Summary: Data mining services require exact input data for their outcomes to be significant, but privacy concerns may influence users to provide fake information. We study here, with respect to mining association rules, whether or not users can be confident to provide correct information by ensuring that the mining process cannot, with any reasonable degree of certainty, breach their privacy. We will present a novel method in genetic algorithm, based on random distortion of user data that can simultaneously provide a high degree of privacy to the user and retain a high level of accuracy in the mining results. In this method, first we apply different weighted sum multi-objective optimization inside the fitness functions. Finally, the performance of the scheme is validated against representative real and synthetic datasets.