Insertion of a local search technique is often considered an effective mechanism to increase the efficiency of a global optimization algorithm. In this paper we propose and analyze the effect of two local searches namely; Trigonometric Local Search (TLS) and Interpolated Local Search (ILS) on the working of basic Differential Evolution (DE). The corresponding algorithms are named as DETLS and DEILS. The performances of proposed algorithms are investigated and compared with basic DE, modified versions of DE and some other evolutionary algorithms. It is found that the proposed schemes improve the performance of DE in terms of quality of solution without compromising with the convergence rate.