bool operator()(const std::shared_ptr<SearchCell>& a, const std::shared_ptr<SearchCell>& b) const
		{
				if (a->get_f() <= b->get_f())
						return true;

				else if (a->get_f() > b->get_f())
						return true;
		}

I don't get this.
if A <= B then you return true, but if A > B then you also return true. So why bother comparing something - just return always true.

Edit: too late...

bool operator()(const std::shared_ptr<SearchCell>& a, const std::shared_ptr<SearchCell>& b) const
		{
				if (a->get_f() <= b->get_f())
						return true;

				else if (a->get_f() > b->get_f())
						return true;
		}

I don't get this.
if A <= B then you return true, but if A > B then you also return true. So why bother comparing something - just return always true

        bool operator()(const std::shared_ptr<SearchCell>& a, const std::shared_ptr<SearchCell>& b) const
        {
                if (a->get_f() <= b->get_f())
                        return true;

                else if (a->get_f() > b->get_f())
                        return true;
        }

I don't get this.
if A <= B then you return true, but if A > B then you also return true. So you bother comparing something - just return true always