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What are advantages of using meta-heuristic algorithms on optimization problems?

What are the advantages and disadvantages of using meta-heuristic algorithms on optimization problems? Simply, why do we use meta-heuristic algorithms, like PSO, over traditional mathematical techniques, such as linear, non-linear and dynamic programming?

I actually have a good understanding of Meta-huristic algorithms and I know how they work. For example one advantage of these kind of algorithms is:

  • Finding an optimum solution in a reasonable time

However my lack of knowledge about other methods and techniques brought this question to my mind.