The aim of this paper is to present a new hybrid metaheuristic approach based on Ant colony algorithm and the variable neighborhood search noted by ACS_VNS to solve a permutation flowshop scheduling problem. In this context, several criteria are considered which are: the makespan, the total flowtime and the total tardiness of jobs. The proposed approach uses the compromise programming model and the concept of satisfaction function taking into account, explicitly, the decision-maker preferences (DMP). It has been tested through a computational experiment and the obtained results are compared to others for all criteria and for the makespan criterion. The obtained results show the performance of the proposed approach which can be considered as a good tool for multicriteria scheduling problem, especially since it does not necessitate a long computational time.