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This paper presents a critical analysis of the Pareto-Following Variation Operator (PFVO) when used as an approximation method for Multiobjective Evolutionary Algorithms (MOEA). In previous work, we have described the development and implementation of the PFVO. The simulation results reported indicated that when the PFVO was integrated with NSGA-II there was a significant increase in the convergence speed of the algorithm. In this study, we extend this work. We claim that when the PFVO is combined with any MOEA that uses a non-dominated sorting routine before selection, it will lead to faster convergence and high quality solutions. Numerical results are presented for two base algorithms: SPEA-II and RM-MEDA to support are claim. We also describe enhancements to the approximation method that were introduced so that the enhanced algorithm was able to track the Pareto-optimal front in the right direction.