In recent years there has been a growing trend in the application of Memetic Algorithms for solving numerical optimization problems. They are population based search heuristics that integrate the benefits of natural and cultural evolution. In this paper, we propose an Adaptive Memetic Algorithm, named LA-DE which employs a competitive variant of Differential Evolution for global search and Learning Automata as the local search technique. During evolution Stochastic Automata Learning helps to balance the exploration and exploitation capabilities of DE resulting in local refinement. The proposed algorithm has been evaluated on a test-suite of 25 benchmark functions provided by CEC 2005 special session on real parameter optimization. Experimental results indicate that LA-DE outperforms several existing DE variants in terms of solution quality.