSearch< Real >::run	(	Real const	x_sol[],
		Real	h )

Runs the optimization algorithm starting from the provided solution.

Parameters

x_sol	Initial solution to start the optimization.
h	Initial step size for the search.

search()

template<typename Real>

void Utils::HJPatternSearch< Real >::search

(

)

Performs the main search algorithm.

This method executes the Hooke-Jeeves pattern search algorithm iteratively.

set_max_fun_evaluation()

template<typename Real>

void Utils::HJPatternSearch< Real >::set_max_fun_evaluation

(

integer

mfev

)

Sets the maximum number of function evaluations.

Parameters

mfev	The maximum number of function evaluations allowed.

set_max_iterations()

template<typename Real>

void Utils::HJPatternSearch< Real >::set_max_iterations

(

integer

mit

)

Sets the maximum number of iterations.

Parameters

mit	The maximum iterations allowed.

set_max_num_stagnation()

template<typename Real>

void Utils::HJPatternSearch< Real >::set_max_num_stagnation

(

integer

nstg

)

Sets the maximum number of allowed stagnation iterations.

Parameters

nstg	The maximum number of allowed stagnation iterations.

set_tolerance()

template<typename Real>

void Utils::HJPatternSearch< Real >::set_tolerance

(

Real

tol

)

Sets the convergence tolerance.

Parameters

tol	The new tolerance value.

set_verbose()

template<typename Real>

void Utils::HJPatternSearch< Real >::set_verbose ( integer level )

inline

Sets the verbosity level for output messages.

Parameters

level

The verbosity level (0: none, 1: basic info, 2: detailed info).

setup()

template<typename Real>

void Utils::HJPatternSearch< Real >::setup	(	integer	dim,
		HJFunc &	fun,
		Console const *	console )

Sets up the pattern search with the specified dimension and objective function.

Parameters

dim	The dimension of the problem.
fun	A reference to the objective function to minimize.
console	Optional pointer to a console for output messages.

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The documentation for this class was generated from the following files:

• /Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/UtilsLite/src/Utils_HJPatternSearch.hh
• /Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/UtilsLite/src/Utils_HJPatternSearch.cc