In this paper, we address the weighted multi-objective re-entrant flow-shop scheduling problem considering release dates in order to minimize makespan, total completion time, total tardiness, maximum idle time, and number of tardy jobs. Each job is taken into account with deterministic processing times, and release dates. The flow-shop comprised of two workshops in whose jobs are entered to the main workshop and after the first part of the processing, they are transferred to the second workshop and after this stage, the jobs are returned to the main workshop for the last part of the processing. We model the problem by a new mixed integer programming based on formulating sum of idle time as a new concept. Moreover, a hybrid evolutionary algorithm is proposed based on some dispatching rules, ant colony optimization, and genetic algorithm. The performance of the proposed algorithm on some test instances is compared to the mixed integer linear programming model as well as the state-of-the-art algorithms called genetic algorithm, tabu search, bio-geography based optimization, and artificial bee colony. The computational experiments show that our proposed approach outperforms other algorithms and the results indicate efficiency and capability of the proposed algorithm in comparison with the traditional algorithms.