An important function of a Smart Grid (SG) is the Demand Side Management (DSM), which consists on controlling loads at customers side, aiming to operate the system with major efficiency and sustainability. The main advantages of this technique are (i) the decrease of demand curve's peak, that results on smoother load profile and (ii) the reduction of both operational costs and the requirement of new investments in the system. The customer can save money by using loads on schedules with lower taxes instead of schedules with higher taxes. In this context, this work proposes a simple metaheuristic to solve the problem of DSM on smart grid. The suggested approach is based on the concept of day-ahead load shifting, which implies on the exchange of the use schedules planned for the next day and aims to obtain the lowest possible cost of energy. The demand management is modeled as an optimization problem whose solution is obtained by using an Evolutionary Algorithm (EA). The experimental tests are carried out considering a smart grid with three distinct demand areas, the first with residential clients, other one with commercial clients and a third one with industrial clients, all of them possessing a major number of controllable loads of diverse types. The obtained results were significant in all three areas, pointing substantial cost reductions for the customers, mainly on the industrial area.