# dlib C++ Library - find_max_global_abstract.h

    // Copyright (C) 2017  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #undef DLIB_FiND_GLOBAL_MAXIMUM_ABSTRACT_hH_
    #ifdef DLIB_FiND_GLOBAL_MAXIMUM_ABSTRACT_hH_

    #include "upper_bound_function_abstract.h"
    #include "global_function_search_abstract.h"
    #include "../metaprogramming.h"
    #include "../matrix.h"
    #include "../threads/thread_pool_extension_abstract.h"
    #include <utility>
    #include <chrono>
    #include <functional>

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------

        template <
            typename T
            >
        auto call_function_and_expand_args(
            T&& f,
            const matrix<double,0,1>& args
        ) -> decltype(f(args or args expanded out as discussed below));
        /*!
            requires
                - f is a function object with one of the following signatures:
                    auto f(matrix<double,0,1>)
                    auto f(double)
                    auto f(double,double)
                    auto f(double,double,double)
                    ...
                    auto f(double,double,...,double)  // up to 40 double arguments
                - if (f() explicitly expands its arguments) then
                    - args.size() == the number of arguments taken by f.
            ensures
                - This function invokes f() with the given arguments and returns the result.
                  However, the signature of f() is allowed to vary.  In particular, if f()
                  takes a matrix<double,0,1> as a single argument then this function simply
                  calls f(args).  However, if f() takes double arguments then args is expanded
                  appropriately, i.e. it calls one of the following as appropriate:
                    f(args(0))
                    f(args(0),args(1))
                    ...
                    f(args(0),args(1),...,args(N))
                  and the result of f() is returned.
        !*/

    // ----------------------------------------------------------------------------------------

        struct max_function_calls
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is a simple typed integer class used to strongly type the "max number
                    of function calls" argument to find_max_global() and find_min_global().

            !*/

            max_function_calls() = default;

            explicit max_function_calls(size_t max_calls) : max_calls(max_calls) {}

            size_t max_calls = std::numeric_limits<size_t>::max();
        };

    // ----------------------------------------------------------------------------------------

        const auto FOREVER = std::chrono::hours(24*356*290); // 290 years, basically forever

        /*!
           WHAT THIS OBJECT REPRESENTS
              A call-back that returns true when the search should stop.

              It is useful when the user either wants to terminate the search based on special knowledge
              of the function, the user's preferences regarding what is a "good-enough" solution, or
              based on the results of some external process which may have found a solution and this search
              is no longer required.
         !*/
        using stop_condition = std::function<bool(double)>;
        // The default condition.
        const stop_condition never_stop_early = [](double) { return false; };

    // ----------------------------------------------------------------------------------------

        template <
            typename funct
            >
        std::pair<size_t,function_evaluation> find_max_global (
            thread_pool& tp,
            std::vector<funct>& functions,
            const std::vector<function_spec>& specs,
            const max_function_calls num,
            const std::chrono::nanoseconds max_runtime = FOREVER,
            double solver_epsilon = 0,
            const std::vector<std::vector<function_evaluation>>& initial_function_evals = {},
            stop_condition should_stop = never_stop_early
        );
        /*!
            requires
                - functions.size() != 0
                - functions.size() == specs.size()
                - solver_epsilon >= 0
                - for all valid i:
                    - functions[i] is a real valued multi-variate function object.  Moreover,
                      it must be callable via an expression of the form:
                      call_function_and_expand_args(functions[i], specs.lower).  This means
                      function[i] should have a signature like one of the following:
                        double f(matrix<double,0,1>)
                        double f(double)
                        double f(double,double)
                        etc.
                    - The range of inputs defined by specs[i] must be valid inputs to
                      functions[i].
                - if (tp.num_threads_in_pool() != 0) then
                    - it must be safe to call the given functions concurrently from multiple
                      threads.
                - initial_function_evals.empty() || initial_function_evals.size() == functions.size()
                - for all valid i:
                    - for (item : initial_function_evals[i]):
                        - functions[i](item.x) == item.y
                          i.e. initial_function_evals contains a record of evaluations of the given
                          functions.
            ensures
                - This function performs global optimization on the set of given functions.
                  The goal is to maximize the following objective function:
                     max_{i,x_i}: functions[i](x_i)
                     subject to the constraints on x_i defined by specs[i].
                  Once found, the return value of find_max_global() is:
                    make_pair(i, function_evaluation(x_i,functions[i](x_i))).
                  That is, we search for the settings of i and x that return the largest output
                  and return those settings.
                - The search is performed using the global_function_search object.  See its
                  documentation for details of the algorithm.
                - We set the global_function_search::get_solver_epsilon() parameter to
                  solver_epsilon.  Therefore, the search will only attempt to find a global
                  maximizer to at most solver_epsilon accuracy.  Once a local maximizer is
                  found to that accuracy the search will focus entirely on finding other maxima
                  elsewhere rather than on further improving the current local optima found so
                  far.  That is, once a local maxima is identified to about solver_epsilon
                  accuracy, the algorithm will spend all its time exploring the functions to
                  find other local maxima to investigate.  An epsilon of 0 means it will keep
                  solving until it reaches full floating point precision.  Larger values will
                  cause it to switch to pure global exploration sooner and therefore might be
                  more effective if your objective function has many local maxima and you don't
                  care about a super high precision solution.
                - find_max_global() runs until one of the following is true:
                    - The total number of calls to the provided functions is == num.max_calls
                    - More than max_runtime time has elapsed since the start of this function.
                    - should_stop(f(x)) returns true
                - Any variables that satisfy the following conditions are optimized on a log-scale:
                    - The lower bound on the variable is > 0
                    - The ratio of the upper bound to lower bound is >= 1000
                    - The variable is not an integer variable
                  We do this because it's common to optimize machine learning models that have
                  parameters with bounds in a range such as [1e-5 to 1e10] (e.g. the SVM C
                  parameter) and it's much more appropriate to optimize these kinds of
                  variables on a log scale.  So we transform them by applying std::log() to
                  them and then undo the transform via std::exp() before invoking the function
                  being optimized.  Therefore, this transformation is invisible to the user
                  supplied functions.  In most cases, it improves the efficiency of the
                  optimizer.
                - The evaluations in initial_function_evals are incorporated into the solver state at
                  startup.  This is useful if you have information from a previous optimization attempt
                  or just know some good initial x values that should be attempted as a baseline.
                  Giving initial_function_evals allows you to tell the solver to explicitly include
                  those x values in its search.
                - if (tp.num_threads_in_pool() != 0) then
                    - This function will make concurrent calls to the given functions.  In
                      particular, it will submit the calls to the functions as jobs to the
                      given thread_pool tp.
        !*/

