A lot of studies were devoted to find a rigorous mathematical convergence proof for GAs. In fact analytical techniques could have been used to derive the convergence. However, no concrete answer is there to this query.
Dear B.K. Tripathy
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I should think that a very small portion of the instances of the small problems you can think of might be solved quite correctly - but for the vast majority of problem instances it will fail.
The main bug - and it's a very BIG bug - is that there is no certificate of optimality built into the method. Of course you always test the KKT condition at every iteration, but that's too costly. The smart thing with math programming tools is that the certificate of optimality is typically built in directly into the methodology - and that is a very big + for math programming.
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