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Multiple Attribute Decision Making (MADM) is an important part of decision science which helps us to select a preferred alternative among many alternatives which are compared with conflicting criteria. So, many solution approaches have been introduced such as permutation method; Interactive Simple Additive Weighting Method (ISAW) an etc. The time of the solution is sensitive to the size of the problem (numbers of alternatives and criteria), so by using meta heuristic we are trying to conquer this problem. In this paper, first we want to find an initial solution with permutation method based on genetic algorithm then by using ISAW method we try to propose proper exchanges in each iteration. By the proposed approach we can find the best permutation of alternatives by improved Genetic Algorithm. Finally the proposed approach will be illustrated more by some numerical examples.