A clear candidate is to utilize mathematical optimization. It has the rather nice property that there is a strong theory on optimality conditions, which can not only be used to assess whether a feasible vector is optimal - it also suggests improving directions of movement when the vector is not optimal. I find metaheuristics lacking rigour - you don't know what you get, and you won't know if you stumble upon an optimum; you will in fact keep moving away from it.

In any case you need to educate yourself a lot, as I fear that you do not yet have all the tools that are needed in order to be successful - and recall that metaheuristics provide NO guarantee to find an optimum for you. So why should you want to only consider that technique?

Is there any reason you are not discussing an actual problem for which the metaheuristic is being applied to? Algorithm design is all about solving problems, it is a problem-centric venture (not the other way around). Usually throwing an overarching metaheuristic at an arbitrary optimization problem just isn't going to give you a positive result many times or can be completely excessive. Problems have structure and you should design the algorithm (based on said structure, proving a theorem or two perhaps) to capitalize on the structure or special properties that problem has. Perhaps your approach just by happenstance works for some optimization problems, but not for others.

I understand some are focused heavily on just using metaheuristics like a hammer going around looking for nails, but it just seems excessive and unwise as you often have little to tell you about the optimum.

I'd recommend Michael's suggestion if you really want some guarantees, or get the paper out and start proving theorems with respect to the problem at hand (or see if the literature has any answers). For example, if you can show a problem has a nice property perhaps your heuristic algorithm can capitalize on it (or could be even better, something like an approximation algorithm where you have a direct connection between the optimum value and the objective value).

I understand the interest in finding new paradigms for solving problems, but I find, similar to Michael, that very little care is put into caring about problem instances and often times it could have been almost any problem the technique is thrown at, with no regard for the structure of the problem. You could be applying a completely incorrect technique to "solve" a problem that might actually have a nice and clean heuristic approach (I write heuristic as one usually doesn't care about finding the actual optimum once they've subscribed to using a metaheuristic).

Good of you, Daniel Page - spot on!

So, Thieu Nguyen - what is your plan, now that two rather experienced dudes have provided hints on what you can do?

Thanks, Prof. Michael Patriksson and Dr. Daniel Page for a comprehensive reply.

As I know, referring to No Free Lunch (NFL) theorem, in general, meta-heuristics proposed so-far show an equivalent on average if we apply them to all possible optimization tasks. As a results of NFL theory is that there is no algorithm performance best for all optimization problems. That's the reason, which encourages most of the researcher design new efficient optimizers.

After working with optimization and meta-heuristics for a long time, my personal thought is the same as Prof. Michael. Meta-heuristic algorithms lack rigor, even with powerful mathematical modeling algorithms such as whale optimization. For problems belong to the NP-hard problems, even if we find the optimal results, it is still not sure if it is global optimization. That's why I ask about techniques to improve meta-heuristics.

OBL in the eyes of mathematics, considering the solution that is opposite to the current solution in the search space, its task is simply to help expand the algorithm that can search the entire space. But when applied to meta-heuristics, it still falls into the case as I said above, we are still not sure if it is global or local optimization.

Levy-flight is similar to OBL, which helps the algorithm move quickly to the optimal point according to the Levy distribution trajectory. But we are not sure if that point is global or local optimization.

For me, I'll take the adviser of both of you. Focus on designing the actual problem under the mathematical model. Take advantage of the mathematical optimization theory to solve (in the direction of improving the existing one or think of a new mathematical model - this may be harder than improving the existing one)