In this paper, we compare three multi-objective algorithms based on Variable Neighborhood Search (VNS) heuristic. The algorithms are applied to solve the single machine scheduling problem with sequence dependent setup times and distinct due windows. In this problem, we consider minimizing the total weighted earliness/tardiness and the total flowtime criteria. We introduce two intensification procedures to improve a multi-objective VNS (MOVNS) algorithm proposed in the literature. The performance of the algorithms is tested on a set of medium and larger instances of the problem. The computational results show that the proposed algorithms outperform the original MOVNS algorithm in terms of solution quality. A statistical analysis is conducted in order to analyze the performance of the proposed methods.