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Association rule mining is one of the most important and well-researched techniques of data mining, that aims to induce associations among sets of items in transaction databases or other data repositories. Currently Apriori algorithms play a major role in identifying frequent item set and deriving rule sets out of it. But it uses the conjunctive nature of association rules, and the single minimum support factor to generate the effective rules. However the above two factors are alone not adequate to derive useful rules effectively. Hence in the proposed algorithm we have taken Apriori Algorithm as a reference and included disjunctive rules and multiple minimum supports also to capture all possible useful rules. Although few algorithms   are dealing the disjunctive rules and multiple minimum supports separately to some extent, the proposed concept is to integrate all into one that lead to a robust algorithm. And the salient feature of our work is introducing Genetic Algorithm (GA) in deriving possible Association Rules from the frequent item set in an optimized manner. Besides we have taken one more add-on factor `Lift Ratio' which is to validate the generated Association rules are strong enough to infer useful information. Hence this new approach aims to put together the above points to generate an efficient algorithm with appropriate modification in Apriori Algorithm so that to offer interesting/useful rules in an effective and optimized manner with the help of Genetic Algorithm.