Smart grid enables consumers to control and schedule the consumption pattern of their appliances

minimize energy cost

peak-to-average ratio (PAR) and peak load demand. In this paper

a general architecture of home energy management system (HEMS) is developed in smart grid scenario with novel restricted and multi-restricted scheduling method for the residential customers. The optimization problem is developed under the time of use pricing (TOUP) scheme. To optimize the formulated problem

a powerful meta-heuristic algorithm called grey wolf optimizer (GWO) is utilized

which is compared with particle swarm optimization (PSO) algorithm to show its effectiveness. A rooftop photovoltaic (PV) system is integrated with the system to show the cost effectiveness of the appliances. For analysis

eight different cases are considered under various time scheduling algorithms.