The present research is designed to present an Improved Success-History based Adaptive Differential Evolution (L-SHADE) to solve a practical Economic Dispatch Problem (ED P). Simultaneously involving both of the multiple fuel option and valve-point effects make the EDP formulation more and more complex non-smooth optimization issue. Noting that the L-SHADE serves to introduce an adaptive mechanism whereby improves the control parameters selection and through the application of a linear population size reduction technique, reduces linearly the population size throughout the optimization process. Thus, enabling to yield better offspring for the next generation. For an effective evaluation of the proposed design's relevant performance, the L-SHDE optimizer is subjected to the IEEE 10 unit test system involving multiple fuel option and valve point effect. The experiment results confirm the ability of the L-SHADE algorithm to obtain best optimum results with lowest computational time in respect of the state of-the-art optimization approaches.