Yes, for sure. You can find these examples in the scheduling literature in which amazing heuristics have been proposed. BTW, nowadays the focus has shifted towards hybrid methods (Heuristic+Metaheuristic) and reaping the benefits of both in a single procedure. 

But Hybrid metaheuristic can not guarantee that solutions are optimal. Please, can you provide  any paper the literature from the literature about the shortage in metaheuristic and/or hyperheuristics comparing with heuristic method 

You know that neither heuristics nor metaheuristics can guarantee an optimal solution. You can take a look at papers by Professor. Ruben Ruiz in scheduling literature to grasp the performance of these two compared to each other in fair settings.

Both heuristics and metaheuristics cannot guarantee the optimality of the solutions they provide. But in general, heuristics tend to be faster than metaheuristics. In addition to that, a lot of studies have established worst-case performance ratios for many heuristics. Thus, although you won't be able to prove optimality, at least you'll know that your solution is at most C times the optimum (Where C is the worst-case performance ratio ; the closer it is to 1, the better). Plus, some proposed heuristics in the literature are considered to be quite efficient.

So, I would recommend using heuristics rather than metaheuristics or hyperheuritics if you need a solution to your problem within a short time or if you need some kind of guarantee on the quality of your solution(s).

In order to precise your question you can use heuristics to help complete methods as forward checking or others to be more efficient to solve problems and to obtain optimal solutions. When these kind of techniques are not able to find the solution in a reasonable time you can think to use a metaheuristic to find a near optimal solution. When you need to find quickly a candidate solution with an acceptable quality you can try using a hyperheuristic.

Are you sure that you want to compare heuristics and Meta/Hyper-heuristics? Because the first one (Meta) is like a pattern or a strategy designing an heuristic for your problem and the second one is a bunch of heuristics which are selected according to the current instance. Therefore, for any cases you can find what you're looking for.

Hi,

Most of metaheuristics have a predefined and standard structure and most of the time their application is not so hard for any problem. They all have a general pattern that mostly starts with an initial solution or a group of solutions and finally ends to an efficient (but not guarantee for optimal) solution. This pattern requires an adequate CPU time for the convergence of the algorithm. Samples of metaheuristics are genetic algorithm, simulated annealing, particle swarm optimization algorithms, etc.

Contrarily, heuristic algorithms don't have a standard pattern and they deffer from an optimization problem to another one, and mostly lead near optimal solutions and sometimes the optimum one and mostly in much less CPU time, so far that the comparison between metaheuristic' and heuristics' CPU time does not make sense.

Consider some examples of heuristic algorithms in scheduling problems that find the optimum schedule, like Johnson rule for two machine flow shop for makespan, Shortest processing time first in single machine for total completion times etc.

What makes the heuristic algorithms worthy compared with metaheuristics is their creativity that lies behind them. As mentioned before, each problem may have several heuristic methods but the question is what heuristic performs well. But the solution logic guides the researcher to create the suitable heuristic algorithm for his/her problem. This question that how to create a heuristic algorithm makes it  valuable (while metaheuristics have a standard procedure).

Best regards.