        template <
            typename funct
            >
        std::pair<size_t,function_evaluation> find_max_global (
            std::vector<funct>& functions,
            const std::vector<function_spec>& specs,
            const max_function_calls num,
            const std::chrono::nanoseconds max_runtime = FOREVER,
            double solver_epsilon = 0,
            const std::vector<std::vector<function_evaluation>>& initial_function_evals = {},
            stop_condition should_stop = never_stop_early
        );
        /*!
            this function is identical to the find_max_global() defined immediately above,
            except that no threading is used.
        !*/

        template <
            typename funct
            >
        std::pair<size_t,function_evaluation> find_min_global (
            std::vector<funct>& functions,
            const std::vector<function_spec>& specs,
            const max_function_calls num,
            const std::chrono::nanoseconds max_runtime = FOREVER,
            double solver_epsilon = 0,
            const std::vector<std::vector<function_evaluation>>& initial_function_evals = {},
            stop_condition should_stop = never_stop_early
        );
        /*!
            This function is identical to the find_max_global() defined immediately above,
            except that we perform minimization rather than maximization.
        !*/

        template <
            typename funct
            >
        std::pair<size_t,function_evaluation> find_min_global (
            thread_pool& tp,
            std::vector<funct>& functions,
            const std::vector<function_spec>& specs,
            const max_function_calls num,
            const std::chrono::nanoseconds max_runtime = FOREVER,
            double solver_epsilon = 0,
            const std::vector<std::vector<function_evaluation>>& initial_function_evals = {},
            stop_condition should_stop = never_stop_early
        );
        /*!
            This function is identical to the find_max_global() defined immediately above,
            except that we perform minimization rather than maximization.  We also allow you to
            give a thread_pool so we can make concurrent calls to the given functions during
            optimization.
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            typename funct
            >
        function_evaluation find_max_global (
            thread_pool& tp,
            funct f,
            const matrix<double,0,1>& bound1,
            const matrix<double,0,1>& bound2,
            const std::vector<bool>& is_integer_variable,
            const max_function_calls num,
            const std::chrono::nanoseconds max_runtime = FOREVER,
            double solver_epsilon = 0,
            const std::vector<function_evaluation>& initial_function_evals = {},
            stop_condition should_stop = never_stop_early
        );
        /*!
            requires
                - bound1.size() == bound2.size() == is_integer_variable.size()
                - for all valid i: bound1(i) != bound2(i)
                - solver_epsilon >= 0
                - f() is a real valued multi-variate function object.  Moreover, it must be
                  callable via an expression of the form: call_function_and_expand_args(f,
                  bound1).  This means f() should have a signature like one of the following:
                    double f(matrix<double,0,1>)
                    double f(double)
                    double f(double,double)
                    etc.
                - The range of inputs defined by function_spec(bound1,bound2,is_integer_variable)
                  must be valid inputs to f().
                - if (tp.num_threads_in_pool() != 0) then
                    - it must be safe to call the given function f() concurrently from multiple
                      threads.
                - for (item : initial_function_evals):
                    - f(item.x) == item.y
                      i.e. initial_function_evals contains a record of evaluations of f().
            ensures
                - This function performs global optimization on the given f() function.
                  The goal is to maximize the following objective function:
                     f(x)
                     subject to the constraints on x defined by function_spec(bound1,bound2,is_integer_variable).
                  Once found, the return value of find_max_global() is:
                    function_evaluation(x,f(x))).
                  That is, we search for the setting of x that returns the largest output and
                  return that setting.
                - The search is performed using the global_function_search object.  See its
                  documentation for details of the algorithm.
                - We set the global_function_search::get_solver_epsilon() parameter to
                  solver_epsilon.  Therefore, the search will only attempt to find a global
                  maximizer to at most solver_epsilon accuracy.  Once a local maximizer is
                  found to that accuracy the search will focus entirely on finding other maxima
                  elsewhere rather than on further improving the current local optima found so
                  far.  That is, once a local maxima is identified to about solver_epsilon
                  accuracy, the algorithm will spend all its time exploring the function to
