With the emergence of automated environments, energy demand by consumers is increasing rapidly. More than 80% of total electricity is being consumed in the residential sector. This brings a challenging task of maintaining the balance between demand and generation of electric power. In order to meet such challenges, a traditional grid is renovated by integrating two-way communication between the consumer and generation unit. To reduce electricity cost and peak load demand, demand side management (DSM) is modeled as an optimization problem, and the solution is obtained by applying meta-heuristic techniques with different pricing schemes. In this paper, an optimization technique, the hybrid gray wolf differential evolution (HGWDE), is proposed by merging enhanced differential evolution (EDE) and gray wolf optimization (GWO) scheme using real-time pricing (RTP) and critical peak pricing (CPP). Load shifting is performed from on-peak hours to off-peak hours depending on the electricity cost defined by the utility. However, there is a trade-off between user comfort and cost. To validate the performance of the proposed algorithm, simulations have been carried out in MATLAB. Results illustrate that using RTP, the peak to average ratio (PAR) is reduced to 53.02%, 29.02% and 26.55%, while the electricity bill is reduced to 12.81%, 12.012% and 12.95%, respectively, for the 15-, 30-and 60-min operational time interval (OTI). On the other hand, the PAR and electricity bill are reduced to 47.27%, 22.91%, 22% and 13.04%, 12%, 11.11% using the CPP tariff.