Differential evolution (DE) is a popular evolutionary technique which can be applied in various constrained and unconstrained optimization problems along with the real time problems by modifying its operators like mutation, crossover and selection. In this paper initialization process of population along with the mutation rate is modified using the concept of logistic map and wavelet transformation in DE respectively. This modification increases the convergence rate. The modified proposal is tested on various benchmark problems. Also the evaluated results are compared for performance with state of the art algorithms, along with three real time non linear engineering problems, which dictates that the modified DE is easily applicable to the real time optimization problems.