                  find other local maxima to investigate.  An epsilon of 0 means it will keep
                  solving until it reaches full floating point precision.  Larger values will
                  cause it to switch to pure global exploration sooner and therefore might be
                  more effective if your objective function has many local maxima and you don't
                  care about a super high precision solution.
                - find_max_global() runs until one of the following is true:
                    - The total number of calls to f() is == num.max_calls
                    - More than max_runtime time has elapsed since the start of this function.
                    - should_stop(f(x)) returns true
                - Any variables that satisfy the following conditions are optimized on a log-scale:
                    - The lower bound on the variable is > 0
                    - The ratio of the upper bound to lower bound is >= 1000
                    - The variable is not an integer variable
                  We do this because it's common to optimize machine learning models that have
                  parameters with bounds in a range such as [1e-5 to 1e10] (e.g. the SVM C
                  parameter) and it's much more appropriate to optimize these kinds of
                  variables on a log scale.  So we transform them by applying std::log() to
                  them and then undo the transform via std::exp() before invoking the function
                  being optimized.  Therefore, this transformation is invisible to the user
                  supplied functions.  In most cases, it improves the efficiency of the
                  optimizer.
                - The evaluations in initial_function_evals are incorporated into the solver state at
                  startup.  This is useful if you have information from a previous optimization attempt
                  of f(x) or just know some good initial x values that should be attempted as a
                  baseline.  Giving initial_function_evals allows you to tell the solver to explicitly
                  include those x values in its search.
                - if (tp.num_threads_in_pool() != 0) then
                    - This function will make concurrent calls to the given function f().  In
                      particular, it will submit the calls to f() as jobs to the given
                      thread_pool tp.
        !*/

        template <
            typename funct
            >
        function_evaluation find_min_global (
            thread_pool& tp,
            funct f,
            const matrix<double,0,1>& bound1,
            const matrix<double,0,1>& bound2,
            const std::vector<bool>& is_integer_variable,
            const max_function_calls num,
            const std::chrono::nanoseconds max_runtime = FOREVER,
            double solver_epsilon = 0,
            const std::vector<function_evaluation>& initial_function_evals = {},
            stop_condition should_stop = never_stop_early
        );
        /*!
            This function is identical to the find_max_global() defined immediately above,
            except that we perform minimization rather than maximization.
        !*/

        template <
            typename funct
            >
        function_evaluation find_max_global (
            funct f,
            const matrix<double,0,1>& bound1,
            const matrix<double,0,1>& bound2,
            const std::vector<bool>& is_integer_variable,
            const max_function_calls num,
            const std::chrono::nanoseconds max_runtime = FOREVER,
            double solver_epsilon = 0,
            const std::vector<function_evaluation>& initial_function_evals = {},
            stop_condition should_stop = never_stop_early
        );
        /*!
            This function is identical to the find_max_global() defined immediately above,
            except that we don't take a thread_pool and therefore don't make concurrent calls
            to f().
        !*/

        template <
            typename funct
            >
        function_evaluation find_min_global (
            funct f,
            const matrix<double,0,1>& bound1,
            const matrix<double,0,1>& bound2,
            const std::vector<bool>& is_integer_variable,
            const max_function_calls num,
            const std::chrono::nanoseconds max_runtime = FOREVER,
            double solver_epsilon = 0,
            const std::vector<function_evaluation>& initial_function_evals = {},
            stop_condition should_stop = never_stop_early
        );
        /*!
            This function is identical to the find_min_global() defined immediately above,
            except that we don't take a thread_pool and therefore don't make concurrent calls
            to f().
        !*/

    // Finally, there are a bunch of overloads of find_min_global() and find_max_global() that make do
    // the following for you:
    //   - They make is_integer_variable optional.  If you don't provide it then we assume no parameters
    //     are integers.
    //   - The order of num and max_runtime can be exchanged.  You can also leave one of these arguments
    //     out so long as you provide the other.
    //   - If f() takes just a single double then bound1 and bound2 can also just be doubles.

    }

    #endif // DLIB_FiND_GLOBAL_MAXIMUM_ABSTRACT_hH_