C++11: bind std::sort for user-defined type and then use that bind as an argument in ctor

This is complicated. I wanted to create a class than can hold a sorting algorithm (mostly to compare how they work). Array that is to be sorted will be of type: std::vector<std::shared_ptr<Item>>. I am going to use different functions to sort it, I have tested std::sort() with a function looking like bool func(std::shared_ptr<Item> const& a, std::shared_ptr<Item> const& b) and it worked correctly

The algorithm class also contains other data, for example name (std::string) and amount (int) of items to be sorted

The problem begins when I want to put and object of type algorithm into std::vector<std::shared_ptr<Algorithm>>

I have already found on SO that std::bind is not an object, so first I need to create something like this:

struct std_sort {
    template <typename RndIt, typename Cmp>
    void operator()(RndIt begin, RndIt end, Cmp cmp) {
        std::sort(begin, end, cmp);
    }
};

The problem begins when I try to add an object of type algorithm

vect.push_back(std::make_shared<Algorithm>(std::string("std::sort()"), zero, zero, amount,
        std::bind
        (
            static_cast<void(*)
            (
                std::shared_ptr<Item> a,
                std::shared_ptr<Item> b,
                std::function
                <bool(
                        std::shared_ptr<Item> const& c, std::shared_ptr<Item> const& d
                )>
            )>
            (std_sort()), //error on this line
            std::placeholders::_1, std::placeholders::_2, std::placeholders::_3
        )
    ));

Everything goes well except for the last argument, the expected argument is of this type:

typedef std::function
    <void(
            std::shared_ptr<Item> a,
            std::shared_ptr<Item> b,
            std::function
            <bool(
                std::shared_ptr<Item> const& c, std::shared_ptr<Item> const& d
            )>
    )>
    sorting_function;

The error I get (from MinGW)

error: invalid static_cast from type 'std_sort' to type 'void (*)(std::shared_ptr<Item>, std::shared_ptr<Item>, std::function<bool(const std::shared_ptr<Item>&, const std::shared_ptr<Item>&)>)'

If I remove static_cast I get tons of typical template errors