In data envelopment analysis (DEA), the problem of curse of dimensionality is a tough nut to crack when a relatively large dimension of inputs and outputs exists, especially in the context of big wide data. To evade the curse of dimensionality, the least absolute shrinkage and selection operator (LASSO), a regularization approach for variable selection, is recently used to combine with DEA and its variation, the so-called sign-constrained convex nonparametric least squares (SCNLS), which produces several fresh approaches such as LASSO-SCNLS and LASSO+DEA. In this paper, we further adapt the adaptive LASSO (ALASSO) to DEA, and propose the ALASSO-SCNLS and ALASSO+DEA approaches. In addition, we propose a hybrid approach by combining non-negative least squares (NNLS) regression with DEA, and call it NNLS+DEA. Compared with LASSO+DEA, NNLS+DEA has a simpler penalty function for regularization, does not have a tuning parameter and does not require cross-validation. Our Monte Carlo simulations show that: (1) LASSO+DEA clearly dominates ALASSO+DEA and ALASSO-SCNLS despite the merit of consistent variable selection of the adaptive LASSO; (2) NNLS+DEA shows slightly better performance than LASSO+DEA for relatively small sample sizes or considerably large dimensions; (3) NNLS+DEA clearly dominates LASSO+DEA in the computing time, especially for large dimensions. These results suggest that NNLS+DEA could be considered as an effective alternative to the existing methods, especially in the case of big wide data with small sample sizes and large dimensions.