I am afraid that, in general, the (meta)heuristic algorithm will converge (if the convergence even occurs) to a local optima only. Without any additional information about the problem properties, you might not be able to say much about the quality of the solution you found. Of course, you might have access to some lower/upper bounds, which might help.

Sometimes, such as for convex optimization problems, you might be able to say that the local optimum corresponds to the global one. But that happens only rarely.

The question "why the premature convergence happens" has already been discussed some time ago: https://www.researchgate.net/post/Why-premature-convergence-happens .

Various techniques are used to handle the premature convergence, such as restarts of the algorithm, tuning of its parameters to improve the exploration, etc. You may wish to check, e.g., the free book Essentials of Metaheuristics available here: https://cs.gmu.edu/~sean/book/metaheuristics/ .

Thanks for your response.

I don't see why not metaheuristics could either terminate at a non-local point, or forever jump around. In general it will not converge even to a local optimum - and there is no devise in it that tells it to stop at such points. Metaheuristics are not a uniform family of methods, but a plethora of methods, some of which are rather sophisticated, while most are very simple - and therefore are not geared to guarantee anything at all about any point where the method might stop, if ever.

It must converge though optimal solution not guarenteed. Check basic framework and parameter tunings.

Premature convergence (local optimum) is one of the problems of metaheuristics but a good way to escape from this local optimum is to combine different metaheuristics (hybrid metaheuristics) where it is possible to explore and exploit the entire search space.

When any metaheuristic algorithm is applied then how we can say that the problem is free from premature or local convergence?

One way is to compare several robust metaheuristics and determine if the obtained value is similar or the same. Another way is to place a greater or lesser number of individuals in the metaheuristic (if it is based on populations) since many times a few individuals do not allow exploring or exploiting the entire search space while a very large number of individuals can saturate of information to the metaheuristic which also leads to premature convergence.

Try using a different optimizer, like Adam-it typically works really well