In optimization problem often we use local optimum but is it global? Or are there any meta-heuristics algorithm to obtain global solution? If there any then what is the name of that algorithm and if possible how we can get that solution?
I wish not to let you down, but the basic answer is "very seldom", and another one is "you will not know if you have stumbled upon an optimal solution, because there is no natural termination criterion in the algorithm built in that is based on the concept of optimality". (In contrast, a branch-and-bound, or branch-and-cut, methodology is based on local AND global bounds on the optimal value generated throughout the procedure, and in most cases the correct procedures will either fix some variables to their optimal values before termination, and they will be able to discard a very large portion of the search space based on parts of the search space being infeasibie or inferior, in which case we do know for sure that an optimum has been reached.)
If you have a structure of the problem that makes it emanable to be solved by special methods, such as Benders decomposition - when you have a mix of integer variables and continuous variables. you also have a fail-proof method.
If I were you I would study mathematical optimization theory and algorithms, and stop using those rather unscientific methodologies. If you study the mathematical optimization-based approaches, you will discover a beautiful theory that also works, AND you can bet a lot on your being able to transfer what you have learnt to other problem types as well!
I wish not to let you down, but the basic answer is "very seldom", and another one is "you will not know if you have stumbled upon an optimal solution, because there is no natural termination criterion in the algorithm built in that is based on the concept of optimality". (In contrast, a branch-and-bound, or branch-and-cut, methodology is based on local AND global bounds on the optimal value generated throughout the procedure, and in most cases the correct procedures will either fix some variables to their optimal values before termination, and they will be able to discard a very large portion of the search space based on parts of the search space being infeasibie or inferior, in which case we do know for sure that an optimum has been reached.)
If you have a structure of the problem that makes it emanable to be solved by special methods, such as Benders decomposition - when you have a mix of integer variables and continuous variables. you also have a fail-proof method.
If I were you I would study mathematical optimization theory and algorithms, and stop using those rather unscientific methodologies. If you study the mathematical optimization-based approaches, you will discover a beautiful theory that also works, AND you can bet a lot on your being able to transfer what you have learnt to other problem types as well!
https://www.sciencedirect.com/search?qs=solution%20via%20any%20meta-heuristics%20algorithm&show=25&sortBy=relevance
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