Demand side management (DSM) is one of the important functions in a smart grid that allows customers to make informed decisions regarding their energy consumption, and helps the energy providers reduce the peak load demand and reshape the load profile. This results in increased sustainability of the smart grid, as well as reduced overall operational cost and carbon emission levels. Most of the existing demand side management strategies used in traditional energy management systems employ system specific techniques and algorithms. In addition, the existing strategies handle only a limited number of controllable loads of limited types. This paper presents a demand side management strategy based on load shifting technique for demand side management of future smart grids with a large number of devices of several types. The day-ahead load shifting technique proposed in this paper is mathematically formulated as a minimization problem. A heuristic-based Evolutionary Algorithm (EA) that easily adapts heuristics in the problem was developed for solving this minimization problem. Simulations were carried out on a smart grid which contains a variety of loads in three service areas, one with residential customers, another with commercial customers, and the third one with industrial customers. The simulation results show that the proposed demand side management strategy achieves substantial savings, while reducing the peak load demand of the smart grid.