There are numerous many-objective real-world problems in various application domains for which it is difficult or time-consuming to derive Pareto optimal solutions. In an evolutionary algorithm, variation operators such as recombination and mutation are extremely important to obtain an effective solution search. In this paper, we study a machine learning-enhanced recombination that incorporates an intelligent variable selection method. The method is based on the importance of variables with respect to convergence to the Pareto front. We verify the performance of the enhanced recombination on benchmark test problems with three or more objectives using the many-objective evolutionary algorithm AϵSϵH as a baseline algorithm. Results show that variable importance can enhance the performance of many-objective evolutionary algorithms.