Due to increasing need of using distributed databases, high demand presents on sharing data to easily update and access the useful information without any interruption. The sharing of distributed databases causes a serious issue of securing information since the databases consist of sensitive personal information. To preserve the sensitive information and at the same time, releasing the useful information, a significant effort is made by the researchers under privacy preserving data publishing that have been receiving considerable attention in recent years. In this work, a new privacy measure, called c-mixture is introduced to maintain the privacy constraint without affecting utility of the database. In order to apply the proposed privacy measure to privacy preserving data publishing, a new algorithm called, CPGEN is developed using genetic algorithm and multi-objective constraints. The proposed multi-objective optimization considered the multiple privacy constraints along with the utility measurement to measure the importance. Also, the proposed CPGEN is adapted to handle the cold-start problem which commonly happened in distributed databases. The proposed algorithm is experimented with adult dataset and quantitative performance is analyzed using generalized information loss and average equivalence class size metric. From the experimentation, we proved that the proposed algorithm maintained the privacy and utility as compared with the existing algorithm. Keywords: Privacy, Utility, Distributed databases, Data publishing, Optimization, Sensitive information